tag:blogger.com,1999:blog-85374943210679594932024-03-13T18:27:12.542-07:00BorschtWithAnnaAnna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.comBlogger92125tag:blogger.com,1999:blog-8537494321067959493.post-27300707136275315112023-07-05T22:02:00.001-07:002023-07-05T22:02:15.543-07:00Implementing Building Thinking Classrooms with Students with Learning Differences<p>Last week, I presented at the Building Thinking Classrooms Conference in Franklin, Indiana on implementing BTC with students with learning differences. I definitely tried to cram too many things into a 45-minute session so this is my attempt to unpack what will likely need to be split into (at least) two presentations going forward. <a href="https://docs.google.com/presentation/d/1NgvlxCowquEQbcMWx99fsiZfJH-9_4AmA1hC2Y3iFYw/edit#slide=id.p" target="_blank">Here's</a> the original presentation, and now let's get into the unpacking.</p><p><br /></p><p><b><u>Part 1: Why students with learning differences benefit from a BTC approach</u></b></p><p>At my previous school, I got a lot of pushback when using a problem-based approach with students with learning differences so I did my research when I changed schools and learned that I would be working primarily with this population. The benefits are very clear, when implemented thoughtfully and with supports: students with learning differences benefit immensely from teaching approaches that emphasize process and sense-making; meaningful contexts; connections to previous learning; opportunities to discuss and improve metacognition; frequent feedback; integration of concepts, procedures, and language; and a growth mindset (source: Teaching Mathematics Meaningfully). Oh hey, these are all built into BTC already! At the same time, they also benefit from opportunities to reduce math anxiety and learned helplessness, address misconceptions and unfinished learning from previous years, and receive more explicit directions and teacher-directed synthesis and instruction to make sense of the math they are working on and how to connect it to existing schema. And this is exactly where adjustments to BTC come in handy.</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2wH9BS95vyeU0kkBkPQP_dV41Nd2_EIUa3C_n_ZHbFsF47rxYGzDZNxt6NrjH8dTmMVoqkA7iWBWD1W4W4eYvehfD8NFIQeMGkhgFVHECtWZPfLBkEj5wnhxvLJGLrDwM6WtEF7HVNVyxeisgfqlPAZg1jNk4DVift0FB8kG5X87cIELQlxd48kYaIaE/s450/giphy.webp" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="240" data-original-width="450" height="171" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2wH9BS95vyeU0kkBkPQP_dV41Nd2_EIUa3C_n_ZHbFsF47rxYGzDZNxt6NrjH8dTmMVoqkA7iWBWD1W4W4eYvehfD8NFIQeMGkhgFVHECtWZPfLBkEj5wnhxvLJGLrDwM6WtEF7HVNVyxeisgfqlPAZg1jNk4DVift0FB8kG5X87cIELQlxd48kYaIaE/s320/giphy.webp" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><p></p><p><b><u>Part 2: Adjusting the first toolkit (</u></b><b><u>what, </u></b><b><u>where, and who should students work with)</u></b></p><p>The first toolkit is all about where students work, who they work with, and the types of problems they work on. The original practices have students working on vertical whiteboards, in random groups of three, and on tasks that require thinking and problem solving. The main adaptations that I have implemented provide more structure, fewer distractions, and supports for students with memory and visual processing challenges. For example, I found that assigning random pairs of students each day rather than trios along with having students take turns with clear roles, which I call driver and navigator (where the driver can only write what the navigator says), and using <a href="https://docs.google.com/document/d/1veOte1rt7yCmMAl9Fy0Br2k1lVF5YJ8kwdTipQlUl4k/edit" target="_blank">sentence starters</a> were helpful for getting students to work together with greater focus and engagement.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlxJmDxQ_y-Ihnfiaujya1udEHX_KyMuOB18l96VELXI756BWKSV-YfOHrlicd2Vm9c3gVv3YsLgn9KNu1hqioa0yBeNgl59FWEG3G8zQQRli0SZLII6_ZAOvKMWnPw9Hpn_ZwHX6BDrRAD-s6AKLG8tIG8JrZE93nYdIivreU2H734gcqvvYOfHVesOg/s1334/Screen%20Shot%202023-07-05%20at%203.38.06%20PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="836" data-original-width="1334" height="402" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlxJmDxQ_y-Ihnfiaujya1udEHX_KyMuOB18l96VELXI756BWKSV-YfOHrlicd2Vm9c3gVv3YsLgn9KNu1hqioa0yBeNgl59FWEG3G8zQQRli0SZLII6_ZAOvKMWnPw9Hpn_ZwHX6BDrRAD-s6AKLG8tIG8JrZE93nYdIivreU2H734gcqvvYOfHVesOg/w640-h402/Screen%20Shot%202023-07-05%20at%203.38.06%20PM.png" width="640" /></a></div><p style="text-align: left;">Spending time at the start of the year teaching routines for getting supplies, finding your whiteboard, and working productively with others paid dividends for the rest of the year. </p><p style="text-align: left;"><br /></p><p style="text-align: left;">It also proved extremely helpful to think very carefully about the level of challenge and explicitness in the tasks and problems provided. A lot of my students were coming in with high levels of math anxiety and a stated dislike for math. They needed to experience a lot of small successes early on to start to see themselves as having agency and be willing to try and persevere with challenge. I leveraged high-interest warm-ups that encouraged discussion, multiple viewpoints, and easy entry for everyone. Some fan favorites were <a href="https://www.visualpatterns.org/" target="_blank">visual patterns</a>, <a href="https://estimation180.com/" target="_blank">estimation 180</a>, <a href="http://fractiontalks.com/" target="_blank">fraction talks</a>, <a href="https://slowrevealgraphs.com/" target="_blank">slow reveal graphs</a>, and <a href="https://wodb.ca/" target="_blank">which one doesn’t belong</a>. When selecting non-curricular tasks to start the year, I used tasks recommended for a few grades below my students' actual grade level and started with tasks that had a clear, explicit goal and a very low floor. When using <a href="https://mathwithmsmatherson.com/how-to-create-and-use-thin-sliced-math-problems/" target="_blank">thin slicing</a> to move students through content-learning, I started with review problems related to that day's learning (again, to lower the floor) and increased the difficulty very slightly between problems, often giving a few problems at the same level of difficulty before ramping up. I would sometimes also start with a <a href="https://problemproblems.wordpress.com/category/worked-examples/" target="_blank">worked example à la Michael Pershan</a> as that day's warm-up to build student confidence and activate prior knowledge before asking them to solve a new, related problem. Structuring problems so that students experienced early success, as well as mixing in whiteboarding with other activities and gradually increasing the amount of time students spent in groups were all critical to building problem-solving endurance.</p><p style="text-align: left;"><b><u><br /></u></b></p><p style="text-align: left;"><b><u>Part 3: Adjusting the second toolkit (teacher moves to start and maintain flow</u></b><b><u>)</u></b></p><p style="text-align: left;">The second toolkit is all about teacher moves in giving the tasks, monitoring and supporting students while they work, and empowering student autonomy. Again, ramping up the explicitness and positive feedback went a long way in supporting struggling students. While Peter recommends giving tasks orally, with everyone in a huddle in the center of the room, I found it helpful to ask for volunteers and act out the task, if possible, checking for understanding along the way. <br /><br />My students also benefited from getting copies of the questions and key visuals in clear plastic sleeves so they could write on them with dry erase markers, taped up at the boards. To keep students in flow, I once again relied on routines and celebrations of small successes. Students were provided with a list of <a href="https://docs.google.com/document/d/11dHf5xWH2p_Kqx5t-GpzjDpzEJKKS5yqAwxifvExkJE/edit" target="_blank">questions to ask yourself if you're feeling stuck</a> and I frequently refered to these when checking on progress. </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlMLMWSA3H4LNevDuDyXERX_JJTDQolbZtzr7ZaEppdCc3WDyuS_U03K6JP-4sCT5c6UkwpLUijBhDZuCRLSOSr5ra927wuZd-I8uHQKm6OiEVcymGUMveqjgrTM81mde0yHpZgQqLSwm22d4VM-pvvO8MjOX_PuLQ8__40g8p4qGBAFBL3SCMZ02tzc0/s1202/Screen%20Shot%202023-07-05%20at%204.34.26%20PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="684" data-original-width="1202" height="364" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlMLMWSA3H4LNevDuDyXERX_JJTDQolbZtzr7ZaEppdCc3WDyuS_U03K6JP-4sCT5c6UkwpLUijBhDZuCRLSOSr5ra927wuZd-I8uHQKm6OiEVcymGUMveqjgrTM81mde0yHpZgQqLSwm22d4VM-pvvO8MjOX_PuLQ8__40g8p4qGBAFBL3SCMZ02tzc0/w640-h364/Screen%20Shot%202023-07-05%20at%204.34.26%20PM.png" width="640" /></a></div><p style="text-align: center;"><br /></p><p style="text-align: left;">We also spent time early on practicing several of the routines from Routines for Reasoning (<a href="https://www.heinemann.com/products/e07815.aspx" target="_blank">book</a>, <a href="https://www.fosteringmathpractices.com/routinesforreasoning/" target="_blank">website</a>). Each routine combines ask yourself questions, sentence frames and starters for discussing with partners, and annotation to help students make sense of new problems in a structured, repeatable way. Combining these routines with the thinking classrooms framework has made problem-based learning significantly more accessible to my students with learning differences. </p><p style="text-align: left;">A strategy that I used to implement, but which had fallen away during the pandemic and that I want to bring back, is giving each group three colored cups (green, yellow, and red) to help them monitor and reflect on their state of flow. I first learned about this strategy from <a href="https://twitter.com/averypickford" target="_blank">Avery Pickford</a>, but a quick Google search shows that a few others have blogged about it - <a href="https://mathequalslove.net/red-yellow-green-team-cups-posters/" target="_blank">here's</a> a great description from the Math = Love blog. The idea is that every group starts with the green cup on top of their stack and shifts to yellow on top if they feel stuck, but haven't yet tried all of the routines and ask-yourself questions that could get them unstuck. They switch to red once they have exhausted all of their resources and need help from a teacher or classmate in another group to continue making progress. I really appreciate how this strategy makes visible where groups are at, as well as reminding students that there is a key step between "doing great" and "totally stuck," in which they have the tools and resources to move themselves back into flow.</p><p style="text-align: left;">To promote student autonomy, I relied heavily on <a href="https://docs.google.com/presentation/d/1VC5jwRNJoB2ovySO8uZ9yK24Hfq0FijtVvtc4V_IlGY/edit#slide=id.g13531742e09_0_0" target="_blank">collaboration rubrics</a> and positive reinforcement. Instead of giving feedback on collaboration at the end of class, I would give feedback (or ask students to self-assess) 10 minutes in, which would give students a tighter feedback cycle and an opportunity to improve their collaboration that same day. </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuc7A684Lb_TCFnjo2fr1OX3Ow-OrouF1Oq5ou8C5Okker0XENuK71hVtM6_WAk4MAghWD4HjAPIY66kgRnM853Je5Tu52-wUcQgZNf8anOZNoQhk2DXNurl4KQnrdfKXgMEawyYW1Le-jW9j_XWTbQbGVIbQ3OMmTNplnj31inA77yq83UawxdHY9Om8/s780/Screen%20Shot%202023-07-05%20at%2010.55.23%20PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="390" data-original-width="780" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuc7A684Lb_TCFnjo2fr1OX3Ow-OrouF1Oq5ou8C5Okker0XENuK71hVtM6_WAk4MAghWD4HjAPIY66kgRnM853Je5Tu52-wUcQgZNf8anOZNoQhk2DXNurl4KQnrdfKXgMEawyYW1Le-jW9j_XWTbQbGVIbQ3OMmTNplnj31inA77yq83UawxdHY9Om8/w640-h320/Screen%20Shot%202023-07-05%20at%2010.55.23%20PM.png" width="640" /></a></div><p style="text-align: left;">I actively sent students to check out peers' whiteboards or to stand in the middle of the room and look around to get ideas if they were stuck. While circulating and looking at student work, I would also identify interesting work by students who were less confident or likely to share with others and ask them to help another group or tell them that I would like to use their work during consolidation. At the end of class, I would have students give shout-outs to classmates who contributed to their learning in a positive way that day (sometimes accompanied by a sticker reward from me... never underestimate the power of a sticker for students of just about any age).</p><p><b><u>Part 4: Adjusting the third toolkit (moving from collective to individual knowing</u></b><b><u>)</u></b></p><div>I'm ignoring the hints/extensions part of this toolkit since that's more closely related to part 3. Consolidation has perhaps been the most challenging BTC practice for me to implement with struggling students. Even when I could reliably get students engaged and working hard with classmates on problems, the energy and enthusiasm would evaporate within minutes of trying to consolidate. I wrote a <a href="http://borschtwithanna.blogspot.com/2022/02/consolidation.html" target="_blank">whole other post on consolidation</a>, but the things that ended up making a big difference were basically more routines and positive feedback. We practiced how to stand (a nice semi-circle in front of the whiteboard we were looking at so everyone could see), how to comment and respond to questions about the work that was being shared (yep, back with the sentence stems: “I notice…”, “I wonder…”, “One difference between these methods is…”, “I like the first/second method more because…”), and how to find a new random partner for a stand-and-talk to discuss the work that was being shared. </div><div><br /></div><div>I also started using the <b>4 R's</b> strategy from Routines for Reasoning (<a href="https://achievethecore.org/peersandpedagogy/math-instructional-routines-creating-opportunities-students-disabilities-grapple-grade-level-math/" target="_blank">more here</a>). In this strategy, a student shares an observation or summary and the teacher follows up by doing the following:</div><div><br /></div><div>Repeat = ask someone to repeat what was shared (this helps to ensure that everyone heard)</div><div>Rephrase = ask someone to restate in their own words (this helps to ensure that everyone understood)</div><div>Reword = teacher states again, but inserting mathematical language (this helps to build academic vocabulary and increases precision) - this is also a key time to connect to previous concepts, if relevant</div><div>Record = annotate (add notes and vocabulary words, circle key components, and otherwise create a written record of what was shared)</div><div><br /></div><div>Another strategy to try during this phase is to have students apply the method that was discussed to a new problem. Students can hold mini-whiteboards during consolidation and respond to checks for understanding individually or go back to their group whiteboards and try a new problem together using the specified strategy. I have also experimented with moving the consolidation phase to the beginning of the next class period rather than trying to rally the troops who are tired from 45 minutes of hard math work. Another option is to do a mini-consolidation half-way through before students tire out, leaving part 2 of the consolidation process for the next day. When all else fails, stickers for participating and engaging with this phase can be a clutch teacher move. Keeping consolidation short, snappy, teacher-directed, and fun and varying the strategies and questions used while still maintaining the key routines have made a big difference in its effectiveness in my classroom.</div><div><br /></div><div>Let's talk about notes. This is another tricky thing to get right with students with learning differences who may be struggling with attention issues, dysgraphia, processing speed, and other challenges to traditional note-taking. At the same time, having a clear and easy to use reference may be especially helpful for students with these challenges. I have had some success with students building out a course pack, which organizes and summarizes key concepts from the entire year. <a href="https://docs.google.com/document/d/1wi9BvkpJsk6MJ3iFGPeBflWnpDtroAyPVlazJbzxxXw/edit?usp=sharing" target="_blank">Here</a> is an example of a course pack for a class that's a mix of 8th grade Math and Algebra 1. You can see that each unit starts off with some review of key concepts students saw the previous year. </div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQCW7cmC5-NugK_fuhF8riof9a0WAFMRut5I1nuuTLIkmLwE4ANk7ElSWj2Y-Avsr6SiQFrKdOuuieXh76Iz4Ln94AsdiHpLuMPz2pp05SOUYFZmYA5EW3t10ehNEmFjOvTmd0Re9OHqCA5LH6zVakeQNCLSvGIizlguVEJvvxFqMnrtImpshwJaFBr3c/s1232/Screen%20Shot%202023-07-05%20at%209.57.00%20PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="776" data-original-width="1232" height="405" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQCW7cmC5-NugK_fuhF8riof9a0WAFMRut5I1nuuTLIkmLwE4ANk7ElSWj2Y-Avsr6SiQFrKdOuuieXh76Iz4Ln94AsdiHpLuMPz2pp05SOUYFZmYA5EW3t10ehNEmFjOvTmd0Re9OHqCA5LH6zVakeQNCLSvGIizlguVEJvvxFqMnrtImpshwJaFBr3c/w640-h405/Screen%20Shot%202023-07-05%20at%209.57.00%20PM.png" width="640" /></a></div><br /><div style="text-align: center;"><br /></div><div>I got this idea from Sara VanDerWerf, who blogged about providing reference sheets to students <a href="https://www.saravanderwerf.com/green-reference-sheets/" target="_blank">here</a>. Because most lessons start with problems students have seen before as a way to review and pull in prior knowledge, it is really helpful for students to already have some notes on these topics. The rest of the course pack is organized into blank half-page sections labeled with content topics. When students take notes, I provide a half-sheet with sections for key concepts, examples, and vocabulary. Sometimes, I provide an example (like below). </div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_E3PuqWnkA7KRd53sc458J4SqHB1v9QrL0vr0J-TuF7j1Dd2UoltspBykTXQbOSjLCf65BnPlnoJQK35BWPiDVArWLo5jQ0me4FReYyNc-Kn0ruaH9x8HBAZyjXouuOlzMIY4tBclUSsfe9c2o2y1p5juCg5RpLvekRYwOkh9pX_YPhV3QOLyV8OaCI8/s1586/Screen%20Shot%202023-07-05%20at%2010.06.00%20PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="724" data-original-width="1586" height="293" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_E3PuqWnkA7KRd53sc458J4SqHB1v9QrL0vr0J-TuF7j1Dd2UoltspBykTXQbOSjLCf65BnPlnoJQK35BWPiDVArWLo5jQ0me4FReYyNc-Kn0ruaH9x8HBAZyjXouuOlzMIY4tBclUSsfe9c2o2y1p5juCg5RpLvekRYwOkh9pX_YPhV3QOLyV8OaCI8/w640-h293/Screen%20Shot%202023-07-05%20at%2010.06.00%20PM.png" width="640" /></a></div><br /><div style="text-align: center;"><br /></div><div>Other times (later in the year), students pick an example or two from the day's whiteboarding work to put into their notes. This half-sheet gets taped into the course pack and over time, that becomes a valuable reference tool for students. </div><div><br /></div><div>Notes is an area with which I am very much actively experimenting. I'm eager to try a new way of doing notes that was shared at the Building Thinking Classrooms Conference this past June, in which students work together in a group on whiteboards to first finish a partially completed example provided by the teacher, then solve an entire example from start to finish (where the teacher provides the initial question), then create their own example and solve it, and finally summarize key points from that day's lesson as "notes to my future forgetful self." They then have this model as well as the models created by other groups as a reference in order to write down their own individual notes on paper.</div><div><br /></div><div><p><b><u>Part 5: Adjusting the fourth toolkit (grading aligned to values and to inform students</u></b><b><u>)</u></b></p><div>There is a lot I can say about grading and the BTC model of aligning grades to goals and making progress and areas of growth visible to students. However, most of it will not be very useful to others since every school has its own grading policies and expectations and this is an area of teaching where teachers have the least say. However, I will share two tweaks to the grading practices in BTC that have worked well for my students.</div></div><div><br /></div><div>First, I know that Peter is very clear in the book about not grading homework or other "studenting behaviors" because we want students to be doing them for the right reasons and to develop their intrinsic motivation. However, I have found that it really helps my students if data regarding these behaviors is tracked because it makes the connection between "studenting behaviors" and progress in the class more obvious and allows for better goal setting and reflection. At my school, we are also required to give an "Approaches to Learning" grade that can affect the final semester grade so that is a good way for me to use a small amount of extrinsic motivation to help students who have not yet seen the value of "studenting." I organize the approaches to learning into a category separate from content understanding or mathematical practices and give students feedback on these using standards-based grading. There are four standards in this category: </div><div><ol style="text-align: left;"><li>Turning work in on time, checking answers, and revising errors, if possible</li><li>Seeking out challenge, persevering, and asking for help</li><li>Coming to class on time and with supplies, staying engaged and participating in class activities</li><li>Collaborating with other students, giving constructive criticism, supporting a positive class culture</li></ol><div>The second addition to this toolkit that has worked for my students is having each one keep a digital Math reflection journal. Approximately once every three weeks or so, students look over their digital gradebook to check on their progress, read over what they wrote the last time they reflected in their journal, and fill out a slide that has the following sentence stems:</div></div><div><ol style="text-align: left;"><li>The goal I have been working on is... </li><li>I have or have not made progress on this and my evidence is... </li><li>My next steps are... (continue working on previous goal or set a new goal and how you will try to reach it)</li><li>Pick one and delete the others:</li><ol><li>Something that’s going well recently is… </li><li>My teacher/parents can help me by…</li><li>I’d like Anna to know that…</li></ol></ol><div><br /></div></div><div>They then email a link to their reflection journal to me and to their parents/guardians, which opens the door for communication about the student's progress between everyone. It does take 10 minutes of class time every few weeks, but has been invaluable in making sure that students are regularly reading and understanding my feedback and that they're making goals and connecting their progress to behavior that's under their control. </div><div><br /></div><div>It might be more evident now why this giant blog post dump did not work as a 45-minute presentation (I also tried to do a math task with participants to show some of the tweaks I was sharing, so yep, way too ambitious). If I do this presentation again, I will likely focus in on just one or two toolkits rather than trying to hit all four. And of course, I would love to revise and add on, if you have other ideas that have worked well for you or that you have read about and want to try. </div><div><br /></div><div><b><u>References:</u></b></div><div><ul style="text-align: left;"><li>“Teaching Mathematics Meaningfully,” Allsopp, Lovin, and van Ingen</li><li>“Routines for Reasoning,” Kelemanik, Lucenta, and Creighton</li><li>“Dyscalculia Pocketbook,” Hornigold</li><li>“Can I Tell You About… Dyscalculia,” Hornigold</li><li>“11 Effective Strategies for Teaching Math to Students Who Have Given Up on Learning,” Smith</li></ul>If you got this far, kudos to you! Please feel free to connect with me on here or via <a href="https://twitter.com/ablinstein" target="_blank">Twitter</a> or <a href="https://mathstodon.xyz/@ablinstein" target="_blank">Mastodon</a>.</div>Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com0tag:blogger.com,1999:blog-8537494321067959493.post-57579352604452225032022-02-24T19:37:00.001-08:002022-02-25T15:32:41.547-08:00Consolidation<p>I'm part of a Facebook group for teachers who are implementing some components of Building Thinking Classrooms (BTC) based on the <a href="https://www.amazon.com/dp/B08X4DD6TF/ref=cm_sw_r_tw_dp_HS3FYAES8F56TCSC5XS0" target="_blank">book by Peter Liljedahl</a>. A question that comes up frequently in the group is how teachers are handling consolidation, which is the wrap up of big ideas that Peter recommends at the end of class, using student work from class as a means to summarize and help students make key connections. This is pretty similar to the final three practices in <a href="https://www.amazon.com/dp/1680540165/ref=cm_sw_r_tw_dp_1VR7GT5Z2RK8CV0MHQNE" target="_blank">5 Practices for Orchestrating Productive Mathematics Discussions</a> (Selecting, Sequencing, and Connecting). We want students in all math classes to see beyond the specific problems they solved. This is especially important in a math classroom that doesn't follow the "I do, we do, you do" model since students are figuring out how to solve problems without being shown a general principle or model to follow and need to see how the work they did establishes something generalizable and useful. In both the BTC and 5 Practices approach, the teacher selects several pieces of student work, decides on what order to discuss them, and helps students make sense of this work and the big ideas of the lesson that they encompass. This is often the most challenging part of class since many students are much less interested in listening, summarizing, and comparing than in solving problems, which is inherently a more active process. </p><p><br /></p><p>I am by no means an expert on consolidation, but it is something that I worked a lot on this year, partly because I am working with a population of students right now where the vast majority have documented learning differences and who have historically struggled with motivation in Math. These challenges are most evident when students are asked to analyze classmates' work and participate in a class discussion about the day's problems. Here are some strategies that I have found helpful for this part of class:</p><p></p><p></p><p></p><h4><ul style="text-align: left;"><li>Keep it short</li></ul><div><span style="font-weight: normal;">I try to never spend more than 10 minutes of a 50 minute class on consolidation (usually aiming for less than that). Middle school students and students with attentional challenges do not have the bandwidth for a class discussion that lasts longer than that. This forces me to be pretty strategic about what we discuss and does mean we can't talk about every interesting thing that comes up in class. Something that is especially interesting but that doesn't fit into the 10-minute time frame can be moved to a warm-up question for the next day. </span></div><ul style="text-align: left;"><li>Involve other students in discussing a group's work</li></ul></h4><p></p><p></p><div style="text-align: left;"><span>I almost never have the students whose work is being discussed share their process since listening passively is not that engaging for the rest of the class. The students who did the work often know what they meant and why they did what they did and gloss over those parts. To involve everyone else, I usually first ask everyone in the class to quietly study the group's work we are looking at and give a small thumbs up when they finish reading it (props to <a href="https://twitter.com/mpershan" target="_blank">@mpershan</a> for this lovely teacher move). I then ask for volunteers to explain a few key parts (if there aren't many volunteers, I will first have students take turns explaining each step of the work with a partner), asking follow up questions, like "Why did they do ... here?," "What would they have done if the problem instead asked for...?" Other ways to involve more of the class is to ask for students who can restate what someone has said. This can give students who need more processing time an opportunity to participate and gives everyone the opportunity to hear big ideas a few times. This does mean that students have to show clear work so that it's understandable by others so that is definitely something I emphasize a lot. </span><br /></div><h4><ul style="text-align: left;"><li>Give students something to do during/after consolidation</li></ul><div><span style="font-weight: 400;">Related to the point above, many students struggle with listening/talking for an extended period of time. My students engage more readily when given opportunities to discuss with a partner, write something down in their notes, or do a related problem using the method we just discussed. I often have them grab a mini-whiteboard so that everyone can write down their answer to a discussion question or solve a related problem similar to the one we just discussed. If the energy level is low, I have students find a partner to discuss with who is not standing next to them to build in a bit more movement. </span></div><ul style="text-align: left;"><li>Focus on connections and similarities/differences when looking at multiple pieces of student work</li></ul></h4><div>Consolidation often involves connecting different approaches or comparing related, but different problems. I have found it helpful to sequence the student work I want to discuss in such a way that we only focus on the step by step work of the first group. It can get repetitive if we go through each group's work in the same way. For the second or third piece of work, I ask students instead to identify what this group did the same or differently from the first group and hypothesize why they made those choices. Students can vote on their favorite method or say which method they would use in which situation and why.</div><h4><ul style="text-align: left;"><li>Set norms for class discussion</li></ul></h4><div>Something we have worked on all year is how to participate in academic discussions. This involves lots of modeling and practicing showing interest in a speaker with body language, eye contact, nodding along if things make sense, and looking quizzical when they don't. Every consolidation is an opportunity for students to practice these skills and give each other feedback. I have found it helpful to be very explicit about the behavior I am looking students to exhibit during class discussions and treat it as a skill that can be practiced and improved upon. </div><div><br /></div><div style="text-align: left;">Please share your best tips for helping students consolidate and participate in class discussions centered on student work!! This has been the most challenging aspect of running a problem-based math class for me and I'd love to learn more. </div><div><br /></div><p></p>Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com2tag:blogger.com,1999:blog-8537494321067959493.post-31621518354496899832021-07-21T21:54:00.009-07:002022-04-04T21:17:39.103-07:00Standards based grading - aligning with Building Thinking Classrooms<p>I have been using standards based grading (SBG) for a few years, but after reading <a href="https://www.amazon.com/Building-Thinking-Classrooms-Mathematics-Grades/dp/1544374836" target="_blank">Building Thinking Classrooms</a> by Peter Liljedahl last year, want to share how I've revamped my gradebook, workflow, and how students will track their progress.</p><p><br /></p><blockquote style="border: none; margin: 0px 0px 0px 40px; padding: 0px;"><p style="text-align: left;"><b><span style="color: #674ea7;">Side Note:</span></b> if you're interested in starting the standards based grading journey, better bloggers than I have done the leg work, and I highly recommend reading through their posts first to get grounded in this shift in assessment.</p></blockquote><p></p><ul style="text-align: left;"><ul><li><a href="https://twitter.com/fnoschese" target="_blank">Frank Noschese</a> at <a href="https://fnoschese.wordpress.com/category/standards-based-grading-2/" target="_blank">Action-Reaction</a></li><li><a href="https://twitter.com/mr_rablin?lang=en" target="_blank">Tyler Rablin </a> at <a href="https://teacher-totter.blogspot.com/search/label/assessment" target="_blank">Teacher Totter</a></li></ul></ul><div><br /></div><div>My standards-based gradebook is a <a href="https://docs.google.com/spreadsheets/d/1fCx7GM_VUB0Pkk3w7b3Tgh8TvQbrL7Z8MLdhdkIxmKI/edit#gid=0" target="_blank">big Google spreadsheet</a> with a tab for each unit of content and tabs for tracking IB criteria and my observations on students and their work, as I'm now teaching at an IB school and need to give an IB criteria grade as well as report out on "Approaches to Learning". There's also a student tracking sheet that I will print out for students to track their own progress (<a href="https://docs.google.com/document/d/1Gfo9Q1spIOVT-u_Wg8jF8OFyKAWENAcjhKARTcuwXGw/edit" target="_blank">tracking sheet for IB Criteria/Approaches to Learning</a>; <a href="https://docs.google.com/document/d/1VIpSyh49aDI0dWg9Jzs9syP_SaI8FmE7U0pcHJcswDE/edit?usp=sharing" target="_blank">exemplar tracking sheet for content</a> - this one is for Geometry). I conference approximately once per month with each student to compare notes and talk about strengths and next steps. </div><div><br /></div><div>Here's how I use each part of my gradebook and how it aligns with (or deviates from) Thinking Classrooms.</div><div><br /></div><h3 style="text-align: left;"><span style="background-color: #fcff01;">Content Tabs</span></h3><div><span style="background-color: #fcff01;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbLgOxtZ2LqJjVMBbuoTatbRHA3TL5t0Nsvxy2ySWBAi2_QUAphHMe1_BvITuXBNzbM6rd-xqbNrNlaOeWS0kUxD8D_M1no-jcAls3QlGoiNx1859qf-_pYCNpcKErqHNF-1hjLx2j8DA/s686/Screen+Shot+2021-07-21+at+11.00.33+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="553" data-original-width="686" height="516" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbLgOxtZ2LqJjVMBbuoTatbRHA3TL5t0Nsvxy2ySWBAi2_QUAphHMe1_BvITuXBNzbM6rd-xqbNrNlaOeWS0kUxD8D_M1no-jcAls3QlGoiNx1859qf-_pYCNpcKErqHNF-1hjLx2j8DA/w640-h516/Screen+Shot+2021-07-21+at+11.00.33+PM.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: center;">(click to enlarge)</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div>For each unit in the year, I have created a list of prerequisite topics (these are either topics from last year or topics from earlier in the year once we're a few units in), "Need to Know" topics, and extension topics. For some units, I include prerequisite topics in the content grade whereas for others, they are already integrated as sub-components of the "Need to Know" topics so don't need to be scored separately. Extension topics are not included in the total score. As I create assessments, I indicate the problem numbers for each quiz, etc where that topic was assessed in column A. I also list resources for each topic, whether that's Khan Academy links, other online resources, or page numbers in students' reference book. I don't break up the topics into Basic, Intermediate, Advanced as the book suggests because I find it really hard to delineate the levels and don't find it necessary to do so. </div><div><br /></div><div>Now, on to the actual scoring - this is the part that I'm changing based on Building Thinking Classrooms. I am recording a mark for each student as I grade their quizzes or based on classroom observations or later reassessments. The cells are set up with conditional formatting so they turn red if there's an ✗ (haven't shown this yet), yellow if there's a P (precision error) or H (got it with some help or working in a group), and green if there's a ✓ (got it). Students get a score of 0, 1, or 2 for each topic, depending on whether they were able to consistently show mastery (two ✓ in a row) over the course of the semester. Their score for the unit is just the total score out of (# of topics) • 2. This tab allows me to scan down and see what topics a particular student is struggling with as well as to scan across and see what topics the whole class might need to revisit. The color-coding is key here! My system is sort of a mix of the system in the book and event-based grading since I do actually want to see how students did on a particular assessment so am separating out some scores, although at the end of the day, it's all data points and they are mostly chronologically listed from left to right. The preview is given right before the unit starts, quizzes and observations happen during the unit, and reassessments happen in subsequent units. Most reassessments are fairly natural to work in as they are prerequisite topics for later units so will show up when needed again. I do need to go back and add that data and change the student's score in the original unit that topic showed up if they show mastery of it later in the year, but it's all good. </div><div><br /></div><h3 style="text-align: left;"><span style="background-color: #fcff01;">Learning and IB</span></h3><div>Feel free to ignore this tab if you don't want to record any data about non-content things. My school has teachers track several "Approaches to Learning" and also follows the IB criteria required for an IB-certified school, and I am required to report out a grade for these so I do track students' progress over time with respect to these criteria. </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuvJk5GnPvK-96TVUVo2IMy-law7KLE5RFP_lLtAKw97pI-qwDmkLeRQCdHng37ukPHujkISoeofs21DLFB_Gf0LAadutDpY_0QGnGeJfrLajl_c0ghNZ2knujcK6b02OVSvl-MM85SPQ/s534/Screen+Shot+2021-07-21+at+11.01.53+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="534" data-original-width="524" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuvJk5GnPvK-96TVUVo2IMy-law7KLE5RFP_lLtAKw97pI-qwDmkLeRQCdHng37ukPHujkISoeofs21DLFB_Gf0LAadutDpY_0QGnGeJfrLajl_c0ghNZ2knujcK6b02OVSvl-MM85SPQ/w628-h640/Screen+Shot+2021-07-21+at+11.01.53+PM.png" width="628" /></a></div><br /><div><br /></div><div><br /></div><div>Because these lie on more of a spectrum than content mastery, I use a different rubric:</div><div><br /></div><div><span data-sheets-userformat="{"2":15297,"3":{"1":0},"9":0,"10":1,"11":4,"12":0,"14":[null,2,3450963],"15":"Palatino","16":11}" data-sheets-value="{"1":2,"2":"✓+ = exceeded standard\n✓ = met standard\n✓– = almost met standard\n✗ = did not meet"}" style="color: #34a853; font-family: Palatino, Arial; font-size: 11pt;">✓+ = exceeded standard<br />✓ = met standard<br />✓– = almost met standard<br />✗ = did not meet</span></div><div><br /></div><div>These are also assessed more often and happen mostly through observations so I don't delineate specific assessment events here and just record the data chronologically. A given student might have something like ✓ ✓– ✓ ✗ ✓ ✓ for a given criterion, which I will convert into a score and an IB grade at the end of the semester, but no one outside of the IB world understands their complex scoring rubrics so I'll just skip over that part. </div><div><br /></div><div><h3><span style="background-color: #fcff01;">Assignments and Student Notes</span></h3><div>While I don't give a grade for homework assignments and don't use them to assess students' content mastery like a good little SBG-rule-follower, I do like to record observations about them. Students generally have lots of choice about what to do for homework each week and then self-assess each week and set goals for next week. I look at their homework once a week, respond to their self-assessment slash goal, and record this in my gradebook. I guess I just really love recording things?? This is less time-consuming than you might think though since I'm not actually grading the homework or checking their answers or anything like that. Students have the answers to check against, have had time in class to go over questions, and homework is mainly for checking your understanding and reflection on next steps, as well as practice with writing out math steps and reasoning clearly. I write a comment or two in response to their reflection or to the easiness of following their process and reasoning and use voice to text to record this comment into my grading spreadsheet. Easy peasy. (Full caveat: I'm teaching at a tiny school next year and will have very small classes so this may not be manageable with large class loads)</div><div><br /></div><div>I also like to record observations about how students are working in class or what I'm noticing or wondering about them and find these really helpful when conferencing with them, especially when discussing approaches to learning and ways to improve. Finally, there are usually one or two open investigations and a lab or project each unit that students write up and these I do give more feedback on, which is recorded in this tab or sometimes linked to a separate rubric for these bigger assignments. The one-point rubrics on the left are there to help remind me what I'm looking for on different types of assignments. This tab is also a convenient place to record whether students are doing homework assignments since this is information that is often useful to discuss when conferencing with students about their progress or when communicating with parents.</div></div><div><br /></div><h3 style="text-align: left;"><span style="background-color: #fcff01;">Student tracking sheet</span></h3><div><span style="background-color: #fcff01;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiT1dyY4-lcwrQ0flxsoQrbhAJjYvKKXF5TXfy-3HXbils9SfFey9ZL7titZtYl-WWq98j_jMamYp6fvyGGTfzjSNQoMvhGaNKy5uassJjTzXa79o4KNsEGJHD67mYuV3agC7PqGhQdoMA/s1159/Screen+Shot+2021-07-21+at+10.17.58+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="496" data-original-width="1159" height="274" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiT1dyY4-lcwrQ0flxsoQrbhAJjYvKKXF5TXfy-3HXbils9SfFey9ZL7titZtYl-WWq98j_jMamYp6fvyGGTfzjSNQoMvhGaNKy5uassJjTzXa79o4KNsEGJHD67mYuV3agC7PqGhQdoMA/w640-h274/Screen+Shot+2021-07-21+at+10.17.58+PM.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;">Assignment Page, click to enlarge</div><div class="separator" style="clear: both; text-align: center;"><br /></div></div></div><div>This is something new I'm trying this year. In the past, I made and maintained a complex web of interlocking spreadsheets so that each student could see their progress on content standards and my notes on their assignments in real time and could also self-assess and reflect in their spreadsheet and have that information feed back to my master spreadsheet. Gahh. Maybe it's this past year of remote teaching and screen fatigue or maybe it's the nifty arrow rubrics that Peter Liljedahl showed off in his book, but I'm going to be doing things more old-school this year and printing off three pages for students to keep in their math binders. </div><h4 style="text-align: left;"><ul style="text-align: left;"><li>Assignment page<span style="font-weight: normal;">: Each week, they will use the next blank row on the Assignment page to self-assess, reflect, and set goals using the little arrow rubric provided. They'll get a new page each unit.</span></li><li>Content page: <span style="font-weight: normal;">When getting a quiz back, they will look at my feedback and record their progress relative to the content standards on the content page using the same key that I use (✓, H, P, or ✗). Students can also add to this page if they show me something during class. This page looks just like my content tab to make it easier to compare notes. Students will keep this page in their binder until they show mastery for all of the topics in that unit.</span></li><li><span style="font-weight: normal;"></span>Learning and IB page: <span style="font-weight: normal;">Before conferencing with me, they will self-assess on the Learning and IB page based on the work they have done in the last few weeks. They will keep using this page for the entire semester.</span></li></ul><div><span style="font-weight: 400;"><br /></span></div><div><span style="font-weight: 400;">Welp, that's just what I've been working on the past few weeks. Feel free to use any part of my grading template spreadsheet or the student tracking sheet! As always, I welcome comments, feedback, and questions here or over on Twitter at <a href="https://twitter.com/ablinstein" target="_blank">@ablinstein</a>.</span></div></h4><p></p>Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com3tag:blogger.com,1999:blog-8537494321067959493.post-48714940555323677822020-08-14T13:08:00.007-07:002020-08-15T10:47:36.759-07:00Remote Teaching - the community edition<p> I just finished remotely teaching two one-week courses for rising 9th graders in which at least half the class was brand new to the school. Each group met for 3 hours every morning for a week and I had the luxury of creating my own curriculum that didn't have to cover any particular topics, but did need to be fun, engaging for students with a variety of math backgrounds, introduce new students to how we teach math at my school and how to learn math remotely, and most importantly, foster a sense of community.</p><p><br /></p><p>Fortunately, Michael Pershan shared some words of wisdom about the need to build student-student connections over student-teacher connections in a remote space and this helped me rethink my original plan for each week.</p>
<blockquote class="twitter-tweet"><p dir="ltr" lang="en">Teachers have been worrying what online learning would look like when you don't have relationships with students. What I'm seeing in my camp teaching is the much bigger issue is kids not having relationships with each other.</p>— Michael Pershan (@mpershan) <a href="https://twitter.com/mpershan/status/1283750389175783426?ref_src=twsrc%5Etfw">July 16, 2020</a></blockquote><p>Based on his experiences with a virtual math camp this summer, I did a few things that I think helped students get to know each other and feel safer sharing and discussing than they would have otherwise. Here are some things that seemed to go well (at the end, I'll post some things that didn't go as well, not to worry).</p><p><br /></p><p></p><h3><ul style="text-align: left;"><li><b>Low stakes whole class interactivity</b></li></ul></h3><div>I started the week with an activity in which students had to drag their name somewhere on a set of axes so we could learn about each other. </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0KUug8ouM_dphMQKTs4v5ZWAAonkyMjKrk_uEl8ISM2VO2e93K6M0pEVsiAvpCqKfm0PxheH6QYnLj5O7b-N_-ELIwUojWbljN-PmmVMX4O3pmrfR7_-kf_miFPW6QT_X-lBQFkJ7EcI/s733/Screen+Shot+2020-08-14+at+12.25.40+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="618" data-original-width="733" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0KUug8ouM_dphMQKTs4v5ZWAAonkyMjKrk_uEl8ISM2VO2e93K6M0pEVsiAvpCqKfm0PxheH6QYnLj5O7b-N_-ELIwUojWbljN-PmmVMX4O3pmrfR7_-kf_miFPW6QT_X-lBQFkJ7EcI/s640/Screen+Shot+2020-08-14+at+12.25.40+PM.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrICvUS8EWto0afQbBFwMhEXHVtd7p7AE5OrFwhI6ENGSo94hiusCB7nIjM0e1v4aMTJHyq5kSR1oHPDGl82BeU4315t5vSrPYKkLF3cRuLQ5M3j88W6q-Qn_vDmqy6o_UZHq1tE1ArAY/s711/Screen+Shot+2020-08-14+at+12.25.52+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="598" data-original-width="711" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrICvUS8EWto0afQbBFwMhEXHVtd7p7AE5OrFwhI6ENGSo94hiusCB7nIjM0e1v4aMTJHyq5kSR1oHPDGl82BeU4315t5vSrPYKkLF3cRuLQ5M3j88W6q-Qn_vDmqy6o_UZHq1tE1ArAY/s640/Screen+Shot+2020-08-14+at+12.25.52+PM.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjA9-AUr7CRJ1pxE7VrqPsoL-2_Q6F0Ub0LcGyaJ6zua5nAn0xeucfdWIL1Q93xPz-WSqBb2HQu-zfyLJLHGqWG1L-ghnKvkJiVWJ7_E59wx6RZFC7GhKX7Qqqh0-f9nGTUag12s9I35R4/s978/Screen+Shot+2020-08-14+at+12.26.10+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="642" data-original-width="978" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjA9-AUr7CRJ1pxE7VrqPsoL-2_Q6F0Ub0LcGyaJ6zua5nAn0xeucfdWIL1Q93xPz-WSqBb2HQu-zfyLJLHGqWG1L-ghnKvkJiVWJ7_E59wx6RZFC7GhKX7Qqqh0-f9nGTUag12s9I35R4/s640/Screen+Shot+2020-08-14+at+12.26.10+PM.png" width="640" /></a></div><div><br /></div><div>I asked some chill follow-up questions about each set of axes as kids dragged their names, which they could answer in the chat or out-loud (almost everyone opted for the chat).</div><div><br /></div><div>I then had kids drag their names somewhere onto an oval and go around the oval, saying their name out loud and answering another easy icebreaker question, the goal being - everyone knows how to unmute their mics, everyone gets to hear how each student wants their name pronounced. </div><div><br /></div><div>Every morning started with a low-stakes interactive component. We did a <a href="http://wodb.ca/" target="_blank">"Which One Doesn't Belong" </a>with kids dragging their names into a quadrant and typing their reason for that choice into the chat box. We did a <a href="http://www.fosteringmathpractices.com/contemplate-then-calculate/" target="_blank">"Contemplate then Calculate,"</a> with kids typing their numerical expression into the chat box. We did an <a href="https://estimation180.com/days/" target="_blank">"Estimation 180"</a> task, where kids typed their "too low/too high/best guess" into the chat box. Just something small and relatively low-stakes where every kid interacted with the whole class. As the week went on, kids were more likely to use their mics voluntarily to participate, especially if I sent them into breakout rooms for a few minutes to pair-share first. The chat box is maybe the best feature of teaching remotely though - getting kids comfortable using it and setting the norm that it's basically a backchannel for classroom discussions, where kids can type questions and ideas and respond to those of their classmates was a huge component of building community for my students. </div><h3><ul style="text-align: left;"><li><b>Breakout rooms</b></li></ul></h3><div>Breakout rooms was where most of the community building happened though. I'm no remote teaching expert, but in my limited time doing this (spring + summer), kids are approximately 1500% more likely to talk out-loud in a breakout room than in a whole class setting. Each day, I created visibly random breakout rooms that stayed together for most of the day's activities. They started with an icebreaker here too. The first day, I used "personality coordinates" shared by <a href="https://blog.mrmeyer.com/2013/personality-coordinates-icebreaker/" target="_blank">Dan Meyer a while back</a>, which translated really well to a remote space.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXdTM7KeKj86pa97OJnrkZ0HSKZMsGKawsEILzsHWaW4kFhEdsth3UV5wXi6N1aRjTuDvw1h-AB9hhXrXTYJU3fg4opMPQoLPJEC7Mxi8MMSH5fEea2hGSKmH_rby2KdCadXv4__Pgwps/s1025/Screen+Shot+2020-08-14+at+12.43.48+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="589" data-original-width="1025" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXdTM7KeKj86pa97OJnrkZ0HSKZMsGKawsEILzsHWaW4kFhEdsth3UV5wXi6N1aRjTuDvw1h-AB9hhXrXTYJU3fg4opMPQoLPJEC7Mxi8MMSH5fEea2hGSKmH_rby2KdCadXv4__Pgwps/s640/Screen+Shot+2020-08-14+at+12.43.48+PM.png" width="640" /></a></div><div><br /></div><div>Each breakout room worked on one slide in the slideshow, putting their names next to the dots first, and then coming up with variables that could be placed on the axes to make this graph true for their group. Kids had a great time with this activity and came up with some clever and hilarious variables for their groups that we then shared out in the whole class. Following days had more traditional ice breakers, but I also had every student bring in a photo of something meaningful to them and add it to their group's slide and share about that photo, something I likely wouldn't have done in-person. That was another favorite.</div><h3><ul style="text-align: left;"><li><b>Games</b></li></ul></h3><div>Games are another low-stakes way for strangers to interact and build some familiarity and trust. I mostly used two-person games, borrowed from <a href="https://mathwithbaddrawings.com/2020/04/22/six-strategic-games-from-a-strange-and-bottomless-mind/" target="_blank">this list</a> by Ben Orlin. Fortunately for me, Mike Flynn had already created online templates for two of the games (<a href="https://twitter.com/mikeflynn55/status/1261592954248089600" target="_blank">Black Hole</a> and <a href="https://twitter.com/MikeFlynn55/status/1263887409722339330" target="_blank">Ultimate Tic Tac Toe</a>) and I made one for <a href="https://docs.google.com/presentation/d/1xsXw5-kwB4V0keCWvemzv2cVxDFALJT-tG23PWqhuF8/edit#slide=id.g90b5b1bd64_0_56" target="_blank">Magical Squares</a> so we had a variety of games to play. I think games like Sprout, Nim, and Hex would translate well to remote space if you want more ideas. After students played a game against an opponent, I asked them to share out possible strategies and things they noticed in the whole group and got kids to participate who were quiet otherwise. </div><h3><ul style="text-align: left;"><li><b>Norms</b></li></ul></h3> Throughout these activities, but especially at the start, I was very explicit about the ways that I wanted students to engage with each other. The first time that students went into breakout rooms, I assigned a group leader and gave that person several tasks.<div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgb0pPFYY_HtxWFpdFCYmg-3qSr9Tke_fcD2CQ30Sxo3TEc0BMVWjt8BsaAx0mSg9PX5A3V2veJN5gKzg6PM8EA0vGRNse3LLVg0P34QiM1z_4x3imx12PQ3EuzzmiRdaaoJeN6g0WnoXY/s1054/Screen+Shot+2020-08-14+at+12.54.46+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="584" data-original-width="1054" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgb0pPFYY_HtxWFpdFCYmg-3qSr9Tke_fcD2CQ30Sxo3TEc0BMVWjt8BsaAx0mSg9PX5A3V2veJN5gKzg6PM8EA0vGRNse3LLVg0P34QiM1z_4x3imx12PQ3EuzzmiRdaaoJeN6g0WnoXY/s640/Screen+Shot+2020-08-14+at+12.54.46+PM.png" width="640" /></a></div><div><br /></div><div>Each day, I had students reflect on how they supported each other, had students name peers who supported them along with what they did that was supportive, and asked students to share out strategies that were helpful in promoting effective collaboration. This was mostly done in a Google doc journal that students wrote in at the end of each day, but I also asked students to share out some of these things in breakout rooms at the start of the day. I frequently reminded them of our norms and why they were there. </div><div><h3><ul style="text-align: left;"><li><b>Choice</b></li></ul></h3><div>My last hot-tip for building community remotely is about giving kids choice for how they interact with each other. While I really wanted kids to work together, I also gave them opportunities to work on their own, if they wanted to do so, or to pick specific peers to work with rather than be randomly assigned. Knowing that some of the time, they would have choice for how they worked and who they worked with seemed to increase buy-in and willingness to work with new peers during the times that I asked kids to collaborate with strangers. I also tried to give kids different ways to participate - even though the norms asked for participation, we talked about different ways that this could happen, whether by typing in the chat box, asking others questions, affirming or pushing back on ideas, writing out the group's work on a shared virtual whiteboard, or using nonverbal cues if their camera was on, like looking at the speaker, nodding along, giving a thumbs up. I didn't require kids to have their cameras on, but tried to make it a safe space to do so and where there would be a reason to be seen and heard by others.</div><div><br /></div><div>This is not to say that everything was amazing and the students are now life-long friends. Creating a community virtually is going to be a challenge, even with all the tricks and best intentions because it's a weird, awkward space that's not conducive to vulnerability and intimacy. For example, the last hour of the last day was a choice project, and the majority of the new students chose to work on their own. I didn't force the issue, but I would have loved to see them choosing more collaboration. Something that I plan do differently in a few weeks when I meet my year-long classes is to have more opportunities for substantive sharing. I feel like we didn't really get past the easy icebreaker stage, and partly that's due to only being together for a week, and partly it's because I wasn't sure how much to push kids to share. I did have students share a Google doc with me in which they wrote a reflection at the end of every day, and those were much more substantive and raw. I'd like to have kids feel comfortable sharing those types of written reflections with each other and not just with me. With a class that I will have for longer, I'd also like to spend more time having students model and practice participation norms. </div><div><br /></div><div>I'd also love to hear your ideas of how you plan to foster community in your classes remotely this fall. Please reach out on <a href="https://twitter.com/ablinstein" target="_blank">Twitter</a> or in comments to this blog!</div><div><br /></div><p></p> <script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script></div>Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com11tag:blogger.com,1999:blog-8537494321067959493.post-30956193180351978962020-07-19T19:42:00.003-07:002020-07-19T23:04:26.501-07:00Remote Teaching - prepping for next yearI'm in the same boat as a lot of others, without a concrete plan for the fall yet, but with schools in my area leaning more and more towards starting remotely. Even if not fully remote, we will be at least hybrid in order to reduce the number of students coming to school at any time so my current plan is to assume remote instruction and to have in-person students join via Zoom to work with at-home students, if we do end up hybrid for some of the time. If conditions improve beyond current expectations, it's a lot easier to roll back and move towards face-to-face instruction than the other way around. This past month of summer break has given me a bit more time time to play around with tech tools, listen to webinars, look at my curriculum, and build on the work I did in the spring in teaching synchronously while remote. This blog post is an attempt to organize some of the work and thinking I've done so far in preparing for next school year. It's pretty long so I have no expectation that others will read, but I need to write out my plans for my own sanity.<br />
<br />
As I mentioned in my <a href="https://borschtwithanna.blogspot.com/2020/03/remote-teaching.html">previous blog post</a>, I'm working in a small school where all students have school-issued laptops and where classes will be run synchronously via Zoom, which influences the types of instruction I can do, but please don't hesitate to reach out here or on <a href="https://twitter.com/ablinstein">Twitter</a> if you have any questions for how this might look at your school.<br />
<br />
I'm jumping into tech tools first to get them out of the way, but the important stuff is below, my unpacking of the most difficult part of remote learning - students' need for relationships, understanding, and agency.<br />
<br />
<b>Tech Tools during Class</b><br />
The most useful tech tools that I used during class in the spring and that I plan to keep using in the fall were <a href="https://teacher.desmos.com/">Desmos Activity Builder</a>, <a href="https://classkick.com/">Classkick</a>, and virtual collaborative whiteboards for breakout rooms. I used Desmos AB and Classkick for students working individually - both platforms allowed me to see students working in real time and to give them feedback via comments in Desmos and by writing directly on their papers in Classkick. Desmos was better for content that involved graphing and making and testing predictions, while Classkick was better for students writing out their steps, working especially well for the small minority of my students who had iPads or tablets and could write with a stylus instead of their trackpad (but it also worked pretty well for kids with laptops only). I remade a number of my lessons as Desmos activities or simply imported pdfs of problems into Classkick. The drawbacks of both of these platforms were that they did not foster collaboration between students, even if I put them in breakout rooms and told them to talk to each other. This was very surprising as students had been used to collaborating effectively in my classes before we went remote so there's clearly something about a remote space that is much less conducive to working easily together. One strategy I plan to use in the fall (as shared by <a href="https://twitter.com/mpershan">@mpershan</a> a few days ago) is to assign one student in each breakout room the role of sharing their screen.<br />
<div style="text-align: center;">
<br /></div>
<div style="text-align: center;">
<br /></div>
<blockquote class="twitter-tweet">
<div dir="ltr" lang="en" style="text-align: center;">
OK this went so much better this morning. Did a short icebreakers WITH each breakout rooms. (This is camp and I have counselors in each room. Would be tougher if it was me and 20 kids but I think possible.) Also made clearer expectations: someone is sharing screen in every room.</div>
<div style="text-align: center;">
— Michael Pershan (@mpershan) <a href="https://twitter.com/mpershan/status/1283772703267225600?ref_src=twsrc%5Etfw">July 16, 2020</a></div>
</blockquote>
<div style="text-align: center;">
<script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script><br /></div>
<div style="text-align: center;">
<br /></div>
<div style="text-align: center;">
<br /></div>
<div style="text-align: left;">
Teaching students how to work together in breakout rooms is clearly a new skill and one we'll need to explicitly teach and practice in the fall rather than relying on their face-to-face collaboration skills to just extend into online interactions. I'm considering how to amend structures like group roles and <a href="https://samjshah.com/2011/07/12/participation-quizzes/">participation quizzes</a> to work in breakout rooms, since I can no longer observe multiple groups at once. For example, new roles could be: 1. Someone who ensures that a screen is being shared and everyone knows what they're working on, 2. Someone who pauses the room every 5 minutes and checks for understanding and who can call in the teacher if there's a group question 3. Someone who ensures that everyone is writing out their work and there is documentation for the breakout room.</div>
<br />
It might be good to shift teacher feedback on collaboration to a peer- or self-assessment model in which students set goals around collaboration, then reflect to themselves or to group members ("in what ways did you contribute to your group today?", "in what way could you be a better group member next time?", "tell your group one thing they did well today" , "give a specific shout-out to a peer who helped you learn today"). A very concrete thing might just be to ask students to track the number of times they asked or answered a question in their group. I think it might also be possible to do an amended form of a participation quiz where I pop into breakout rooms and record what I see in a shared document, although I won't be able to project it to them in real time.<br />
<br />
I'm also going to be looking to inject more fun and interactivity into breakout rooms - icebreakers, sharing something non-academic, Anne's <a href="https://abrandnewline.wordpress.com/2015/07/28/my-session-all-the-circles-tmc-2/">concentric circles activity</a>, something small that gets kids talking and sharing their screens and builds their comfort level with digital participation. In whole class discussions, using the chat feature of Zoom (set to "chat to host only") was incredibly helpful in drawing in shy students in the spring and I will continue using it to invite more participation and to get insights into kid thinking in real time.<br />
<br />
In the spring, I also used virtual whiteboards quite a bit when I wanted kids to work on novel problems together or to go over homework questions. I bounced around a few different ones - assigning a page in <a href="https://jamboard.google.com/">Jamboard</a> or a slide in a shared Google slideshow per group were great for students adding photos of their handwritten work and incorporating typed comments, but not great for handwriting. <a href="https://bitpaper.io/">Bitpaper</a> was best for writing and graphing math, but unfortunately, due to increasing use, they removed their free version for new users a few months ago (if you made an account before this and had some boards, you can keep using these for free, which is what I'm doing). <a href="https://goboard.com/">GoBoard</a> is probably my second favorite for writing out math work and has handy integrations with Desmos and LaTeX. If you have some money to spend, either Bitpaper or <a href="https://ziteboard.com/">Ziteboard</a> work really well for writing out math work and integrating photos of work on paper with handwriting and typing on a computer. If not, Jamboard and GoBoard are decent options.<br />
<br />
Online whiteboards are going to be a big part of my remote plan this year as well, and I need to also be explicit about norms there - the role of writer should rotate, everyone works on the same problem, students should look for multiple methods or connections between problems, there should be a check for understanding before moving on to the next problem, work must be clear enough that someone not in the group could understand your process. As these will be largely used in breakout rooms, these norms will need to be incorporated with the breakout room participation norms. So! Many! Norms! I will have to be very intentional about rolling these out sequentially and creating a small enough list that won't overwhelm students. But I know that time invested up front in fostering effective group work will pay huge dividends in how well students are able to learn from each other and work productively together for the rest of the year in a remote environment.<br />
<br />
The big new tech thing that I plan to use in the fall is <a href="https://www.onenote.com/classnotebook">OneNote</a> digital class notebooks. There was a pretty steep learning curve to figure out how they work from the teacher side, but I think they're now ready to go for the start of school and should greatly simplify the coordination of classwork and homework, as well as giving easy feedback to students in real time so that I may no longer need tools like Classkick or Google Classroom to organize assignments and feedback. It also means that I'll want to build in some time at the end of class for students to take photos of their handwritten and Desmos or whiteboard work to insert into their digital class notebook and reflect briefly on their understanding. One of my big takeaways from the spring was that everything takes 50% longer when teaching a class remotely, but it is also documented more thoroughly. There is potential here for deeper learning, but I will have to account for the amount of time that things take and be focused on the most essential topics in the curriculum.<br />
<br />
It might also be helpful to state that I'm not planning on investing a lot of time and energy into making content videos. I have provided curated <a href="https://docs.google.com/spreadsheets/d/1vO7nKIZJX4dhCTJMNEZB7imr32HqNCkIQdoEQUJRmeM/edit?usp=sharing">video resources</a> for students in every class for several years now and based on student feedback and my own priorities, I'm going to continue outsourcing this. I don't think it's worth it for me to record a lot of videos teaching math content when there are already so many out there, many made by people with way better video recording technology and know-how. In the spring, I did often make short videos in response to student questions or common errors on their work, and I will make these as needed again this year, using the Notability app for iPad and iPad's native screen capture or by recording a Zoom call with just myself in it and screen sharing from my iPad so that my face is also in the video. But these videos are going to be in response to student work, not a replacement for synchronous class time.<br />
<br />
<b>Relationships/Communication/Support</b><br />
I'm thinking a lot about teacher-student as well as student-student relationships for the coming year and while I list out individual ideas below, I know that a conversation with my department and school about values and priorities is going to be the most important. We need to plan out how to care for students remotely, how to know how they are doing and what we can do to support them as students, but also as kids and people who are lonely, bored, scared, and disconnected from their normal support networks.<br />
<br />
I loved a suggestion from <a href="https://twitter.com/a_mcsquared">Audrey</a> around students sending her photos of things that have meaning for them (sounds like pets were a crowd pleaser) and starting each class with a student talking about that photo. She then compiled all of the photos for an end-of-year slideshow. Several others have also proposed converting Sara VanDerWerf's <a href="https://www.saravanderwerf.com/week-1-day-1-name-tents-with-feedback/">Name Tents</a>, which is how I usually start the school year, into a digital form where students respond to prompts either in writing or via short <a href="https://blog.flipgrid.com/home">Flipgrid</a> videos. Teachers and students could respond to these with their own videos. This also made me reflect on the power of audio or video feedback to foster teacher-student relationships as this was something mentioned by several teachers who regularly teach online. I'm excited that OneNote will allow me to easily record an audio response to student work. I had been planning to use <a href="https://voicethread.com/products/k12/">Voicethread</a> to do this before I committed to OneNote, but I know that students really appreciated video responses to their work in the spring and that they help to humanize what could otherwise feel like dry content-focused interactions.<br />
<br />
Another idea that I liked that was shared this morning in response to <a href="https://twitter.com/jreulbach/status/1284564506669195265">Julie's post on teaching in a hybrid model</a> (in which students are split into two groups and each week, they rotate which group is at school and which group is at home) was assigning each student in a group a buddy in the other group who could help them know what was going on during class or let the teacher know if there were issues when their buddy was learning from home. In the spring, I used <a href="https://padlet.com/dashboard">Padlet</a> for students to post and answer each others' homework questions and ran an after school homework help time over Zoom where students could drop in and work with peers and math teachers for a few hours each week. I will continue using Padlet and running after school Math Lab, but am also considering other outside-of-class structures that might encourage more interactions between students. Study groups? More group projects? This is an area where I could really use the wisdom of the collective - how are others planning to foster student-student relationships in their schools?<br />
<br />
One of the things I took away from a <a href="https://globalonlineacademy.org/what-we-do/educator-courses/designing-for-online-learning">"Designing for Online Learning"</a> course I completed at the start of the summer from Global Online Academy is the importance of clearly organized course materials and easy to access supports for students. I used a Google Site in the spring with a daily agenda so that students could easily follow the sequence of a lesson and know what was going if their audio or video cut out or they lost their Zoom connection. Moving to OneNote will make it easier to share monthly, weekly, and daily plans with students so that they have a clear understanding of the content goals and work they are completing.<br />
<br />
I am also going to cycle in <a href="http://www.spencerauthor.com/the-power-of-student-conferencing/">one-on-one conferences</a> with students to find out how things are going, build relationships, set goals, and go over feedback together. I conferenced with the majority of my students in the spring and although it was a lot of time and work to set up, I felt that they were incredibly worthwhile, even more so in a remote setting than in face-to-face school. My students benefited, but I also benefited tremendously in my ability to empathize and support specific students. In my experience, making these meetings required and ongoing (once a month is a good frequency, I've found) is key. My school will also be setting aside one day each week for tutorial slots so those will also be great opportunities for students to access support. I will also continue seeking feedback from students on how things are going and using that feedback to correct course. Short, anonymous student surveys once or twice each semester, rather than an end-of-year longer survey, have been more helpful for me in getting actionable feedback. Relationships and timely feedback were critical in the spring for motivating students to show up to class, engage with content, and reach out for support, and I know they will be even more so with a new crop of students who don't know me or each other very well yet.<br />
<br />
<b>Curriculum</b><br />
My biggest content take-away from the spring was the importance of student agency in motivating students to stay engaged and work remotely, without the norms of being inside a school building. I built <a href="https://drive.google.com/file/d/1BjqpnJdfeEeMTD5k84ciV9wl1Ui2PiEB/view?usp=sharing">choice into assignments</a>, I let students select their own breakout rooms every few class periods and let me know how they would like to work during class, and I designed the <a href="https://docs.google.com/document/d/1GOQAMQeNgn-aTKHHONTbpPYShywBRUER9kwesRBTF4A/edit?usp=sharing">end-of-semester projects</a> to have options and to include a variety of student interests. Student choice to support differentiation is something that's been important to me for a long time and I <a href="https://docs.google.com/presentation/d/1xS-pE7pU-kysNMF7CEWQHrnSZhEClnfI_nDLg7a_OwU/edit?usp=sharing">presented on it</a> this summer, but in a remote environment, I need to be way more organized with helping students set goals, receive timely feedback, and revise. I've done a bunch of curriculum work this summer to hopefully be in a place where more of my time is spent giving feedback and conferencing with students and less on writing problem sets and planning lessons. And I'm hoping that OneNote is a platform that supports organization of assignments, quick feedback, and revisions.<br />
<br />
With respect to deepening the curriculum, I've also revised several projects to include more choice and to bring an anti-racist lens to student mathematical thinking. For example, the first 8th grade project for the last several years has been to find a proof of the Pythagorean Theorem from the many options available and present it to the class.<br />
<br />
<div style="display: block; font-family: "helvetica" , "arial" , sans-serif; font-size: 14px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 12px auto 6px auto;">
<a href="https://www.scribd.com/document/469719782/5-3-Pythagorean-Proof-Project-Google-Docs#from_embed" style="text-decoration: underline;" title="View 5.3 Pythagorean Proof Project - Google Docs on Scribd">5.3 Pythagorean Proof Project - Google Docs</a> by <a href="https://www.scribd.com/user/518705195/Anna-Blinstein#from_embed" style="text-decoration: underline;" title="View Anna Blinstein's profile on Scribd">Anna Blinstein</a> on Scribd</div>
<iframe class="scribd_iframe_embed" data-aspect-ratio="0.7729220222793488" data-auto-height="false" frameborder="0" height="600" id="doc_97871" scrolling="no" src="https://www.scribd.com/embeds/469719782/content?start_page=1&view_mode=scroll&access_key=key-LrdUqqrLuLWfOo5HJtbh" title="5.3 Pythagorean Proof Project - Google Docs" width="100%"></iframe><br />
<br />
The revised project will include more of a humanistic look at how different cultures have used and thought about this right triangle relationship and why it is that we have named it after a Greek mathematician instead of the many others who also explored it. Students will learn more context and history of the mathematician whose proof they are presenting and the work of non-majority culture mathematicians will be celebrated. A key understanding for this project this year will be to critically examine who gets the credit for a mathematical idea and how different cultures come to understand, apply, and prove mathematical ideas. Two later projects (one on modeling data and one on using concepts of standard deviation and z-scores to analyze outliers) will have a social justice lens this year - students will still have choice in their research questions, but will be working within the realm of social justice topics.<br />
<br />
I will also be focusing more explicitly on retention this year since learning remotely may really impact how deeply students are learning content and there may be more gaps from last spring. Working on a curriculum team this summer, we revised the standards for 8th grade to more explicitly connect back to earlier content and we've rewritten homework problem sets to spiral in previous topics. Sara VanDerWerf has blogged about her <a href="https://www.saravanderwerf.com/green-reference-sheets/">use of green reference sheets</a> to better support students with gaps in prior knowledge and I plan to use a form of this as well, since we already start each unit with a pre-assessment to help us and students know what topics in the upcoming unit will need the most support. I've been incorporating an <a href="https://docs.google.com/document/d/1HXpfLAILjbZoIeMUIwPBYKlAKe8NuPNV0Wii2hczOrw/edit#heading=h.og7y7bhcxtvf">"Important Concepts"</a> section into notes packets, but am still thinking about how to best use this with students. Should students be creating their unit summary page? Should there be more explicit use of teacher-made reviews and references throughout each unit? Since many class periods are structured around problem-solving and student-led exploration, with some time spent synthesizing and applying at the end, rolling out a summary of what students will learn ahead of time seems detrimental to that process. At the same time, many middle school students are not great note-takers and having a clear summary that can help them see the big picture or review and solidify what they explored in class seems like a good idea. I'm going to play around with summary structures this year that build off student thinking and will hopefully, have more to report on this soon. I'd love others' input on how they've integrated review and content summaries with problem-based learning.<br />
<br />
<br />Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com2tag:blogger.com,1999:blog-8537494321067959493.post-47101404074671223212020-03-29T00:48:00.002-07:002020-03-29T00:48:47.064-07:00Remote TeachingAs I end the first full week of remote teaching, I wanted to quickly jot down some of the things that I've tried this week and what is and isn't working for me. First, a bit of context:<br />
<br />
- I'm in San Francisco and teach Math to 7th and 8th graders at a K-12 independent school<br />
- We are 1-to-1 with laptops in the middle and high school and have reached out to students with internet connection issues to help them access remote classes<br />
- We don't have textbooks or give grades, which means that we need to think differently about structures and motivation for kids to engage in remote learning<br />
- Two weeks ago, school rolled out a Remote Learning Plan that involves synchronous video classes over Zoom for most core classes, along with assignments and drop-in hours, but no synchronous class, for P.E., music, art, and electives. We are on an A/B block schedule and classes have been shortened from 75 to 60 minutes so kids get a 20-minute break in between, but otherwise, have 3-4 remote classes four days a week, and then a day to work on homework, projects, work from their asynchronous classes, and meet with teachers one-on-one.<br />
<br />
Some things that I've found really helpful so far:<br />
<br />
<ul>
<li>A class webpage... I use this to structure what we're going to do during each remote class. It was super, duper easy to make a webpage using Google Sites. Mine is not fancy, but has a tab for the day's agenda, another one with assignments students complete outside of class (which are also posted to Google Classroom), and a final tab that organizes class notes and online resources for each topic, since we don't have a physical textbook.</li>
</ul>
<br />
<br />
Here's last Wednesday's agenda for 8th grade:<br />
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj92N9xiqtbvikM6ds3FWXGliUc7mnHvP2EfV1oN6nv01CT4vYHyBQkuL_Ip2iFrDcoJClrTfIVpTwe_QpKw5UD9LfK04f0zYltyh4Gov_WHFX-Xd8tnrWoJ1-37fDFhscbbO69LSP0otM/s1600/Screen+Shot+2020-03-29+at+12.42.02+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="969" data-original-width="1600" height="386" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj92N9xiqtbvikM6ds3FWXGliUc7mnHvP2EfV1oN6nv01CT4vYHyBQkuL_Ip2iFrDcoJClrTfIVpTwe_QpKw5UD9LfK04f0zYltyh4Gov_WHFX-Xd8tnrWoJ1-37fDFhscbbO69LSP0otM/s640/Screen+Shot+2020-03-29+at+12.42.02+AM.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Kids can use this to get to the different parts of that day's lesson, which is especially helpful if they lose their connection and have to reconnect to the Zoom class or have bad audio.</div>
<div class="separator" style="clear: both; text-align: left;">
</div>
<ul>
<li>Structures that break up the class into different types of learning environments seem to be going well. We usually start with a warm-up problem that is linked in Google Slides that we either discuss as a class or in breakout rooms. Then, I have each breakout room work on problems together in a slide on <a href="https://jamboard.google.com/">Jamboard</a>, a virtual whiteboard. </li>
</ul>
<div>
Here's a whiteboard from one breakout room in a 7th grade class from last week:</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9eFj1wZj_WNaQ5jYJyPuFZB6cQU0yvsWbo0QVZnmpAGqo6aJKM_JSurldOKwzw_qlWAsLd-Ly-YdRE9i3org5fxZyngBRFTksm5ipg8ejqlAJN5b560bh2bTvTjCBkYpf0aNp8XcFC2w/s1600/Screen+Shot+2020-03-29+at+12.13.37+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="897" data-original-width="1600" height="358" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9eFj1wZj_WNaQ5jYJyPuFZB6cQU0yvsWbo0QVZnmpAGqo6aJKM_JSurldOKwzw_qlWAsLd-Ly-YdRE9i3org5fxZyngBRFTksm5ipg8ejqlAJN5b560bh2bTvTjCBkYpf0aNp8XcFC2w/s640/Screen+Shot+2020-03-29+at+12.13.37+AM.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div>
<br /></div>
<div>
Some kids are writing using their mouse and trackpad, some kids are using text, others are doing work in a notebook and uploading photos of their work. Having the virtual whiteboard means that I know which groups are struggling and can be more efficient in which breakout rooms I visit while they work together, as well as identifying responses I want to highlight when we debrief as a whole class.</div>
<div>
<br /></div>
<div>
The last part of class is usually a Desmos activity I can use to see how individual kids are doing with the topic and decide on whether I want to see any for one-on-one time. I'm mostly taking Illustrative Mathematics lessons and converting them into Desmos Activities or creating quick exit tickets that I can have students complete in the last five minutes of class.</div>
<ul>
<li>Using Google Classroom to get homework out and collect written work is going really well. Students are submitting photos or scans of their handwritten work on homework assignments and the Classroom app for iPad lets me annotate submissions so that I can give them written feedback on their work. This is another important avenue for me to see how individual kids are doing and to identify kids I want to follow up with one-on-one. That might mean asking a student to see me during office hours or recording and sending them a short video addressing something I am seeing in their homework. I just figured out that my iPad has its own screen recording function so I don't need to download and use a different app, I can just jot and talk through a quick note in Notability, upload it to Google Drive, and send the student a link.</li>
</ul>
<div>
<br /></div>
<div>
Things I still want to work on as California will remain "sheltered in place" for at least for the next month:</div>
<div>
<ul>
<li><b>One-on-one meetings with every student</b>; I have been mostly using office hours as an optional drop-in time for students, although I have reached out to those that I can see are struggling, but I want to schedule a one-on-one meeting with each and every student in the next few weeks to check in and find out how things are going for them and to look over their work together. I'm finding that middle school students are just not great at taking in written feedback over the computer and knowing what to do with that information or what their next step should be. </li>
<li><b>More variety in the activities I am doing with students during class</b>; right now, they seem to like the mix of class discussion, breakout rooms, virtual whiteboarding, and Desmos activities, but I imagine that these will start to get old soon. These are pretty similar to activities we did in class when regular school was in session, but we also did collaborative projects, labs where students gathered and modeled data, student presentations, and explorations with manipulatives, which are all missing from remote Math class. I'd love ideas of what others are doing that might create more balance and variety in working with students remotely. </li>
<li><b>Ways to check in with every student during class</b>; I really miss the ability to walk around the room, scan what students are doing, and ask quick questions to probe their thinking or identify cool ideas that I could then ask them to share with the class. It's really hard to informally see the work of individual students and and talk to them without drawing a lot of attention to it in a video meeting while still keeping an eye on the rest of the class. </li>
<li>I want to <b>build more community and connections between students</b> because I know this is something they're really missing in this remote learning space and is one of the main reasons that kids are excited to go to school and learn. Initially, I focused on structures that would help with content and organization because that's how I deal with stressful situations, but now that classes are running pretty smoothly and we have a system, I want to develop more ways for us to be human and connected together. </li>
</ul>
<div>
<br /></div>
</div>
<br />
<span id="goog_737060683"></span><span id="goog_737060684"></span><br />Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com6tag:blogger.com,1999:blog-8537494321067959493.post-29662332271378511922020-01-16T12:29:00.001-08:002020-01-16T12:32:00.827-08:00Proof in a non-Geometry classroomA beef that I have long had with the standard math curriculum is that for many students who don't take college math courses, proof is a weird one-off that you do in a Geometry class for one year, writing algorithmically in two-columns full of acronyms. You know it's coming, but certainly aren't expected to do anything about it until you get to Geometry, and then, just as enigmatically as it appeared, it vanishes from the curriculum again. Truly, a mystery.<br />
<br />
I began to rethink my own views on proof and how its definition might be broadened to make it a more regular component of ALL math classrooms when I read Avery's <a href="http://www.withoutgeometry.com/2013/11/proof-doesnt-begin-with-geometry.html">blog post on redefining proof</a> several years ago. More recently, I've been thinking a lot about how to help students become more rigorous and formal in their proof writing, while still treating their informal reasoning and ideas as valid and interesting in their own right, not just as a stepping stone to "more correct" proof.<br />
<br />
Teaching an integrated math course to 8th graders this year gave me some unique opportunities to play around with proof and formalization. The year starts with a unit centered on the Pythagorean Theorem and culminates with a <a href="https://docs.google.com/document/d/17WLrgJGfTJQLb-Y4zwz9AIlMIFD4WgME5zKWSOiUKwg/edit">project</a> in which students choose a proof of the theorem (we used a <a href="https://www.cut-the-knot.org/pythagoras/">collection of proofs</a> at Cut the Knot) to study and then present their proof of choice to peers. There's a great variety of proofs there in terms of complexity and usage of algebra/geometry/trig/similar triangle concepts and focusing on analysis of existing proofs emphasizes what it means to understand a proof and be convinced by its reasoning. We also had a great class discussion about the difference between an example or demonstration and a proof, looking at several videos "proving" the Pythagorean Theorem that really only showed it to be true for a specific instance.<br />
<br />
<div style="text-align: center;">
<img alt="Image result for prove pythagorean theorem" src="https://www.onlinemath4all.com/images/pythagorean.png" /></div>
<div style="text-align: center;">
Look, it works!</div>
<div style="text-align: center;">
<br /></div>
<div style="text-align: left;">
That was pretty great, but there was nothing in the curriculum that built on this for the rest of the year so I decided that halfway through the next unit, we would do an exploration of polygon areas that would lead students to <a href="http://jwilson.coe.uga.edu/EMAT6680Fa05/Schultz/6690/Pick/Pick_Main.htm">Pick's Theorem</a> where they could start to write their own proofs, but I really struggled with structuring it in a way that honored students' existing reasoning, but also pushed them to formalize more and consider proof techniques, such as casework. If you haven't seen Pick's Theorem, it's a neat little formula that connects the area of a polygon whose vertices are points on a lattice to the number of lattice dots on the perimeter of the polygon and the number of lattice dots in interior of the polygon. </div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
The structure I eventually created seemed okay, but definitely produced mixed results. All students were able to come up with a conjecture for the area of a lattice polygon, but even with my hints (which I thought were maybe too helpful), virtually no students were able to make progress on proving the theorem on their own.</div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_KflWY2JQYxsO2xCvpwkRZtPH_daT1MCFINaefzrXnzN84loCaO8KFL3Ss9NbAPRhSxHg8hQEPQwoNGdLvg2ObvrEGtxN0ktjEovwQERzrXRzjPgK51tCXRIsE-NEC_gz0FmBk39JF6Y/s1600/Screen+Shot+2020-01-16+at+12.18.27+PM.png" imageanchor="1"><img border="0" height="552" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_KflWY2JQYxsO2xCvpwkRZtPH_daT1MCFINaefzrXnzN84loCaO8KFL3Ss9NbAPRhSxHg8hQEPQwoNGdLvg2ObvrEGtxN0ktjEovwQERzrXRzjPgK51tCXRIsE-NEC_gz0FmBk39JF6Y/s640/Screen+Shot+2020-01-16+at+12.18.27+PM.png" width="640" /></a></div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
<b>Questions I now have:</b></div>
<div style="text-align: left;">
</div>
<ul>
<li>Was it too big of a jump to go from analyzing proofs to having students write their own proof, even with lots of hints?</li>
<li>Is this problem perhaps not the right one for first proof writing?</li>
<li>What other problems or structures could I have used to transition more effectively towards proof-writing that still build on students' original reasoning and perspectives?</li>
<li>Would students have benefited from writing a proof (or the start of a proof) together as a class first?</li>
<li>Where should I go next to develop students' formal proof-writing skills?</li>
</ul>
<div>
<br /></div>
<div>
I do have some thoughts on these, but would love to get more input and ideas from the community.</div>
Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com1tag:blogger.com,1999:blog-8537494321067959493.post-37698741099932879602019-02-19T07:01:00.002-08:002019-11-22T15:42:08.700-08:00Flexible groupingsI wanted to respond to <a href="https://twitter.com/MarkChubb3?ref_src=twsrc%5Etfw%7Ctwcamp%5Etweetembed%7Ctwterm%5E1096853470806708229&ref_url=https%3A%2F%2Ftweetdeck.twitter.com%2F">@MarkChubb3</a>'s tweet (below) in more characters than Twitter would allow.<br />
<blockquote class="twitter-tweet" data-partner="tweetdeck">
<div dir="ltr" lang="en">
I am very interested to hear more about how you or your district implements any intervention for mathematics.<br />
I would love to know your answers to some of the final reflection questions as well:<a href="https://t.co/iwhzqIvNsN">https://t.co/iwhzqIvNsN</a><a href="https://twitter.com/hashtag/iteachmath?src=hash&ref_src=twsrc%5Etfw">#iteachmath</a> <a href="https://twitter.com/hashtag/MTBoS?src=hash&ref_src=twsrc%5Etfw">#MTBoS</a> <a href="https://twitter.com/hashtag/mathchat?src=hash&ref_src=twsrc%5Etfw">#mathchat</a> <a href="https://twitter.com/hashtag/satchat?src=hash&ref_src=twsrc%5Etfw">#satchat</a> <a href="https://twitter.com/hashtag/elemmathchat?src=hash&ref_src=twsrc%5Etfw">#elemmathchat</a></div>
— Mark Chubb (@MarkChubb3) <a href="https://twitter.com/MarkChubb3/status/1096853470806708229?ref_src=twsrc%5Etfw">February 16, 2019</a></blockquote>
<script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script><br />
Mark asks some great questions about groupings, specifically focusing on issues of equity, identity, and experience vs achievement gaps. I would highly recommend going to read his post, where he details his recommendation for a progression between Tier 1 (all students), Tier 2 (small groups), and Tier 3 (individual students) instruction.<br />
<br />
These are questions near and dear to my heart. My school, like many, has tried a variety of approaches to groupings over the years. As a school that targets gifted learners whose needs were not being met, we see huge ranges in students' experience in Math that make purely heterogeneous groupings challenging. However, as Mark points out, the danger of groupings, especially ones that are static, holistic, and that lead to diverging learning and opportunities, are manifold. This year, we have piloted a model in our 5th and 6th grade Math classes that has tried to walk the fine line between the benefits of some groupings, while trying to avoid some of the negative effects of groupings discussed above.<br />
<br />
<b>Flexible groupings model</b><br />
<br />
Our model relies on the fact that for 5th and 6th grade, students have Math at one of two distinct times every day they meet. That means that there are several same grade Math classes scheduled at the same time. The other component of our schedule that makes flexible groupings easier is that these Math classes are happening in classrooms next to each other and two of the rooms share a retractable wall that can be moved out of the way to create a large shared space.<br />
<br />
We started the year with all students who were taking Math at that time in the large shared space, working in random, heterogeneous groups that we mixed up every day. All three Math teachers for that grade were present so that students could get to know the entire teaching team and vice versa. The first unit for both of these grades focuses on Mathematical habits of mind so problems are rich and low-floor/high-ceiling and don't have specific content objectives. Students were able to work with a variety of peers and we were able to gather a great deal of data of how students approach new problems, collaborate and communicate, and write down and process their thinking. We then moved into content-based units, which all followed a similar pattern:<br />
<br />
<b>Key features of our model -- student-facing</b><br />
<br />
<ul>
<li>Students start each new unit in random, heterogeneous small groups within a large shared space with multiple teachers, working on open tasks that introduce some of the new concepts.</li>
<li>At the same time, students complete a take-home pre-assessment that looks at their prerequisite knowledge, as well as knowledge of the concepts and skills to be taught in the upcoming unit.</li>
<li>Teachers create new groupings based on the pre-assessment and observational data of students' learning strengths and needs.</li>
<li>Students move into their new groups, which last for two-three weeks.</li>
<li>There is some student choice built into each grouping - as we review and prepare for an assessment, students select what and how they would like to review and are regrouped based on this choice. </li>
<li>Students are assessed on their understanding of content for this grouping cycle and are given feedback and opportunity for individual revision, intervention, and/or extensions. </li>
<li>These unit assessments and pre-assessments are used to drive groupings for the next cycle. </li>
<li>Most homework assignments are the same for all groups and are differentiated by giving students choice over which problems to work on. </li>
<li>Students regularly reflect on their needs, choice of homework problems, and how they are working in different groupings and settings.</li>
<li>Units that are more project-based (we have three large units like this during the year) are done entirely in heterogeneous groups.</li>
</ul>
<div>
<b><br /></b></div>
<div>
<b>Key features of our model -- teacher-facing</b></div>
<ul>
<li>Teachers who share a common pool of students use a shared spreadsheet to track observations/feedback on classwork, homework, assessments, and projects. This is really important in order to know how students are doing as they move through different groups and work with different teachers. We spend time as a team discussing what we think is important to include in our notes and what our notes reveal about different students' needs.</li>
<li>Each grade level team meets twice per week to discuss lesson plans, how students will be grouped that week, students we are concerned or wondering about, how we're giving feedback, and all the other little things that need to be aligned when co-teaching. </li>
</ul>
<div>
<b><br /></b>
<b>Benefits of flexible groupings</b></div>
<div>
Students and families have been really positive about this implementation. It has many of the benefits of both heterogeneous and homogeneous groupings and has ameliorated a lot of the issues we have seen in the past with groups forming a fixed mindset about their abilities and trajectory. Especially in our project-based units, we see students working productively with a greater variety of peers and having a better understanding of themselves as learners. It supports a philosophy of meeting students where they are and the idea that different students have different mathematical strengths and areas that need more support.</div>
<div>
<br /></div>
<div>
<b>Questions and next steps</b></div>
<div>
I would like to see more heterogeneous mixing within a unit rather than just at the start when the unit is being launched. There should be other opportunities for rich, low-floor high-ceiling tasks that many different students can access and work on together. At the same time, I would also like to see more differentiated materials used for intervention/re-teaching/practice. We currently give students access to a spreadsheet of practice problems and guided notes, but don't have fine-tuned intervention and reteaching strategies or problem sets. I would also like to see more spiral review built in to the curriculum so that students who are still working on concepts can continue with the rest of the grade, but continue to revisit material. </div>
<div>
<br /></div>
<div>
The biggest question that I have is whether this model can continue into the higher grades. In 7th and 8th grade, we have traditionally broken students up into two tracks that had different curricula and that resulted in different placement in high school math classes. Our high school math classes are not grouped or tracked, but students can start at different points in the sequence of classes, which is another way of trying to avoid homogeneous, fixed groups, but is very different and operates on the assumption that students of different grade levels can take Math together. This is really different from our middle school model, where the entire schedule for a student is driven by their grade level. I'm very curious to hear how others (both middle and high school) are solving this issue and whether anyone has been able to make flexible groupings work for higher grades.<br />
<br />
<b>11/22/19 update: </b>I recently co-presented on how the flexible grouping model interfaces with a growth mindset at a conference with one of my coworkers. <a href="https://docs.google.com/presentation/d/1aSEez-z2hwEvujeG0xUnJghsviL-YBCbHHxHwNMHdAM/edit#slide=id.g64c66ae7ee_1_8">Here</a> are the slides from this presentation.</div>
Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com2tag:blogger.com,1999:blog-8537494321067959493.post-25980809690069565962018-12-13T13:40:00.000-08:002018-12-13T13:40:16.748-08:00Differentiation and the limitations of groupworkIt's important in any profession to stay humble, but teaching has a way of reminding you of this in particularly in-your-face ways, I believe. This semester has really brought home this issue for me in the challenges presented by my upper school Math 3 class. The issues have been around productive groupwork, an area in which I have felt particularly strong and well-trained, so it was perhaps an especially humbling experience to see all of my strategies and approaches come crumbling down and leave me turning to my Twitter network and colleagues to find new ways of helping students work together and feel confident in their progress. I wanted to share and summarize here some of the issues I've worked through that might perhaps be helpful to others.<br />
<br />
First, some background.<br />
<br />
I have been incorporating the essential elements of a <a href="http://peterliljedahl.com/wp-content/uploads/Building-Thinking-Classrooms-for-teachers.pdf">Thinking Classroom</a> in all of my Math classes for the past few years, but most notably in my high school class, where the focus on content and pressures to teach to the test are greater. This year, just like last, I had students read and reflect on Thinking Classrooms and we discussed why most of our time together is spent working on problems in random groups, sharing out ideas and conclusions, and using these to synthesize and summarize learning from the bottom up rather than top down via teacher-led instruction. Students initially seemed bought in and supportive of this type of classroom environment. We set up <a href="https://docs.google.com/document/d/1bpikW1Nfl7M3MImmydy7tR3HZIIGwlgrpwCoQLTtNN4/edit">class norms</a> and discussed the use of <a href="https://docs.google.com/presentation/d/1DS07qAEOPv3vg1XBgLHjJg_E4hGFA9rGpZkWy7S74ns/edit?usp=sharing">group roles</a>, how to step up/step back in group environments, and how to be a <a href="https://docs.google.com/presentation/d/14s6qu17H4TN5FV_0XhpYdBjwdzHxS1SyIpGIQm-lwgI/edit?usp=sharing">skeptical peer</a> and give respectful pushback on ideas.<br />
<br />
Several weeks into the semester, however, I started noticing a troubling pattern - some students were disengaging from their collaborative work and seemed very hesitant in sharing their thinking within either small groups or the larger class. Then, I started to hear two different complaints from students - some were feeling that their work during class was unproductive because their groups moved too fast and they were feeling increasingly anxious and uncertain about their mathematical understanding and abilities. They were feeling unprepared to do problems independently on homework assignments or assessments and wanted more teacher guidance and structure, as well as more opportunities to go at their own pace and understand ideas more fully. Other students raised the opposite issue - they felt that the pace of the class was too slow, that they were doing too many problems that they already knew how to do or could figure out quickly and wanted more challenging and deeper problems, both during class and on homework assignments.<br />
<br />
<div style="text-align: center;">
<span style="font-family: Times, Times New Roman, serif; font-size: large;"><b>When group work goes wrong:</b></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkmwQqZlsq11SsocYZhI5seJvLLdKBO4qQvnE5WOSsJFzi2NzlhMdzxh8MFGl5evauZplPM2GzHIRCcNX-Q-MFMAgvceZ8m9ZEpQ66CFvEd_lLbduRwTL5WZL8S5W_40vnucfsFKzjcgo/s1600/bad+group+work.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="599" data-original-width="1002" height="382" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkmwQqZlsq11SsocYZhI5seJvLLdKBO4qQvnE5WOSsJFzi2NzlhMdzxh8MFGl5evauZplPM2GzHIRCcNX-Q-MFMAgvceZ8m9ZEpQ66CFvEd_lLbduRwTL5WZL8S5W_40vnucfsFKzjcgo/s640/bad+group+work.png" width="640" /></a></div>
<br />
<br />
In reflecting on these issues and why they were coming up this year, I realized that we had actually made quite a large change to the Math program without making any changes to our curriculum or pedagogy. This was the first year that we had decided to mix all grades taking a particular Math course - Math had been the only discipline at the Upper School in which students were separated out by grade level. In the past, 9th and 10th graders taking Math 3 (students who had accelerated the normal sequence) were in different sections from 11th graders taking the class (students who were on grade level in terms of their progress through the sequence). This year really was different in terms of prior math experiences, expectations, and desire for challenge/acceleration for students in the same class and the normal groupwork structures were not sufficient to bring together students with such varying backgrounds and approaches.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrYu9WMzUpTEv9hMSKMHI6j4ggBv39Er1LIbuD_G6JoX6HdKQrGG5Q9ExDnRNDG7LrdYD-rLeUHsd-A5DrQXSjcAa7c0g-12KXgvQkDrYaMLnGnxYGDc9kji2er4a0W5mDkZ3vaSwCKhg/s1600/meme.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="335" data-original-width="568" height="376" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrYu9WMzUpTEv9hMSKMHI6j4ggBv39Er1LIbuD_G6JoX6HdKQrGG5Q9ExDnRNDG7LrdYD-rLeUHsd-A5DrQXSjcAa7c0g-12KXgvQkDrYaMLnGnxYGDc9kji2er4a0W5mDkZ3vaSwCKhg/s640/meme.jpg" width="640" /></a></div>
<br />
<br />
My next step was to look for feedback from colleagues as well as the Twitter math teacher community. Some suggestions that I implemented that seemed to make a difference:<br />
<br />
<ul>
<li>Taking a break from random groups to help students regain their trust that the class would meet their needs; doing some work in pairs designed to foster productive collaboration; allowing students choice as to who to work with while also asking them to work with different students at times; being explicit when the goal of a task was to build collaborative skills</li>
<li>Structuring activities so there was time at the start for individual exploration before asking students to share their thinking with others thus giving more processing time for students who worked more slowly; circulating and helping some students get started; building more optional challenge into tasks for students who worked very quickly or who had already had prior experience with a topic; creating tasks that could be approached with a greater variety of methods and building more writing into tasks so that different ways of thinking mathematically could be valued</li>
<li>Meeting students where they were to regain trust and buy-in; this included at times splitting the class into two groups (students chose which group to join) - a more free-form exploratory group with more open and challenging problems and a more structured group where students would get some problems to activate prior knowledge and smaller, more concrete problems that would build over time to greater generalization and abstraction and more teacher guidance and reassurance that they were on the right track</li>
<li>Noticing struggling students' successes and highlighting them publicly; selecting which students would share their thinking to make sure that different voices could be heard over time</li>
<li>Make sure to leave time for synthesis and practice problems (at different levels) during class - this helped address student concerns that they were leaving class with lots of questions and feeling unsettled about the concepts they had explored that day</li>
<li>Giving students more feedback during class about their understanding of a topic rather than relying more heavily on groupwork and self-assessment for students to know how they were doing and what might be helpful next steps</li>
<li>Providing more problems at different levels and helping students navigate which problems might be more helpful for them to do during/after a particular lesson - <a href="https://docs.google.com/document/d/1gyVxylXAHsa-ELEc-Xs4K5fwv-DDh_m1ROZ4VIhv_ho/edit?usp=sharing">here</a> is an example of a tiered homework problem set.</li>
<li>Providing more textbook resources - explicitly linking textbook sections to problem sets for students who wanted more references and examples</li>
</ul>
<div>
We are considering sorting students for next semester by grade level to decrease the heterogeneity of classes - while these strategies have alleviated the issues significantly, it does seem that productive collaboration and exploration is challenged when students in a class are so spread out. Despite these strategies, for example, it usually doesn't make sense for students who have worked quickly and deeply and have figured out challenging extensions to share their ideas with the whole class, most of whom have not even tried these problems. As a result, the class sometimes lacks cohesion and feeling like a true community. Additionally, the amount of work required to run a class with this much differentiation is really, really high. I'm essentially designing at least two different classes, creating both lesson plans and homework assignments that can reach the full spread of student interest and background, and giving individual and frequent feedback to students or small groups of students into which the class has fragmented. This is not really tenable for the whole year given my other preps and teaching responsibilities. However, breaking up students by grade level seems to run counter to our values of equitable access to challenging mathematics for all students and means that Math classes are essentially different from all other classes at the Upper School.</div>
<div>
<br />
I would welcome any feedback or suggestions that others have around this issue - what strategies have worked for you in working with very heterogeneous groups? </div>
<div>
<br /></div>
Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com1tag:blogger.com,1999:blog-8537494321067959493.post-58993547786553598562018-10-19T10:18:00.000-07:002018-10-19T10:18:49.106-07:00Connecting Math and CS with probability game simulationsOne of my goals for this school year was to build out a few interesting and relevant projects into the 7th grade curriculum, which seemed a bit dry and skill-focused. One area that seemed to beg for an application project was the first unit on Data and Probability. Since one of my other goals was to incorporate more computer science into my classes, it was a no brainer. Developing a cross-over computer science project for this grade level proved to be a bit tricky because students are all over in terms of their experience with programming - we have students who have been coding for years as well as new students who have never coded anything before. I tried to develop a project that would differentiate appropriately and allow students to either explore the CS or the Math parts in greater depth, depending on their interest in and experience with programming.<br />
<br />
<a href="https://docs.google.com/document/d/1eQKtT-N-6L_yGlyAq5Oq_e0PqxJwUPWgKfmNSSJH2dY/edit">Here</a> is the project description. You'll notice that I created three distinct strands with different goals and let students select the one that was most appropriate and interesting for them. I was also lucky that the computer science teacher was able to come to my classes for some of the time that students worked on this project. Having many intermediate checkpoints for students to submit pieces of the project was very helpful here in ensuring that I could identify those who were behind or struggling and work with them during class.<br />
<br />
Things that I would still like to build out:<br />
<br />
<ul>
<li>A more robust peer editing process -- I'd like students to be able to present their optimal winning strategy to peers and get critical feedback on how convincing their reasoning is that they would be able to incorporate into their final draft</li>
<li>A revised rubric to make it more concise</li>
<li>Move some pieces of this project out to computer science class - this definitely took up quite a bit of time, especially because I felt that most or all of the coding work should happen during class where students would have support</li>
<li>A clearer division between group and individual aspects - this is always a challenge for me when designing group projects in terms of maximizing student learning and individual accountability. Students seemed to work well together during class, but this isn't an explicit part of the project currently. </li>
<li>Some sort of final presentation - for projects like this, I think that having the final product on display or presented to others creates a much more authentic need for clarity and functionality. I haven't figured out a good way to do that for this project. Should students do a gallery walk of projects within the class? Can this be presented or shared with students in other classes somehow? What about with parents?</li>
<li>Other connections - is this something that can connect to students' work from previous years so that it feels less like a stand-alone project and more like a continuation of ongoing work and thinking? Are there other aspects of this project that can connect to other disciplines, like writing? Can we build on this in future years of either computer science or math curriculum?</li>
</ul>
Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com1tag:blogger.com,1999:blog-8537494321067959493.post-1183989720889639292018-09-27T01:02:00.000-07:002018-09-27T01:02:51.040-07:00Feedback and communicating with familiesA goal I wanted to work on this school year is more systematic feedback on mathematical practices as well as better communication with families about what students were working on and their progress. I also wanted to do it in a way that didn't emphasize grading and evaluation and kept the student at the center of setting goals, reflecting on progress, and owning the process.<br />
<br />
<a href="https://laviemathematique.wordpress.com/2017/11/27/weekly-summaries-updated-11-27-17/amp/?__twitter_impression=true">This blog post</a> had a great suggestion for using Google forms to have students reflect each week and have those reflections emailed to parents. The prompts asked students to describe what they learned that week and how they feel about the class. To be honest, the directions for setting up the emailing were a bit too complicated for me and involved using Add-Ons that our tech administrator wasn't too jazzed about, so I did it in a way that seemed more simple and worked well for me. I'll summarize the deets below, but wanted to first say that I've done this twice now (students are reflecting every other week) and have gotten very positive responses from parents. It takes a lot less time than emailing individual parents, and I think it makes a big difference for parents to hear about progress in their children's own voice.<br />
<br />
I changed the questions to be a bit more focused on goal-setting and learning. The questions I'm asking are:<br />
<br />
<ol>
<li>What have you learned in the last two weeks? Be as specific as you can - feel free to look through your notebook.</li>
<li>How do you feel about your learning of this material, both from class work and homework? (3 = I can teach it to someone else; 2 = I understand it pretty well, but have some questions; 1 = I am very confused and/or have a lot of questions)</li>
<li>How do you feel about your class engagement and work? Have you been engaged and focused? Have you worked productively with a variety of classmates? Have you been a respectful skeptical peer and asked for feedback on your thinking?</li>
<li>How do you feel about your homework effort? Did you allocate time well during the week? Pick problems at a good challenge level? Stick with hard problems? Try different things? Ask questions? Make corrections during class?</li>
<li>What was your goal/next steps the last time you reflected? Did you make progress towards this goal? Why or why not?</li>
<li>What are your next steps? What should you keep doing during class and at home? What should you do differently? Do you need to follow up with your teacher?</li>
</ol>
<div>
To clarify, students have a lot of choice in their homework each week - they have an hour to spend on a problem set that has questions at different levels of challenge and depth so I find it helpful for them to reflect on their choices and make changes, if needed. They also have a single assignment due at the end of each week so they should be thinking about how to best allocate their time during the week to avoid leaving it for the last minute.</div>
<div>
<br /></div>
<div>
I make a new version of the form every two weeks and the responses feed into a spreadsheet. I also ask for their name so I can sort the responses alphabetically. I add a column at the end where I add any additional notes I want to share with the family. Usually, it's things like, "This is a great goal. It sounds like X is ready to try some harder problems on the homework next week." I have a list of parent emails that I can then paste in as well as two somewhat fancy things that make the whole system work (not that fancy in actuality, but let me get excited here for a sec). The first one is a cell that combines all of the student responses in one place for ease of emailing. </div>
<div>
<br /></div>
<div>
The code to make that magic happen is: </div>
<div>
<br /></div>
<div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPOPkBeYpvsJ_5yCo7cwJfl8zfUgsTrhVQzrUSm9zMFx8TmD2AC8IQ9drk4aoRdmRK3_LjXqwOfISQ8LHD7FyqmTD4gK_vyt5mjjz4lzad0jHpKIeclCMAcnPGvnPbcOPPaWYe1d3B8lI/s1600/Screen+Shot+2018-09-27+at+12.30.48+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="109" data-original-width="1600" height="42" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPOPkBeYpvsJ_5yCo7cwJfl8zfUgsTrhVQzrUSm9zMFx8TmD2AC8IQ9drk4aoRdmRK3_LjXqwOfISQ8LHD7FyqmTD4gK_vyt5mjjz4lzad0jHpKIeclCMAcnPGvnPbcOPPaWYe1d3B8lI/s640/Screen+Shot+2018-09-27+at+12.30.48+AM.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
CHAR(10) just creates a line break between responses. The & symbol concatenates responses so that they appear next to the question. Otherwise, it just pulls the responses into a single cell. Drag down the formula to have this for all of the students. Then, add another column to the right that will track whether an email has been sent (this is useful if some students are absent and do this later so you end up running the email script multiple times and don't want to resend the emails that already sent).</div>
<span id="goog_2130882342"></span><br />
When you're done, you have a spreadsheet that looks like this:<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqGTafhAnKGCdP-hMxLJKBI1hoG9dbXuOgJtSI1Xvp-r0CT-rXzJlzIMMoBe8HljRFju137p6XmWCBY9Q5B407qpn__bxlPU9jIr3LIhQFVwZ6rJdknS6o_c8hAuS4gYXn53tg4rehgxs/s1600/Screen+Shot+2018-09-27+at+12.25.45+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="566" data-original-width="1600" height="226" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqGTafhAnKGCdP-hMxLJKBI1hoG9dbXuOgJtSI1Xvp-r0CT-rXzJlzIMMoBe8HljRFju137p6XmWCBY9Q5B407qpn__bxlPU9jIr3LIhQFVwZ6rJdknS6o_c8hAuS4gYXn53tg4rehgxs/s640/Screen+Shot+2018-09-27+at+12.25.45+AM.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
(your email sent column will initially be blank)</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Okay, this is where the fun really begins. Under Tools, select Script Editor. I found a script for emailing from a spreadsheet and amended it to email two addresses. You can use it too. <a href="https://script.google.com/macros/d/MMn7PBQ_O1PHyccVWpfXTeNxYtTVNkiAD/edit?uiv=2&mid=ACjPJvG_OszlUDSm6WZTCNJoyDYbRxJ6oQsM170fAVjua7FIWl6PR54OK3ATmFCH0aHrV66nb6vuKGzd99IqJGwrCCkTIKqmsWbqxOa_-pXNMw4CEI1RwMxysgS61yISEkJBTmkxPjdHhu0">Ta da</a>.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
The code in that link is:</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both;">
// This constant is written in column C for rows for which an email</div>
<div class="separator" style="clear: both;">
// has been sent successfully.</div>
<div class="separator" style="clear: both;">
var EMAIL_SENT = 'EMAIL_SENT';</div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
/**</div>
<div class="separator" style="clear: both;">
* Sends non-duplicate emails with data from the current spreadsheet.</div>
<div class="separator" style="clear: both;">
*/</div>
<div class="separator" style="clear: both;">
function sendEmails2() {</div>
<div class="separator" style="clear: both;">
var sheet = SpreadsheetApp.getActiveSheet();</div>
<div class="separator" style="clear: both;">
var startRow = 1; // First row of data to process</div>
<div class="separator" style="clear: both;">
var numRows = 28; // Number of rows to process</div>
<div class="separator" style="clear: both;">
// Fetch the range of cells desired</div>
<div class="separator" style="clear: both;">
var dataRange = sheet.getRange(startRow, 1, numRows, 4);</div>
<div class="separator" style="clear: both;">
// Fetch values for each column in the Range.</div>
<div class="separator" style="clear: both;">
var data = dataRange.getValues();</div>
<div class="separator" style="clear: both;">
for (var i = 0; i < data.length; ++i) {</div>
<div class="separator" style="clear: both;">
var row = data[i];</div>
<div class="separator" style="clear: both;">
var emailAddress1 = row[0]; // First column</div>
<div class="separator" style="clear: both;">
var emailAddress2 = row[1]; // Second column</div>
<div class="separator" style="clear: both;">
var message = row[2]; // Third column</div>
<div class="separator" style="clear: both;">
var emailSent = row[3]; // Fourth column</div>
<div class="separator" style="clear: both;">
if (emailSent != EMAIL_SENT) { // Prevents sending duplicates</div>
<div class="separator" style="clear: both;">
var subject = 'Bi-Weekly Math Update';</div>
<div class="separator" style="clear: both;">
MailApp.sendEmail(emailAddress1, subject, message);</div>
<div class="separator" style="clear: both;">
MailApp.sendEmail(emailAddress2, subject, message);</div>
<div class="separator" style="clear: both;">
sheet.getRange(startRow + i, 4).setValue(EMAIL_SENT);</div>
<div class="separator" style="clear: both;">
// Make sure the cell is updated right away in case the script is interrupted</div>
<div class="separator" style="clear: both;">
SpreadsheetApp.flush();</div>
<div class="separator" style="clear: both;">
}</div>
<div class="separator" style="clear: both;">
}</div>
<div class="separator" style="clear: both;">
}</div>
<br />
Notice that my script currently starts on the first row and processes 28 rows (I piloted this in two sections only). You might have more students so will need to process a larger number of rows. You do need to make sure you don't go too far and get to an empty row. The script doesn't like it when there's no data in a cell it's calling up. By the way, when parents respond to this script-generated email, their response goes directly to my regular school email address because Google is magical.<br />
<br />
How do students have access to all of their reflections, you ask? I went a bit Google spreadsheet happy and added a tab to my master grading spreadsheet that pulls in the reflection responses for each student using the IMPORTRANGE function. Each student then has their own spreadsheet that pulls in just their reflection responses (as well as feedback on content learning goals). There is now a chain of Google sheets happily talking to each other and emailing parents every two weeks. What a world.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://static.adweek.com/adweek.com-prod/wp-content/uploads/2018/03/millie-brown-GIF-PAGE-2018.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="800" height="320" src="https://static.adweek.com/adweek.com-prod/wp-content/uploads/2018/03/millie-brown-GIF-PAGE-2018.gif" width="640" /></a></div>
<br />
<br />
<br /></div>
Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com0tag:blogger.com,1999:blog-8537494321067959493.post-65261133049555851562018-08-25T08:41:00.000-07:002018-08-25T08:41:59.371-07:00Culture of Mathematics<i><span style="font-family: inherit;"><span style="background-color: white; color: #222222;">This post is part of the </span><a data-saferedirecturl="https://www.google.com/url?q=https://samjshah.com&source=gmail&ust=1535255341454000&usg=AFQjCNHn_eWBdp_uVrCi-51cI5NMplfg4g" href="https://samjshah.com/" style="background-color: white; color: #1155cc;" target="_blank">Virtual Conference on Mathematical Flavors</a><span style="background-color: white; color: #222222;">, and is part of a group thinking about different cultures within mathematics, and how those relate to teaching. Our group draws its initial inspiration from writing by mathematicians that describe different camps and cultures -- from </span><a data-saferedirecturl="https://www.google.com/url?q=https://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf&source=gmail&ust=1535255341455000&usg=AFQjCNFE_6tP1aU5AUurYx0XI9-WM4NhGg" href="https://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf" style="background-color: white; color: #1155cc;" target="_blank">problem solvers and theorists</a><span style="background-color: white; color: #222222;">, </span><a data-saferedirecturl="https://www.google.com/url?q=https://www.maa.org/external_archive/devlin/LockhartsLament.pdf&source=gmail&ust=1535255341455000&usg=AFQjCNG61kL4NEjZVtta7bihrmxHUGJ_IQ" href="https://www.maa.org/external_archive/devlin/LockhartsLament.pdf" style="background-color: white; color: #1155cc;" target="_blank">musicians and artists</a><span style="background-color: white; color: #222222;">, </span><a data-saferedirecturl="https://www.google.com/url?q=http://www.dam.brown.edu/people/mumford/blog/2015/MathBeautyBrain.html&source=gmail&ust=1535255341455000&usg=AFQjCNEMsHHnOz3Vipff2O9HilYZIp4xRA" href="http://www.dam.brown.edu/people/mumford/blog/2015/MathBeautyBrain.html" style="background-color: white; color: #1155cc;" target="_blank">explorers, alchemists and wrestlers</a><span style="background-color: white; color: #222222;">, to </span><a data-saferedirecturl="https://www.google.com/url?q=https://www.math.ualberta.ca/mss/misc/A%2520Mathematician%2527s%2520Apology.pdf&source=gmail&ust=1535255341455000&usg=AFQjCNFEUIJhShPCn-M8VYrLu_RBMLrT6w" href="https://www.math.ualberta.ca/mss/misc/A%20Mathematician%27s%20Apology.pdf" style="background-color: white; color: #1155cc;" target="_blank">"makers of patterns.</a><span style="background-color: white; color: #222222;">" Are each of these cultures represented in the math curriculum? Do different teachers emphasize different aspects of mathematics? Are all of these ways of thinking about math useful when thinking about teaching, or are some of them harmful? These are the sorts of questions our group is asking. </span></span></i><br />
<span style="font-family: inherit;"><span style="background-color: white; color: #222222;"><br /></span><span style="background-color: white; color: #222222;">I am excited to write a post as part of a group of bloggers thinking about the tension between problem solving and theoretical understanding, among other tensions. Moreover, the benefit of procrastinating and getting terribly behind is that I get to read and respond to some of the other blogs written as part of this group. <a href="https://problemproblems.wordpress.com/2018/08/22/a-culture-of-understanding/">Michael's post</a>, in which he discusses the reasons that he has moved away from problem solving as a classroom focus, was one that really struck me and prompted me to want to respond. I think that he makes some excellent points about wanting to move away from answer getting as an inherently inequitable and exclusionary practice in which some students race ahead while others are left behind. It's a great read, and I highly recommend you pause here and read his post in full. </span></span><br />
<span style="font-family: inherit;"><span style="background-color: white; color: #222222;"><br /></span></span>
<span style="font-family: inherit;"><span style="background-color: white; color: #222222;">The main place where I found myself disagreeing was in the setup, in which problem-solving is positioned diametrically opposed to theory-building, and the two trade off against each other. This, to me, seems like a confusing and artificial construction... both are just questions that we are posing about the world, where perhaps problem-solving takes the form of slightly more specific questions and theory-building is what we call questions that are more general. <a href="https://twitter.com/Thalesdisciple">Joshua Bowman</a> calls out this false dichotomy in <a href="https://thalestriangles.blogspot.com/2018/08/dialectics-in-mathematics.html">his post</a> as well, adding it to the list of polarities like applied vs. theoretical and individual vs. communal and urging for math teachers to value both types of thinking because we just don't know what's going to motivate or interest a particular student and the more variety and ways there are to be hooked into mathematical thinking, the better. </span></span><br />
<span style="font-family: inherit;"><span style="background-color: white; color: #222222;"><br /></span></span>
<span style="font-family: inherit;"><span style="background-color: white; color: #222222;">I would say that as teachers, we can't help but be biased towards ways of thinking that are aligned to how we ourselves think and what we value. When I first started teaching, I was very much tapping into my own personal experiences as a math student - the complete disconnect I had felt from math as an intellectual discipline in high school and why I fell in love with math as an undergraduate, thinking for the first time about real (to me) mathematical questions that sparked my curiosity and wonder and ideas that blew my mind and made me want to learn more. I posed problems to my high school students in the way that I would have wanted them posed to me. There were some kids who came along for the ride, but there were also definitely some who were left behind because I was not speaking their language.</span></span><br />
<span style="font-family: inherit;"><span style="background-color: white; color: #222222;"><br /></span></span>
<span style="font-family: inherit;"><span style="background-color: white; color: #222222;">Joshua's conscious choice to provide students with many options and potential hooks is a way to move away from this form of me-centered teaching, which can be such a natural trap. He chooses to be agnostic and let students construct knowledge in the way that works for them. I find it interesting that Michael is perhaps doing the same thing, but in a way that purposefully deemphasizes problem-solving because it is such a dominant paradigm in mathematics so that students are exposed to other ways of doing math. The sentiment behind these teacher decisions definitely resonates for me, and I think should be central in teacher preparation and planning for courses - what values are you emphasizing in your classroom structures, teacher moves, and curriculum? </span></span><br />
<br />
<span style="font-family: inherit;"><span style="background-color: white; color: #222222;">I have certainly seen problem-solving play out in the same troubling ways that Michael referenced in his post - primarily when I have attended math team practice and felt the anxiety I often feel in these types of hyper-competitive-speed-based-publicly-exposed environments. But for me, it isn't problem-solving that's the culprit, but the types of problems that have been posed, the environment in which they are done, and their purpose. For example, I attended <a href="https://pcmi.ias.edu/program-TLP/2018">PCMI</a> last summer - this is a place where math teachers are solving problems together for hours every day. There is a huge amount of variety in mathematical background knowledge, experience with math teaching, and familiarity with the PCMI style. Yet norms are set and problem sets written in such a way that connections, representations, deep and novel ways of thinking and analyzing, and thoughtful questions are what is valued, resulting in a community that while not quite a mathematical utopia, is pretty damn close. Good problems + clear norms + teacher moves to support norms = learning that aligns to the values of the program and access and motivation for many students.</span></span><br />
<span style="font-family: inherit;"><span style="background-color: white; color: #222222;"><br /></span></span>
<span style="font-family: inherit;"><span style="background-color: white; color: #222222;">In my own teaching, I have moved towards student-posed questions and projects as something that more closely matches my values in teaching and moves away from my subjective opinion of what is interesting towards my students' perspectives and interests. I value good problem posing as an opportunity to both pique interest, stimulate thinking, and help students better understand what makes for a good problem so they can move on from problems posed by me to problems they pose themselves. It's much less important to me if the questions they ask are specific (problem-solving) or more general (theory-building) - it's in the asking of questions and seeking to understand and construct the world around them that I see the purpose of my teaching.</span></span>Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com1tag:blogger.com,1999:blog-8537494321067959493.post-78395436942916362492018-06-03T00:01:00.004-07:002018-06-03T15:21:03.121-07:00End of year celebration of knowledge<br />
<a href="https://twitter.com/ddmeyer">Dan Meyer</a> started a discussion on Twitter recently about the unnecessary stress that final exams cause for students at the end of the year, questioning how much insight they really give into student learning. It’s been a helpful reminder that while I definitely agree that high-stakes final exams are terrible, I really don’t have a great system yet for wrapping up the year.<br />
<br />
We certainly don't want students feeling like this:<br />
<div>
<br />
<div style="text-align: center;">
<br /></div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcEHRHn1PrJBtIP8YmXyZ0RGpDBfvYAPmYAeBt7D-O3hkyAw6b5BnWbrxYuEsn_Jfauwoy5LVCZt1PMAk4zqqGsoK7QYoWs7Z7u_FU4Z1spai8mVPi63cgRUvj-LLFp4a86NyO9oroI74/s1600/tina.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="282" data-original-width="500" height="225" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcEHRHn1PrJBtIP8YmXyZ0RGpDBfvYAPmYAeBt7D-O3hkyAw6b5BnWbrxYuEsn_Jfauwoy5LVCZt1PMAk4zqqGsoK7QYoWs7Z7u_FU4Z1spai8mVPi63cgRUvj-LLFp4a86NyO9oroI74/s400/tina.gif" width="400" /></a><br />
<div style="text-align: center;">
<br /></div>
</div>
But what makes for a good alternative?<br />
<br />
It seems challenging to balance the goal of ending the year with celebration and anticipation of more learning, while also gaining information about retention and content synthesis. I want students to end the year on a high note, feeling positive about their progress and provided with the opportunity to dig deeply into a particular topic, but it would also be great to be able to identify topics from the entire year that would benefit from review and work with them to do that.<br />
<br />
In some ideal universe where time doesn't exist and Firefly is still on the air, I would be able to do both: a meaty project in which students can shine and review and an assessment of all of the things. However, even given this bounty of time, I'm not sure that a timed, paper and pencil, silent, individual assessment would really promote the most learning and information for me and students.<br />
<br />
<div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
So I spent a bunch time the last few weeks reading up on various ideas and here is my current compilation.</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBUuxG4p8rdU1wbgdR4SQMmM0mOCne4t-Mi6L1E3JjHENgqeqfQRx843XwmSgfQKaECsFogOX9C9TCoAgL_Bf_VWW7NPPZWwgaGwhc9bnyZa0mqFMQJnd2-mVe5druS12Ry6xwryZI7Dg/s1600/parksrec.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="277" data-original-width="500" height="221" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBUuxG4p8rdU1wbgdR4SQMmM0mOCne4t-Mi6L1E3JjHENgqeqfQRx843XwmSgfQKaECsFogOX9C9TCoAgL_Bf_VWW7NPPZWwgaGwhc9bnyZa0mqFMQJnd2-mVe5druS12Ry6xwryZI7Dg/s400/parksrec.gif" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<ul>
<li>A group whiteboard assessment that looks at problem solving and tying together big concepts from the year, something like what <a href="https://twitter.com/AlexOverwijk">@AlexOverwijk</a> does with his classes:<br />
<blockquote class="twitter-tweet" data-cards="hidden" data-partner="tweetdeck">
<div dir="ltr" lang="en">
S “Because of the low stress in this testing environment it reassures me that I know stuff, lets me know what I need to focus on tonight before the individual test, and really just increases my confidence.”<br />
Me”Glad you feel that way.” <a href="https://t.co/fPFx1uD7cf">pic.twitter.com/fPFx1uD7cf</a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
— Alex Overwijk (@AlexOverwijk) <a href="https://twitter.com/AlexOverwijk/status/1002175936257814528?ref_src=twsrc%5Etfw">May 31, 2018</a></blockquote>
<script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script>This would require careful teacher observation to untangle individual understanding and contribution to the group product, but seems like a much closer fit to what students do in class every day and therefore a more accurate picture of their understanding, as well as obviously being less stressful.</li>
<li>An annotated portfolio of work throughout the term, which would require students to find evidence of learning for previous topics, identify important connections, revise work, and identify topics that need further attention themselves. I really like this option as it puts the student in the driver's seat. However, this would be fairly time-consuming and likely need students to have been tracking their work throughout the semester. It's something I'm strongly considering for next year. If you do this, I'd love more information - directions, rubrics, advice for someone who wants to try it. How do you make this work in large classes?</li>
<li>An oral final exam in which each student has a one-on-one interview and discusses their process and reasoning for one or two problems, which <a href="https://twitter.com/JadeMohrWhite">@JadeMohrWhite</a> proposed:<br />
<blockquote class="twitter-tweet" data-conversation="none" data-lang="en">
<div dir="ltr" lang="en">
My last few yrs in the classroom I did oral finals and loved it. I spent time with each individ S and got to have a math convo with them about what they had learned over the year. They explained reasoning & it wasn’t about right or wrong but the process.</div>
— Jade White (@JadeMohrWhite) <a href="https://twitter.com/JadeMohrWhite/status/999015405443207168?ref_src=twsrc%5Etfw">May 22, 2018</a></blockquote>
<script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script><br />
This seems great for digging deep into mathematical practices and student thinking, but would only give limited content knowledge information due to time constraints. Building in class time for every student to have a 20 minute interview or so also seems a bit daunting in the end-of-year crunch, but could potentially complement a final project or portfolio assignment, during which students are working relatively independently.</li>
<li>Final individual project and group presentation. This is the model I'm trying this year in one of my classes. Students selected a topic of personal interest to them that is related to the content in the course and did research and Math work related to this topic. They were then placed into groups based on some possible common threads between projects and created a presentation that highlighted their individual work AND the connections between them, as well as how what they learned related to their Math course this year. Detailed directions are <a href="https://drive.google.com/open?id=1O1rZvtLlf510HB-33drqCTt4-W8GUb7aFZ9lFwKvRQk">here</a>.<br />
<br />
I like how positive and forward-looking the projects have been this year - it does feel like a celebration and memorable opportunity for students to shine. However, because projects are typically looking at a single topic in a great deal of depth, this way of ending the year misses out on the whole cumulative, wrapping everything up feeling that I like to have. </li>
<li>Bring back the final exam, but have it be extremely low stakes by focusing on retention, connections, and structured so that it can only help a student's grade, not hurt it. This is how I've done final exams before - as a final opportunity for a student to show understanding of a topic from a previous unit and a place to look at cumulative retention and synthesis. It's efficient and serves that purpose well, but isn't the kind of experience I want students to take away with them as their last memory of my class, so if I brought it back, I would definitely want to pair it with one of the above ideas.<br />
</li>
<li><b>Edited to add</b>:<br /><br />
Take-home final exams, as described by <a href="https://twitter.com/benjamin_leis">@benjamin_leis</a> below, seem like another way to get more comprehensive information about content knowledge in a less-stressful setting. I like the idea of removing time pressure from the equation and letting students assess in a more comfortable and familiar setting where they can take breaks and dig deeper into problems. Again, because this more closely replicates the ways that students do math in my class during the year, it should be a better assessment of what they know. I also think questions on a take-home final should be more interesting and less routine than what I would ask on an in-class timed assessment. </li>
</ul>
<div>
<br />
I would love to know of other ideas people have for alternatives to high-stakes final exams or any feedback on these still-cooking ones. Share them in the comments or send out a tweet.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBaSPDGHcqG_A8hYXoWiFoi11k4EswIG7cWmAangIKW1G1v4sgkV_mU7Q65sbIwgSx9MbIAW2uMwE6jEvtv1K6lPCbDqtuRigRIKZqt7lmWuJpoKW3KVhcCz-2SrxqpjFtB403iNVE5us/s1600/jump.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="260" data-original-width="400" height="260" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBaSPDGHcqG_A8hYXoWiFoi11k4EswIG7cWmAangIKW1G1v4sgkV_mU7Q65sbIwgSx9MbIAW2uMwE6jEvtv1K6lPCbDqtuRigRIKZqt7lmWuJpoKW3KVhcCz-2SrxqpjFtB403iNVE5us/s400/jump.gif" width="400" /></a></div>
<div style="text-align: center;">
<br /></div>
<br /></div>
</div>
Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com10tag:blogger.com,1999:blog-8537494321067959493.post-51824783497509148652017-09-24T12:49:00.000-07:002017-09-24T12:49:42.345-07:00Math as a ToolI got into a spirited discussion with <a href="https://twitter.com/karimkai">Karim</a> a few days ago about his desire for math to be an instrument to look <i>with</i> as much as an object to look <i>at</i>, which he wrote about in <a href="http://karimkai.com/saturn-rising/">this blog post</a>. Karim's concern that too many activities billed as applications of mathematics are actually structured to develop conceptual understanding rather than be a true application with a primary purpose of understanding something about the world resonated with me. However, I took some issue with his proposed solution: math teachers taking applications on more fully than they currently do.<br />
<br />
We had a long chat over Twitter about it, in which I argued that perhaps Math teachers aren't in the best position to fully develop authentic applications and investigations of the world in which math is a tool. This does NOT mean that I don't think Math teachers should only teach concepts and never delve into applications. Of course, Math is both a subject onto itself and a tool for better understanding the world. And of course, for all students, understanding and engaging in its use as a tool makes Math more relevant and is a vital part of their education. My argument is primarily that when we shove all math applications into Math class and ask Math teachers to shoulder that full load, that inevitably means teaching less math and very likely, also results in these applications being less authentic and deep than they can be. My counter-solution is that more applications should be happening cross-curricularly in order to harness the expertise of multiple teachers and approach real world applications in the interdisciplinary way they are actually approached in the real world.<br />
<br />
For example, I think teaching a lesson on wage inequality using math to analyze and form a quantitative basis for the discussion is awesome. However, the discussion that I am going to facilitate as a Math teacher in Math class is not going to be as deep as the discussion that an economics teacher would be able to lead on this topic. It's not because I don't care about wage inequality, but because my area of expertise is mathematics and their area of expertise is economics. They're going to have a rich understanding of historical trends and societal pressures and opposing views on this topic that even if I were to spend significant time prepping (keeping in mind that I have three preps every day and want to do application problems from a variety of fields and disciplines in each of them), I would not be able to achieve. Imagine how much more powerful this same lesson would be if we spent a Math class learning different ways linear models allow us to find "break-even" points for situations and then students went next door to Economics/History/Civics class and looked at how these models have been or could be applied to look at wage debates in our country. If we go even further outside the standard school model of siloed subjects, the Economics/History/Civics teacher and I can join forces and teach a lesson together in which the math and its application are interwoven.<br />
<br />
It's not that I don't want math to be applied. It's that I want to see math applied deeply, across various subjects, as much as possible, as a joint project between disciplines rather than a few question prompts crammed in at the end of a math lesson. I want to harness my strengths as a teacher of math in its pure form, as well as a tool that is uniquely powerful exactly because it's so abstract and generalizable, rather than dilute what I am able to accomplish by trying to do it all. Why do applications of Math have to be taught during Math class?<br />
<br />
If your answer to that question is: "because teachers from other disciplines won't do it," I think that accepting that would be a huge fail on our part as Math teachers. Here are some concrete things that I think would help if you are a math teacher:<br />
<br />
- Ask your school's science, history, economics, psychology, etc teachers what topics they are teaching in the next month and if they would like you to come visit their class and co-teach a lesson to include math related to this topic.<br />
- Ask other teachers at your school if they would consider creating a joint assignment that students would turn in for both classes (or turn in one part to one teacher and the other part to the other teacher) that would allow for a more in depth investigation.<br />
- Are there classes that all students at a particular grade at your school take or a field trip that they all go on? That might be a great starting point for a cross-curricular project that involves Math and one other discipline.<br />
<br />
<h4>
Here are some examples of cross-disciplinary application projects I have liked:</h4>
- Students in a History class taken by all 10th graders were analyzing racial relationships in colonial times. They read an article called, "Social Dimensions of Race: Mexico City, 1753," which looked at how perceived racial differences were the basic criteria for social differentiation and employment in Mexico City in the 1750s. In my Math class, we used the data in the article to run a chi-square test of independence to see the level of independence between race and employment. Students then came back to History class the next day to discuss the ramifications of this analysis.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidMAiQrsURbbSeBU8f8aKV_EB15eLikvyiWV0kBQGcYcTsZu7plwcAhhCfXiyNU2hD6SJEoIh-aUUxfLGLFZfbY4vLS1N0fGpjEtMxnEEZLDtiMMToKJLkEdn1tej2Q45xLuH2yRlas7o/s1600/Screen+Shot+2017-09-24+at+12.16.02+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="383" data-original-width="1600" height="152" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidMAiQrsURbbSeBU8f8aKV_EB15eLikvyiWV0kBQGcYcTsZu7plwcAhhCfXiyNU2hD6SJEoIh-aUUxfLGLFZfbY4vLS1N0fGpjEtMxnEEZLDtiMMToKJLkEdn1tej2Q45xLuH2yRlas7o/s640/Screen+Shot+2017-09-24+at+12.16.02+PM.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
- Students in a Math 3 class created original art using Desmos and a variety of functions and conic sections, which they also worked on during their art class and which they had to analyze from an artistic as well as a mathematical perspective. </div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEge1cCTpiWOODjKJ_3WWvWVeOQLejDBUaSnkLlPl33L2KdPqK1JBvj5zo98U32KhoXPFIH8yOgNERQX7cici0qgGDEuvgz5_Wlm9sKKXR-Mvlosl9D9secqYbONUTJ8SrEeXLZEV_SKwVw/s1600/Screen+Shot+2017-09-24+at+12.30.16+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="700" data-original-width="822" height="340" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEge1cCTpiWOODjKJ_3WWvWVeOQLejDBUaSnkLlPl33L2KdPqK1JBvj5zo98U32KhoXPFIH8yOgNERQX7cici0qgGDEuvgz5_Wlm9sKKXR-Mvlosl9D9secqYbONUTJ8SrEeXLZEV_SKwVw/s400/Screen+Shot+2017-09-24+at+12.30.16+PM.png" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKIffsY3O0v6DjcYiYB_9o6DXVrqpigQZUuBbrJIDilYTZBplerTkHEXfQkDYjEk456I3HGKtssl6P1vsG1mxO9ANdnzdrD0Lhv3D4C3dHfEsnatvulFD5pSDEh8pyIhGGd3zsj4yQJ0s/s1600/Screen+Shot+2017-09-24+at+12.31.00+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="798" data-original-width="1330" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKIffsY3O0v6DjcYiYB_9o6DXVrqpigQZUuBbrJIDilYTZBplerTkHEXfQkDYjEk456I3HGKtssl6P1vsG1mxO9ANdnzdrD0Lhv3D4C3dHfEsnatvulFD5pSDEh8pyIhGGd3zsj4yQJ0s/s400/Screen+Shot+2017-09-24+at+12.31.00+PM.png" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
- Students in Math 2 who were studying histograms, box plots, measures of center and variation, and outliers picked topics of interest in a country in which their world language was spoken and used the <a href="http://www.gapminder.org/data/">Gapminder global data set</a> to analyze this topic over time in that country. They then wrote a paper and presented their findings to their world language class. </div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
My argument is that projects like these are inherently more relevant, authentic, and motivating to students than any applications I could find and facilitate on my own. And then I can put more of my time into teaching pure math ;)</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://media.giphy.com/media/wi8srTXLsVgyI/200.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="200" data-original-width="266" src="https://media.giphy.com/media/wi8srTXLsVgyI/200.gif" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com0tag:blogger.com,1999:blog-8537494321067959493.post-84833538305636676952017-07-09T14:21:00.001-07:002017-07-09T14:21:30.403-07:00ReflectionsMy school is committed to having students reflect on their learning, both in terms of math-specific development and student habits*. The research is pretty strong that reflecting on learning is a huge component of solidifying understanding. As John Dewey wrote, “We do not learn from experience... we learn from reflecting on experience.” Reflection as a skill is something that we intentionally cultivate and assess, but I am always working on making it a more integrated component of my classes and something that students value and appreciate.<br />
<b><br />
</b> <br />
Here are some ways that I've worked on doing this over the past few years:<br />
<b><br /></b>
<h2>
<b>Start of year reflections</b>: establishing relational aspects of class and setting goals</h2>
We spend the first two weeks of each course working on open problems and having students read, watch, and discuss ideas that we think are important to setting the tone for the year, establishing classroom norms, and getting buy-in for learning through problem-solving<br />
<br />
<ul>
<li>Students respond to readings about mathematical practices and/or habits of mind:</li>
<ul>
<li><a href="https://docs.google.com/a/nuevaschool.org/forms/d/e/1FAIpQLSeDylb7o_rebZG4XLn5_1G2YsP2PCt01bxLa6klntTBvmPUug/viewform">Reflection questions on first chapter of Make It Stick</a></li>
<li><a href="https://docs.google.com/a/nuevaschool.org/forms/d/e/1FAIpQLScc0mVG0KbvkXEnggFTOwcRAF_ZhLG5nuPA-DjDdtZntR1vrQ/viewform">Reflection questions</a><span id="goog_595068464"></span><a href="https://www.blogger.com/"></a><span id="goog_595068465"></span> on <a href="https://www.youtube.com/watch?v=bxrPy1fjVU4&feature=youtu.be">"How to Learn Math" video</a> from Youcubed and excerpt from Mathematical Mindsets</li>
</ul>
<li>Math autobiography</li>
<ul>
<li><a href="https://docs.google.com/document/d/1n_xjUOlvmSe0Rla3kQeiAs83P4cn_SOof9y_ZPe9wYM/edit">Students reflect on their history as students and mathematicians and set goals for their work in this class</a></li>
</ul>
</ul>
<h2>
<b>Reflections that emphasize content: after each lesson/assignment and after taking an assessment in order</b> to correct course</h2>
<div>
We want students actively thinking about their progress in the course, returning to their goals, reflecting on their learning, and fine-tuning strategies in order to make progress.</div>
<div>
<ul>
<li>At the start of most classes, students summarize the main topics from the last class and homework assignment and reflect on their understanding through this <a href="https://teacher.desmos.com/activitybuilder/custom/57d82d6420bbe80309333268">Desmos Activity Builder</a>.</li>
<li>After most assessments, students reflect on their work in the class, both in terms of content learned and the development of their mathematical practices and student habits</li>
<ul>
<li><a href="https://docs.google.com/document/d/1DAK8rmYMuwV5KRl_8d6cZTTZuEhFFnY0WTgeb7-7x4A/edit">Typical post-assessment reflection</a>; We realized that having students reflect on ALL mathematical practices was a bit much for a single reflection and tried to pull out a specific practice to reflect on </li>
<li><a href="https://docs.google.com/document/d/1-I4f3dMx8d4KA1Cqq8J15Ffvbl7mU8ShgUl-eRO_dZw/edit?usp=sharing">Correct and reflect on errors; plan what to do next</a></li>
</ul>
</ul>
<h2>
Reflections that emphasize practices and habits of learning: projects, homework, note-taking</h2>
<br />
<ul>
<li>Students reflect on their learning and process on all projects and investigations </li>
<ul>
<li><a href="https://docs.google.com/document/d/1iNdqJEKUodTq2oOAld0AFD-AlcVAa-cPkPbSBm_X9yA/edit?usp=sharing">Menu of write-up reflection options</a> (scroll to the bottom)</li>
</ul>
<li>Not strictly reflection, but we are starting to use peer feedback to have students develop specific mathematical practices</li>
<ul>
<li><a href="https://docs.google.com/document/d/1aCwmQdutTubSkrKIsz8gPxH2xsVq1X9lbs8dGO8UpdU/edit">Peer feedback on homework</a></li>
<li><a href="https://docs.google.com/document/d/14-gUW592dyHK6XRlkIn4MahOW3pIkdIyErQjY2bM1tU/edit?usp=sharing">Reflection on note-taking</a></li>
<li><a href="https://docs.google.com/presentation/d/1jLpSvcVRW8tDEMZ_T6cf7Lq00CV2_j3iB4o5dKVGK2s/edit?usp=sharing">Peer feedback on note-taking</a></li>
</ul>
</ul>
</div>
<h2>
Things I still need to work on/think about</h2>
<div>
The reflections were mostly created based on perceived need and don't necessarily spiral and build on each other as clearly as they could. I'd love to spend time going through the prompts and making them more specific - thinking about which mathematical practices should be cultivated at the start of the year, which ones later on, and which ones should be spiraled back to at later times. This would also help make the reflections shorter and more specific, encouraging deeper and more thorough responses. </div>
<div>
<br /></div>
<div>
I'd love to hear about others' experiences with reflections so please comment or <a href="https://twitter.com/Borschtwithanna">tweet at me</a> with questions or feedback.</div>
<div>
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHNUxCrZryEQnupZWZCV4GRT-eJFLX22IeOXqi6o0X6QVUPse-5Z7VcU3QevordBM_AhjUzV8T7T6mIZICuEl8k23d7sIOVLYU0UbnREFvGAfP1LLWHsO6kluSMgMuFC4eUhPzX3h1kjU/s1600/cat+reflection+meme.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="427" data-original-width="500" height="545" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHNUxCrZryEQnupZWZCV4GRT-eJFLX22IeOXqi6o0X6QVUPse-5Z7VcU3QevordBM_AhjUzV8T7T6mIZICuEl8k23d7sIOVLYU0UbnREFvGAfP1LLWHsO6kluSMgMuFC4eUhPzX3h1kjU/s640/cat+reflection+meme.jpg" width="640" /></a></div>
<div style="text-align: center;">
<br /></div>
<div>
<br /></div>
<div>
*<a href="https://docs.google.com/document/d/1snL1uTJSyxMjjfMOQ5L6rUmxFp5Knh9SYUNs3c_w8F8/edit">Rubric of mathematical practices and habits of learning</a></div>
Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com2tag:blogger.com,1999:blog-8537494321067959493.post-51261420170803982632017-04-19T23:15:00.000-07:002017-04-19T23:15:07.779-07:00Formative FeedbackI've been thinking a lot about feedback lately. It started with this tweet:<br />
<br />
<br />
<blockquote class="twitter-tweet" data-lang="en">
<div dir="ltr" lang="en">
<a href="https://twitter.com/MrAbend">@MrAbend</a> I would be really curious as to what the Math learning/cognitive science research says about error types. Does <a href="https://twitter.com/mpershan">@mpershan</a> know?</div>
— Anna Blinstein (@Borschtwithanna) <a href="https://twitter.com/Borschtwithanna/status/853335039316074496">April 15, 2017</a></blockquote>
<script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script><br />
<br />
<br />
<a href="https://twitter.com/mpershan?lang=en">@mpershan</a> was kind enough to respond with an email and sent me down a rabbit hole of articles and blog posts about the usefulness of feedback. Since Michael was the inspiration for this journey, it's only fitting that I try to imitate his style of writing out loud to try to organize my thoughts on this topic (sorry, Michael - reading this back after I've finished the blog post has shown me that you are inimitable. Also, I should probably avoid writing blog posts at 11 pm in the future).<br />
<br />
The central question we discussed was: what is the purpose of feedback? Clearly, it is only useful if it changes a person's thinking. Does pointing out a mistake do this? Does categorizing the mistake do this? Does indicating a student's level of understanding of a topic ala Standards-Based-Grading do this? Do questions do this better than statements? Do students need to reflect on the feedback or do another problem related to the feedback received or implement it in some other way in order to get more benefit from it? Written vs. oral? Immediate vs. delayed?<br />
<br />
<h4>
<u><b>Feedback while kids are working in class:</b></u></h4>
This is the type of feedback I think I know how to do the best. When kids are working on a task, either on their own or with someone else, I am usually able to ask questions, point out features of their work, or connect them with other students' thinking so they can make progress, identify and correct errors, and clarify their own ideas. The one blind spot that I think I still have in this area is when a student thinks about a problem in a way that is really, really different from methods I understand or have seen and thought about before. This doesn't happen very often, but when it does, I'm really stumped. I can help them verify that their answer is incorrect. I can ignore their method and show them a way to think about the problem correctly or point them to another student in the class with a different approach. But if I don't understand it, I can't help them resolve the cognitive dissonance of their incorrect approach, which means that my work is not complete.<br />
<br />
But in general, this is the type of feedback that seems to pay the most dividends. The kid is right there with their work, we can have a conversation, I can see if they are able to implement my feedback and give more or of a different kind, as needed, or ask them to work on a related problem. This is really the best case scenario in feedback world for me.<br />
<br />
<h4>
<b><u>Feedback on homework:</u></b></h4>
Things start to get real hazy real quick when I'm looking at a kid's work outside of class and my feedback is now provided in written form or via a conversation with them the next day. Will they have time/inclination to do anything about my feedback? Without the option of a conversation, I have to make a guess, which I suspect is often not great, about their thinking and the amount/level of information to provide back and how to do that in a way that opens thinking rather than closes it. Honestly, I don't have any evidence that students get a ton out of the written feedback on their homework assignments. I've thought about building in class time to have students read the feedback on their assignment from the previous day and do something with it (since homework is turned in digitally and feedback is provided digitally, I have no idea how thoroughly students would be reading my feedback otherwise), but it seems like I could just use this time to talk to students of concern about their work or have the class do a problem related to an issue that I saw on many papers. We already go over homework questions in class before it's turned in and the answers are provided in advance, so presumably, they know if they are understanding the material. If I'm very concerned, I would rather email a student or talk to them in class or ask them to work with me outside of class. Spending lots of time writing comments and then flinging them into a black hole of ??? doesn't seem like the best use of my limited time. But not providing feedback on homework also seems wrong. So I'm at a bit of an impasse here. I've moved some of my homework grading (especially for bigger projects) to in-person conversation and in an ideal world, I would be able to do that for all of my grading, but time with students is a precious commodity.<br />
<br />
<h4>
<b><u>Feedback on assessments:</u></b></h4>
This type of written feedback seems to go better than homework. I think that there are a few components that have made it more successful:<br />
<br />
<ol>
<li>Students perceive assessments to be more summative and take feedback on them more seriously. They know it's a check of their understanding that will more directly be reflected in their grade (grades as motivation.... laaaaaame, but I'm not sure how to get around this... I have to produce some sort of grade at the end, and I like homework to be purely for feedback so that leaves assessments for grading). As a result, they read comments more carefully and are more motivated to figure out their mistakes and learn from them so that they can show more understanding on the reassessment.</li>
<br />
<li>I separate the feedback and grading parts to help students focus more on the feedback initially. When I grade assessments, I only write comments/questions (and try not to say too much since I know I'll be there in person to continue the conversation). I record their SBG grades on the assessment in the online gradebook only a day or so later, based on the <a href="https://www.ets.org/Media/Research/pdf/RR-08-30.pdf">research</a> that showed that when students receive written comments <b>and</b> a grade on an assessment, they basically ignore the comments and only look at the grade, and that this is not helpful for learning. Getting back their assessments with comments only helps to keep the conversations on concepts and learning only, not on grades, as well as encourages students to work together with less comparison to others. </li>
<br />
<li>We spend class time correcting quizzes, usually in groups that are either assigned randomly or by common error types. The quiz corrections are an assignment that is collected, they are not for "earning back points" (I don't actually understand what that means), but they are required in order to reassess. I ask students to analyze their error (did they misunderstand an aspect of the concept? execute a procedure incorrectly? make a careless mechanical error?), as well as redo the problems on which they made errors. Based on my thinking around this issue, going forward, I'd like them to also state what they plan to do to make progress on the issue identified. Michael seemed to think that identifying the type of error is not particularly helpful to students, but I think that when followed up with a "next step," it is maybe more useful?</li>
<br />
<li>I think that more students actually know what they should do to make progress with assessment feedback. They've done a lot of work with the concepts being assessed. They can talk to peers to understand other approaches, they can talk to me, we can schedule a meeting outside of class to work together, they can refer to online resources organized by content topic to review a concept or procedure, they can do practice problems from homework assignments and previous reviews related to this concept so the feedback is both more closely connected to a concrete goal and to ways of reaching that goal. </li>
</ol>
<div>
<br /></div>
<h2>
<b><br /></b><b>So my main questions right now are:</b></h2>
<div>
<ol>
<li>How can I make feedback on homework more useful in helping students change their thinking?</li>
<li>Are there ways to improve both my in-class and assessment feedback?</li>
<li>How can I move more of my feedback to conversation and away from enigmatic notes that try to strike just the right balance of tantalizing hint/information-giving and hook to motivate kids to want to look at their homework again and rethink their approach, but that mostly get ignored or scanned quickly and not attended to? Did I mention that writing tons of feedback on homework assignments takes a lot of time???</li>
<li>Are there aspects of feedback that I'm not considering?</li>
</ol>
</div>
Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com8tag:blogger.com,1999:blog-8537494321067959493.post-36381775046233887572017-04-16T09:53:00.000-07:002017-04-16T09:53:00.452-07:00Using Canvas to coordinate written feedbackYesterday, <a href="https://twitter.com/druinok">@druinok</a> asked for suggestions on providing more written feedback to many students quickly.<a href="https://www.blogger.com/"></a><br />
<br />
<br />
<blockquote class="twitter-tweet" data-partner="tweetdeck"><div dir="ltr" lang="en">I wish I had the time to give my students more written feedback without a grade attached. How do you fit it all in?</div>— Druin (@druinok) <a href="https://twitter.com/druinok/status/853243686116896773">April 15, 2017</a></blockquote><script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script><br />
<br />
It turns out that we both use Canvas, an LMS, at our schools. There are a lot of features about Canvas that are not the most user-friendly, but in terms of giving feedback to students quickly and easily, it's been really helpful. Here's how I use it:<br />
<br />
<br />
<ol><li>All work that I collect from students passes through Canvas, including work that is not graded, but is just for feedback. I create an assignment with either a link to a pdf for problem sets or to a Google doc for projects/written reflections<br />
<br />
<br />
</li>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZMf7CWPpSrmqP_5BdeHJZvwf4l_-0pN2e8Cz0aeLWJ_mn-NWaJXd-VLFTtBZ2d01FRaBIWqTnKrRzdeELyx_8BYNwHwAkDMeQ5R31wRdqiNKQliVauYM3KuxOil__OkxQ6LCIhHx5sXU/s1600/Screen+Shot+2017-04-16+at+9.23.34+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="393" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZMf7CWPpSrmqP_5BdeHJZvwf4l_-0pN2e8Cz0aeLWJ_mn-NWaJXd-VLFTtBZ2d01FRaBIWqTnKrRzdeELyx_8BYNwHwAkDMeQ5R31wRdqiNKQliVauYM3KuxOil__OkxQ6LCIhHx5sXU/s640/Screen+Shot+2017-04-16+at+9.23.34+AM.png" width="640" /></a></div>
<li>Students complete the work either in their Math notebook or in a Google doc (for projects/written reflections). <b>But all work is submitted digitally.</b> The student's view has an electronic submission button. Most of my students have the Canvas app on their phones and can submit by snapping a photo of their written work. Those that don't have the app take a picture with their computer camera and submit it via the web version of Canvas. I remind students to submit their homework to Canvas after we go over homework questions in class.<br/><br/><br />
</li>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibKPsbq3OboB0ZTbJ0PuXzJDHzXd05qr_K3G-UZDK0Q9VCCx9xtvCHEXXceAuKBAJChd3tQX_IVY8v8V2XCsNRPn0CizzpN8rlycjk4Q2Rnvxw64aX9VBFjRhAX5OPrYFMUDnDiFQY6-A/s1600/Screen+Shot+2017-04-16+at+9.27.42+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="130" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibKPsbq3OboB0ZTbJ0PuXzJDHzXd05qr_K3G-UZDK0Q9VCCx9xtvCHEXXceAuKBAJChd3tQX_IVY8v8V2XCsNRPn0CizzpN8rlycjk4Q2Rnvxw64aX9VBFjRhAX5OPrYFMUDnDiFQY6-A/s640/Screen+Shot+2017-04-16+at+9.27.42+AM.png" width="640" /></a></div><br/><br/>
<li>In grading mode, I see the photo each student took, mark the assignment Complete or Incomplete, and type written feedback. If the assignment is graded, I indicate their level of proficiency and sometimes comment on the specific objectives graded (we use Standards Based Grading so students don't see points, only learning objectives and levels of proficiency).<br />
</li>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIf3rh70nWzS4Somm9iuaVB5Juk8dckxDZpgP62GaooitTL9wThv7JAc3kdgzbqJ3SlmR0lwfpZen-Z-ehNk7Llk2gPUssAPDD1V46UqcD9ynf86ughlr30a7X94kTI_ZNvYnkx1uxXwU/s1600/Screen+Shot+2017-04-16+at+9.33.37+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIf3rh70nWzS4Somm9iuaVB5Juk8dckxDZpgP62GaooitTL9wThv7JAc3kdgzbqJ3SlmR0lwfpZen-Z-ehNk7Llk2gPUssAPDD1V46UqcD9ynf86ughlr30a7X94kTI_ZNvYnkx1uxXwU/s640/Screen+Shot+2017-04-16+at+9.33.37+AM.png" width="305" /></a></div>
<li>The system is quick - I can go through all the work submitted by students, type or copy and paste comments, and click on levels of proficiency if I'm grading the assignment. Students see the feedback on individual assignments and can also look at feedback from past work, chronologically or organized by learning objective.<br/><br/><br />
</li>
<li>I love the fact that students have access to all of their Math work in their notebook at all times - there's no longer the loss of time in turning it in, waiting for me to write feedback, and then getting it back, accompanied by the inevitable loss of someone's work and of me lugging piles of papers back and forth from school. There's no longer a question of whether something was turned in or what the feedback on that work was. We can both always easily see a chronological record of the feedback given over the course of the year and track progress. If I ever create a portfolio system for summative assessment, all of the student's submitted work is already digital and organized.<br />
<br />
</li>
<li>The one drawback that I wish Canvas provided is the ability to annotate directly on student work. If I want to draw a student's attention to a particular problem, I have to write a note that says, "In question #2, look at..." instead of just circling question #2 on their paper. When students upload their files in pdf format, Canvas has an internal marking system that activates and allows you to annotate, highlight, and type directly on the page. But for most students, this would add an extra step of converting their picture to a pdf and uploading it in that format, and I would rather make homework submission as simple as possible. So for now, this is my system.</li>
</ol>Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com0tag:blogger.com,1999:blog-8537494321067959493.post-84999085816091823492017-03-24T00:44:00.004-07:002017-03-24T08:44:50.135-07:00Task MakeoverWe've all been there... you find a task that seems awesome. You start reading it and you get excited. There are so many different strategies that can be tried. There's a visual and algebraic aspect to it and a chance to try specific examples, make generalizations and predictions, test them, and build and justify a model. You spend a bunch of time exploring the different paths you think students might take, how you're going to give them feedback and what you'll assess with this task, how it fits with the rest of your curriculum, how you'll structure individual work time, collaboration and class discussion, how you think the lesson will flow, and how much time you plan to give to each component. Mostly, you're excited because you think it will be engaging and fun for students and will also bring up really interesting and important math ideas and practices. You introduce the task in class, eyes aglow with that special teacher light reserved for days like this, rubbing your hands in anticipation for the awesomeness about to unfold.<br />
<br />
Except that it doesn't. At all. Kids seem confused. Then, frustrated. Heads start to go down onto desks along with pencils. Silent think/work time becomes sad, frustrated time, then out-loud complaining time as you slowly realize that this task is bombing and how. The kids you'd especially hoped and planned to engage, the ones who only sometimes engage, are the first ones to go. You try to rally the troops, but it's a lost cause, and you end the class demoralized and humbled. X years into this thing and every day still has the potential for catastrophe and epic failing (you may or may not be exaggerating the dramatic nature of the experience, most kids probably shrugged their shoulders and went on with their lives, but it was a hard 30 minutes for me, dammit!)<br />
<br />
Where do you go for solace and a sympathetic ear? To the Math Twitter-Blog-o-Sphere, of course!<br />
<br />
<blockquote class="twitter-tweet" data-lang="en">
<div dir="ltr" lang="en">
That feeling when you spend hours planning an awesome investigation for students and they hate it... <a href="https://t.co/0xg8yIPcrh">pic.twitter.com/0xg8yIPcrh</a></div>
— Anna Blinstein (@Borschtwithanna) <a href="https://twitter.com/Borschtwithanna/status/844316684496224256">March 21, 2017</a></blockquote>
<script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script><br />
<br />
<br />
Thanks to the advice and thoughtful questions of all you fine folks, I was able to reflect on the task design and recognize that the sheer wordiness and immediate jumping into very abstract ideas was a huge turn-off for many students.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXg-2r1EPlCWQXqkqxngb_wt9-4h5_VyNYw32DAjp9DVo7a_lS4_PwkYwDNYZh7Xkufu-LeX-ZnCjlCI4GhkARJdNaWcD8r5TmBYSXVAdmA7PHfpX-_6Rwq4LDkOZM4_ylwVHW48cuEnM/s1600/Original+Lots+of+Squares.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="428" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXg-2r1EPlCWQXqkqxngb_wt9-4h5_VyNYw32DAjp9DVo7a_lS4_PwkYwDNYZh7Xkufu-LeX-ZnCjlCI4GhkARJdNaWcD8r5TmBYSXVAdmA7PHfpX-_6Rwq4LDkOZM4_ylwVHW48cuEnM/s640/Original+Lots+of+Squares.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Students had been doing so well with open investigations that even though it had been a little while since we had done one, I had completely abandoned the normal structures that coax kids who are not super sold on this Math thing just yet to try things, engage, take guesses, get a foot in the door, and progress towards increasing abstraction and formality at their own pace.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Fortunately, I had another class the next day with which I had planned to try this task. Back to the drawing board.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
I started with a story. It's my birthday, but I'm really, really obsessed with all things square. My entire party has a square theme. Of course, I demand a square cake and that all pieces served to guests are perfect squares too. I can have my own party and eat the entire square cake myself. I can be a bit more generous and have a party for 4 since I can cut the cake into 4 perfect square slices. I can be even more generous and throw a party for 7 by cutting the cake further. </div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEGqDAQ8Af5ZGp-t25gSZ43sfniTu1t1YVQ6ecNIoSLck9rYhuweiznTCtV9rT8HBA2XlZMiAk4COzxGpyWoKy0dZGJmncOpKIgBLhmuoCd-SZ2hAGePjIq_3wO-LCE0s82Wh7cXWSDVU/s1600/Lots+of+Squares.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEGqDAQ8Af5ZGp-t25gSZ43sfniTu1t1YVQ6ecNIoSLck9rYhuweiznTCtV9rT8HBA2XlZMiAk4COzxGpyWoKy0dZGJmncOpKIgBLhmuoCd-SZ2hAGePjIq_3wO-LCE0s82Wh7cXWSDVU/s640/Lots+of+Squares.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
This was a natural segue to asking students what they noticed and wondered, which brought out all the key features of the problem that in the earlier version were laid out in many, many words. Namely - is it possible to throw a party of any size if the slices must be square (but don't need to be of equal size)?<br />
<br />
<div style="text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg17MHR23psNV1cc0DwQ-fL3LEe3jvKgMlpBvxqUgqvBUunZoaBp6lUkNc0tJfy_wWB7yqxvr-Jhzde3aR4fnz8ysteN4AWSEIpbpFVpRlnn_XYUipkOyElCBYA46Kn73nWoCVTbLgMy28/s1600/1e2accb0-24ed-4a12-a8c4-ef549310905e.jpg" imageanchor="1"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg17MHR23psNV1cc0DwQ-fL3LEe3jvKgMlpBvxqUgqvBUunZoaBp6lUkNc0tJfy_wWB7yqxvr-Jhzde3aR4fnz8ysteN4AWSEIpbpFVpRlnn_XYUipkOyElCBYA46Kn73nWoCVTbLgMy28/s640/1e2accb0-24ed-4a12-a8c4-ef549310905e.jpg" width="640" /></a></div>
<div style="text-align: center;">
<br /></div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
Students immediately had gut reactions and strong opinions. Some were ready to look for patterns right away, but for most, an opening question of: can you make another arrangement that we don't already have on the board? sent them on their way. </div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
Students quickly determined that they could make 1, 4, 9, 16, 25, etc pieces and that they could always add three to the number of pieces by cutting one of them into 4 and add 8 to the number of pieces by cutting them into 9.</div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
There was another breakthrough when a student presented a convincing case for 6 pieces (as well as 11) and others realized that they could always add 5 more pieces by putting another layer on the outside.</div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJC6wO6wgL-m7v0hEfvnwIPPKmBrJeIyX0jhlxFjnwLBt3Ss8iTIlL81-SX97kWk6SF6ebiLELrQxjIYkHxdW5Y8O8Ww8HRNV9R1MGh8bYJPHW-uRH0G1by_BGm2BfHAgHnMGUevIcAt4/s1600/668a550d-6cc8-4c66-85ca-071cf0a509b4.jpg" imageanchor="1"><img border="0" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJC6wO6wgL-m7v0hEfvnwIPPKmBrJeIyX0jhlxFjnwLBt3Ss8iTIlL81-SX97kWk6SF6ebiLELrQxjIYkHxdW5Y8O8Ww8HRNV9R1MGh8bYJPHW-uRH0G1by_BGm2BfHAgHnMGUevIcAt4/s640/668a550d-6cc8-4c66-85ca-071cf0a509b4.jpg" width="640" /></a></div>
<div style="text-align: center;">
<br /></div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
This was the class I'd been hoping and prepping for when I found this task. Engaged, arguing, changing their minds, kids working past the end of class and needing to figure this out. </div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
Take-aways for me? Don't assume that kids have graduated past scaffolds that help them get started and build up to abstraction. If you're going to take them away, be aware and think deeply about how to do that carefully and thoughtfully. It's hard to reclaim a class that's lost its confidence so pay attention to this part.</div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
I went back to the first class and tried again. With the reformulated question, things went much better. One of the students who had struggled the most the first day came up with a great organizational chart (that she said was inspired by Pascal's triangle) for tracking possible party sizes. </div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjvDg56-N9WjcSi2UFb0Mka5SZQXJCzkSX8QeEgC08MElr94Ddy5SLhPI7JhBXpksQuiNj7xPvjiMH4TACHxaecUI1s56ZyyWulHxqx0cLGtGYVe0Wtm_NVtdmVZ6X9ynIqSj-fqXiFwJY/s1600/65414d08-330d-4ffe-9f21-1d1c7dd71044.jpg" imageanchor="1"><img border="0" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjvDg56-N9WjcSi2UFb0Mka5SZQXJCzkSX8QeEgC08MElr94Ddy5SLhPI7JhBXpksQuiNj7xPvjiMH4TACHxaecUI1s56ZyyWulHxqx0cLGtGYVe0Wtm_NVtdmVZ6X9ynIqSj-fqXiFwJY/s640/65414d08-330d-4ffe-9f21-1d1c7dd71044.jpg" width="640" /></a></div>
<div style="text-align: center;">
<br /></div>
<div style="text-align: left;">
She did have to amend it when another student came up with the 6 and 11 square versions since her version only assumed you could have perfect squares and add either 3 or 8.</div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVtt330kuQEfT9tyShf1o0SiWuqTE30i69bx3f7T7Vo5uSrWNeSU9T0uxk8iKfurTBn4zt5Vdamb4IPPUvRE3PkuqWqQQQxga3mO6b8M0Cm5Lp8NeiMAzXabCWT9aNBY0gUpPH-k0_NaU/s1600/fce3df08-a831-4e4a-bf16-18d37e524f3a.jpg" imageanchor="1"><img border="0" height="372" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVtt330kuQEfT9tyShf1o0SiWuqTE30i69bx3f7T7Vo5uSrWNeSU9T0uxk8iKfurTBn4zt5Vdamb4IPPUvRE3PkuqWqQQQxga3mO6b8M0Cm5Lp8NeiMAzXabCWT9aNBY0gUpPH-k0_NaU/s640/fce3df08-a831-4e4a-bf16-18d37e524f3a.jpg" width="640" /></a></div>
<div style="text-align: center;">
<br /></div>
<div style="text-align: left;">
Next step for both classes - helping them transform the patterns and ideas they have into more formal written explanations and justifications.</div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://media.giphy.com/media/VvVeHW0UviOsg/giphy.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="356" src="https://media.giphy.com/media/VvVeHW0UviOsg/giphy.gif" width="640" /></a></div>
<br />
<br />Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com13tag:blogger.com,1999:blog-8537494321067959493.post-25911859160118137402017-02-13T23:20:00.000-08:002017-02-13T23:20:47.779-08:00More ideas on working with students who really, really don't like mathematical explorationAs I've blogged before, the area in which our program has perhaps received the most criticism is in the challenge that open tasks, labs, mathematical explorations, and group problem solving pose for students who crave a more structured, algorithmic, and predictable approach. I met with a student (new to me this semester) last week who told me that she was incredibly frustrated with her current Math class (I am the teacher) because in her prior Math class, homework was 1 through whatever odd and both homework and quizzes were repeat versions of what the teacher had shown students in class. She had found this prior class soothing and comfortable and was an excellent student in this environment, whereas now, she felt that every facet of class was constantly asking her to figure out problems she hadn't seen before and she never knew if she really understood or felt like she was on solid, comfortable ground. She was worried that her confidence was slipping and that she wasn't learning as well as she had in the more traditional environment.<br />
<div>
<br /></div>
<div>
My initial internal reaction was to try to convince her that my pedagogy was sound, that it would indeed be better for her long term to struggle and make sense of novel situations, apply and stretch herself, learn how to tinker and problem solve rather than regurgitate algorithms repeatedly, but I felt that this would be minimizing her experience and negating her sense of her learning and mathematical identity. She had clearly stated that things make sense to her after she is given a method and does a lot of similar problems - only then does she believe that she is able to generalize and form an underlying concept. This isn't how our program is designed and I absolutely believe that it is better for most students to experiment and play first, forming conjectures and identifying patterns before coming to or seeing more formal methods (if needed), but maybe it's not better for her. At the very least, if she is convinced that this is the wrong way for her to learn, then it will be very difficult for her to interpret her experience otherwise, thus creating a self-perpetuating cycle. </div>
<div>
<br /></div>
<div>
So I'm trying something new, and I'm not sure how well it's going to work. Every week, I'm going to email her a list of concepts that we will be working on next week, along with resources either in the textbook or online for her to see these concepts explained and practice problems for her to work on. A preview, if you will. Class will then not be a time for her to explore and invent, like it is for other students, but a time for her to generalize and prove the patterns that have already been revealed and practiced. In exchange, she has agreed that in a few weeks, she will again try exploring a new topic and be open to coaching by me in order to also get better at this way of learning. </div>
<div>
<br /></div>
<div>
I'm hoping that by engaging in good faith, I am able to bridge the divide in expectations and meet this student at her current level of need and that she is able to grow over time in the mathematical habits of mind that I believe are just as important as, if not more than, content knowledge. It is certainly possible that she will continue preferring doing math in predictable and routine ways, following a pattern shown to her by someone else, on mathematical autopilot. I really hope that I can convince her that she can be successful and that it's worthwhile to engage in math in a different way than she has in the past. But it's okay if that's not where she is right now. I have a whole semester to build a relationship of trust and forment and celebrate moments of mathematical success for her.</div>
<div>
<br /></div>
<div>
Have you had students who actively and eloquently resisted your view of math or ways of teaching? What are some ways that you've made progress over time in their willingness to go there with you? Are there students who never changed their minds? Any and all advice welcome, as always :)</div>
Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com3tag:blogger.com,1999:blog-8537494321067959493.post-62423413303571975522017-01-10T17:44:00.002-08:002017-01-10T21:45:00.731-08:00Why might students be motivated in math class?At the end of the first semester, as part of students' self-evaluations, I asked them to reflect on their habits of learning, including curiosity and passion, asking, "Do you do work just to get it done? Do you cultivate your mathematical strengths and interests? How motivated/passionate are you and how might you improve here?" I received some pretty interesting responses to this series of questions, many of which boiled down to: I've never been that interested in or motivated by math and I don't know where to start to develop this.<br />
<br />
In my reflection on this reflection, I came up with four main categories from my experience that describe why students have been interested in or motivated to study and learn mathematics.<br />
<br />
<ol>
<li><h2>
Patterns and beauty inherent in mathematical structures</h2>
</li>
<span style="font-weight: normal;">Some students are intrigued by looking for, identifying, and explaining patterns; others enjoy the beauty inherent in visual representations of mathematical objects and relationships. These students appreciate a teacher who encourages and rewards their curiosity, but overall, require the least amount of effort on the teacher's part to motivate and support since they're often speaking the same language as the teacher already.</span>
<li><h2>
Applications between mathematics and the real world</h2>
</li>
<span style="font-weight: normal;">Other students I have taught were less interested in math in and of itself, but did find the idea of math as a tool to understand, explain, and predict the real world motivating. These were often students with an existing interest in science or social science who saw the usefulness of math in their respective fields of interest. Interesting projects were obvious choices in hooking and motivating these students, as well as a greater emphasis on practice and application than on derivation or justification. </span>
<li><h2>
Being a good student</h2>
<span style="font-weight: normal;">This third category of student is one that is invested in an image of themselves as a good student. They care about doing well and meeting their goals and are motivated by seeing their progress, exerting effort and seeing it pay off, as well as specific feedback on how to improve and clear objectives for the course. </span></li>
<li><h2>
Relationships</h2>
<span style="font-weight: normal;">These students seem to be predominantly motivated by positive interactions with others, whether that's the teacher or their peers. Classroom structures that increase conversations and collaboration between students and that make students feel known and connected to others have been helpful in motivating this group in my experience, as well as putting more of an emphasis on my relationship with them. </span></li>
</ol>
<div>
Obviously, most students are some mix of these categories, but for many in my experience, one is more dominant. I think that a classroom that tries to balance between these different student needs will likely result in broader student success than one that caters to only one type. I would love pushback on my preliminary and perhaps too simplified analysis. Are there any categories you see being useful for thinking about student motivation? What other tools and strategies have you used to help students foster their curiosity and interest about math and motivation to exert effort towards the class?</div>
Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com0tag:blogger.com,1999:blog-8537494321067959493.post-4680387701246291502017-01-06T19:28:00.003-08:002017-01-06T19:28:53.499-08:00#MtbosBlogsplosion - My FavoritesCarl and Julie have kick-started a <a href="https://exploremtbos.wordpress.com/2017/01/05/new-year-new-blog/">new blogging initiative</a>, and the timing is perfect, as I'm trying to get myself blogging more often instead of waiting for An Amazing Inspiration. This week's theme is My Favorites, and I wanted to share a really helpful framing for peer editing created by <a href="https://twitter.com/MandyMudde">my awesome colleague</a>. We've been working on using peer feedback more productively this year, and her document (shared below) gives a good structure for students to reflect on and give feedback to their peers' write-ups and oh hey, they also learn a lot about what makes for a good write-up and use this understanding to do a better job themselves. Mandy has incorporated a peer feedback step for all write-ups, with that night's assignment for students to revise their own work. I would love to do more structured peer feedback in other components of the class, such as homework assignments, note-taking, and studying for assessments. The setup is very basic - students exchange papers, give each other feedback, get their peer's feedback back, and turn it in with their revised write-up, documenting any revisions that they made.<br />
<br />
<iframe height="900" src="https://docs.google.com/document/d/1-xr5UdjmO0FCDgN8tBNHuv-qXWA2pAVfvG1h3viL3Tw/pub?embedded=true" width="700"></iframe><br />
<br />
Here's my first draft for a homework feedback form. Would love any feedback and suggestions for improvement.<br />
<br />
<iframe height="600" src="https://docs.google.com/document/d/1aCwmQdutTubSkrKIsz8gPxH2xsVq1X9lbs8dGO8UpdU/pub?embedded=true" width="700"></iframe><br />Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com0tag:blogger.com,1999:blog-8537494321067959493.post-12860053855293157062017-01-06T16:21:00.001-08:002017-01-06T16:21:49.721-08:00Goals for second semesterAs I've been wrapping up grading from semester 1 and planning semester 2 for my classes, I'm realizing that I did not set goals at the start of this year the way that I have in the past. Better late than never!<br />
<br />
<h3>
Changes for my personal teaching:</h3>
<div>
<ul>
<li>Get back to individual feedback meetings. I blogged about them <a href="http://borschtwithanna.blogspot.com/2015/07/goals-for-2015-2016.html">here</a>, but the general idea is that I set aside 20 or so minutes to meet with each student approximately every two weeks in order to sit down together and look over their work and have a feedback conversation. I've found these incredibly helpful for students to actually attend to my feedback, understand what I mean and why I think it's important, and explain their thinking to me. This year has been very tricky since the schedule was changed and students lost a floating free period that I used to be able to use for these meetings. I am recommitting to instituting them again, using class time, if needed. It's been the best way for me to get through grading big projects in a timely manner since it's actually fun and rewarding to sit and discuss students' work with them rather than grading on my own after a long day (since, let's face it, grading gets put off and off).</li>
<li>Be more on top of students who are struggling. I am committing to looking at work that is turned in every week to check up on students who are missing work or need additional support. If anyone has a good system for keeping track of interactions/observations/progress for all students and how they make sure that no one is falling through the cracks, I'd love to chat.</li>
<li>More nuanced and thoughtful reflection questions - I think that the balance of reflection vs. doing math has been better this year, but I'd like to focus the questions I ask students in order to hone in on specific mathematical practices rather than just general "what's going well? what do you need to work on?" type questions. I also want to bring back, "what's one good thing that happened this week?" - it was a great way to regularly check in and connect with students.</li>
<li><a href="https://samjshah.com/2011/07/12/participation-quizzes/">Collaboration quizzes</a> to give more direct feedback to students on their groupwork and engagement and help them internalize expectations more effectively.</li>
<li>More peer feedback. I've started doing this more this year, and love how much motivation it creates for students to express themselves more clearly and justify their thinking. I'm hoping to use peer feedback this semester to help students get better at analyzing strategy, getting positive feedback for extensions they create, and to deepen their understanding of different approaches. One of the lesson study groups worked on peer feedback last semester and I'm really excited to learn from them. I would also like to use a Slack channel for classes so that students can discuss and share ideas outside of class more easily.</li>
<li>Better differentiation. I'd like to meet with students to set individual goals and do more follow up to help them stay on track with these. I think that there's already a fair amount of choice in problem sets and homework assignments, but I'd like to do a better job of teaching students how to use those choices better. One way will be to have them reflect at the end of class on the type of work they need to do to follow up on that day's learning (review of prior concepts, practice, connections, and/or reach problems). I know that they are learning project management skills in their other classes, but in Math, the product is the process, which is more abstract and harder for them to track and plan. </li>
<li>Continue and get better at classroom routines that foster reflection and a clear arc from start to finish. </li>
<ul>
<li>I have often used Desmos Activity Builder to <a href="https://teacher.desmos.com/activitybuilder/custom/57d82d6420bbe80309333268">start</a> and <a href="https://teacher.desmos.com/activitybuilder/custom/57d82f37f56dbb8f0773c429">end</a> class, but would like to do this more consistently and help students get better at constructing meaning from problem-based lessons by selecting useful reflections and comments to share. I still have work to do on making sure that meaning and connection emerges from students' own thinking and not ignoring times when they don't emerge or simply telling students what they should have learned. One way is to do more planning of student responses and how to connect these and have the main ideas of the lesson emerge from them, sharing methods and responses that did not emerge as part of that process. </li>
<li>This also connects to better note-taking. I have given feedback to students once or twice on their note-taking and organization and definitely need to do this again. I haven't really figured out a solution for sharing board work and "notes" from class since I've emphasized process and individual needs. I do share presentations, if they were used, but those generally do not contain worked solutions. If anyone has good ideas on this, I'm all ears. </li>
<li>I would also like to do this on a unit-level rather than just lesson-by-lesson by using student-generated essential questions, concept maps, and study-guides more this semester. There is still a fair amount of tension between student-generated conclusions/connections and teacher-generated ones that are more "efficient" and feel more comfortable and structured for students, especially if they're oriented towards maximizing content acquisition. I am working to help students get better at this and at understanding why I think that it's important, both of which are necessary to get more buy-in for the process and rewards that actualize when students do more of this work. One way is to be more transparent about the structures that I'm using and why - I observed a teacher recently giving an intro to a lesson by explaining the groupwork structure that he would be using and what he hoped it would achieve, and I think that enlisting students as teammates in this process is hugely beneficial. </li>
</ul>
<li>Continue the following changes I implemented last year:</li>
<ul>
<li>Each assessment includes reassessment of previous content</li>
<li>Visibly Random Groupings (new groups daily) and whiteboarding</li>
<li>Homework that's spiraled and includes Retention, Review, Reflect, and Reach sections; students self-select problems to do (should sometimes group students by homework problems completed the next day though)</li>
<li>Students submit all work digitally, all feedback is recorded digitally in one place (online gradebook)</li>
</ul>
</ul>
</div>
<h3>
Big Picture Curriculum:</h3>
<div>
<ul>
<li>Decide on <a href="https://drive.google.com/open?id=1snL1uTJSyxMjjfMOQ5L6rUmxFp5Knh9SYUNs3c_w8F8">mathematical practices and habits</a> that should be emphasized within a given year/semester/unit and link them to specific lessons and activities. I've been doing a much better job this year of giving students regular feedback on these, but haven't been very intentional about which habits will be emphasized when, noticing which ones students are making progress on and which ones need more work, and how (besides getting feedback) they might get better at them.</li>
<li>Create more opportunities for interdisciplinary connections. I've put out some feelers to Science teachers and will do the same for Computer Science, English, and History to see where we can join forces and create projects that can support and enrich both disciplines.</li>
<li>Formulate a more cohesive picture of our curriculum and mission so that our core sequence is less content-driven and so that we can explain to students and families why acceleration is not necessary or desirable. This will require a reducing/reworking of our acceleration pathways, enriching/differentiating core classes, and deciding how electives should support the overall program. </li>
<li>Start developing a portfolio assessment for one Math course. It might not be ready to go this semester, but if I can pilot a beta version in one class, I can work on tweaking/developing it more over the summer so that it's ready to go in more classes next year.</li>
<li>Work on developing group assessments (and other differentiated assessments) for at least one unit in each class.</li>
</ul>
</div>
<h3>
Professional Development:</h3>
<div>
<ul>
<li>Continue lesson study this semester and figure out good systems for sharing the results that each group has found, both within the discipline team and with the school community more broadly. Possibly help other disciplines/divisions begin the lesson study process. Think about presenting about lesson study next year and the types of resources and supports teachers would need to get started with this.</li>
<li>Figure out what I want to work on over the summer. Major contenders currently are:</li>
<ul>
<li>Attending PCMI</li>
<li>Teaching at summer institutes for teachers</li>
<li>Start compiling our existing curriculum into a more easily shared and edited form for students, families, and teachers</li>
<li>Curriculum development for my school, focusing on alignment between courses, portfolio assessment, projects that connect to other disciplines and class trips, parent education, and developing new electives</li>
<li>Summer math support for students who are doing independent work or working more directly on accelerating/remediating/enriching</li>
<li>Coordinating with the middle school on curriculum, parent education, and development of mathematical practices</li>
</ul>
</ul>
</div>
Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com0tag:blogger.com,1999:blog-8537494321067959493.post-1829710058814880312016-12-14T17:15:00.001-08:002016-12-14T17:15:54.597-08:00Lessons from this year - supporting struggling studentsOne of the big issues that's been emerging for me this year is how to support struggling students. As a school, we've made a commitment not to track and to differentiate instruction so that students from a variety of backgrounds can be supported and pursue their interests fully. The desire to provide challenging content to all students is one I very much support and know the research backs it up. The problem, of course, is that if students are grouped heterogeneously, but the content is the same as what would be taught in an honors section, students who have not been successful in Math in the past do not magically overcome those challenges. What does end up happening is that half the class is frustrated and feels like the pace of instruction is too slow and the other half of the class has their preexisting images of themselves as unsuccessful Math students confirmed.<br />
<br />
I have also been quite surprised to see that it's often students who are struggling who give pushback to teaching methods that emphasize choice, group work, student-constructed knowledge, and open problems. They feel unsuccessful with these teaching styles and crave direct instruction, structure, and concrete, repetitive problems. These students (and their families) have been asking for textbooks, lecture, and an explicit curricular progression in which students are walked through algorithms and given lots of practice. In teaching these students, when I see how much more scaffolding they need to successfully mediate their relationship with mathematics, I understand their perspective and needs much better than I did before. Their gaps are often not in prior knowledge (although that's there too), but in how to learn Math. As a department, I think that we've done a great job of building a rigorous and interesting curriculum that works well for successful Math students who jump into open problems, ask questions, tinker and test, iterate, confer with peers, look for connections and patterns, reflect on their understanding, and figure out what they do and don't know independently. When they lack some of these skills, they are receptive to feedback and observation of peers who model them. We have not yet, however, figured out how to teach all of these skills while simultaneously asking students who don't yet have them to grapple with difficult mathematics in an environment that requires these skills to be successful in that work. <br />
<br />
One solution to this issue is to give the students what they want: a choice between a track of open/challenging/problem-based math and a track of traditional/lecture-based math. For many reasons, this is not a solution that I can get behind. Perhaps I'm wrong, but I have not seen incontrovertible evidence that there are some students who just can't learn Math without lecture and repeated drill. If we really think this, we are basically saying that these students can't learn Math and let's just teach them how to regurgitate some procedures so they can get by on their standardized tests. I would have a very hard time supporting a bifurcated system like this.<br />
<br />
Other ideas I have had that might help this issue are:<br />
<br />
<ul>
<li>Provide an extra Math class for struggling students that would focus on just content or just mathematical practices/habits; either make this optional or required</li>
<li>Provide a summer bridge program for students who we worry might struggle in our program, focusing on building up their ability to learn and mathematical practices</li>
<li>Start the year with work on mathematical habits and ways of learning Math with little to no focus on content for all classes. </li>
<li>Work on improving our curriculum so that it incorporates more of the principles of Complex Instruction and can highlight students' strengths.</li>
</ul>
<div>
I would love to hear from others who have grappled with this issue and ways that they and their schools have approached it, either successful or not. </div>
<div>
<br /></div>
Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com2tag:blogger.com,1999:blog-8537494321067959493.post-5865372755888207232016-10-20T11:43:00.002-07:002016-10-20T11:43:57.601-07:00Starting Lesson Study and Update on ClassesThis isn't going to be a very coherent post, but I need to get our current work into writing to better organize my thoughts. Here are the projects that are in progress right now:<br />
<br />
<br />
<ul>
<li>Lesson Study</li>
</ul>
<ol>
<ul>
<li>We've broken up our Upper School Math teachers into several groups of 3-4 teachers who teach across different grade levels. We considered doing a more traditional lesson study in which teachers plan a lesson centered around specific content, but decided to focus our efforts on developing our practice around a particular instructional routine that would be relevant across many grades and that would help us fine tune a specific pedagogical approach and learn from colleagues with whom we rarely get to work.</li>
<li>Everyone read <a href="https://ww2.kqed.org/mindshift/2015/09/14/lesson-study-technique-what-teachers-can-learn-from-one-another/">this</a> article from KQED to orient themselves to the lesson study process in advance of our first meeting.</li>
<li>Each group selected an instructional routine to plan out, teach, and refine this cycle. The routines selected were:</li>
<ul>
<li>Differentiation for students who learn at different paces</li>
<li>Guided investigation</li>
<li>Students giving feedback to each other</li>
</ul>
</ul>
</ol>
<br />
<ul><ul>
<li>In the next meeting, groups will plan a specific lesson around their instructional routine based on the first teacher who will be modeling it and decide on an observation time and what to look for when observing</li>
<li>I'm super excited for this initiative to be gaining traction! We got some time to work on this while students were taking the PSAT or doing other activities, but I'm worried that if we don't get specific time off to work on this, people will become significantly less enthusiastic. </li>
</ul>
</ul>
<div>
<br /></div>
<ul>
<li>Parent Math Night</li>
<ul>
<li>Our team is working on developing an informational night to help parents better understand our program, available resources, and philosophy. It's just in the planning stages, but I think will be really helpful in getting on the same page with families. Right now, whatever information they receive when applying is the extent of it. </li>
<li>This needs to be thoughtful and informative for parents while also clearly conveying our position and getting buy-in and understanding of the program. If you have any resources or ideas to share, would love to have them.</li>
</ul>
</ul>
<div>
<br /></div>
<ul>
<li>Math 1 is finishing our unit on Counting, Probability, and Sets, designing a <a href="https://drive.google.com/open?id=1AeO-LAcxFBb0qb9Di-jn7rwBoqN3yeGo-aEfz6OnFnU">game</a> that has students analyzing probability and expected value to determine best strategy and fair outcomes. Next week, students will be playing each other's game and reflecting on what they've learned. This is a good opportunity to differentiate and identify gaps in understanding linear functions and algebraic manipulation skills as we prepare to move into a functions unit next.</li>
<ul>
<li>We're starting each unit with a "preview" assignment to look at prior knowledge and pre-requisite skills and concepts so that those students who have gaps can be identified and given extra support. <a href="https://drive.google.com/open?id=0B_Vjfvjet27eTVAtc3o0RG5sWFU">Here</a> is the preview assignment for linear functions.</li>
<li>We're also starting the unit with another open investigation, this one more directly related to functions ("<a href="https://drive.google.com/open?id=0B_Vjfvjet27eSG1ZZEMydi1EVGs">Cutting the Pie</a>" task from IMP Year 1). I'm curious to see if students pursue a recursive or closed rule for this function. When we worked with Pascal's triangle patterns, students had a hard time moving from "each row is twice the previous row" to the rule f(x) = 2^(x-1).</li>
</ul>
</ul>
<div>
<br /></div>
<ul>
<li>Math 2 is still in the depths of statistics, working through the Central Limit Theorem and connecting probability and the normal and binomial distributions. I'm realizing how much better I understand the material in my third year of teaching it and how much less formulaic and prescriptive my teaching is now that I have deeper content knowledge in this mathematical space. I have known that strong content knowledge is necessary, but it's amazing how much more depth is needed if you want students to explore and create and test their own theories, both in terms of creating those scenarios and in guiding the discussions that ensue. Maybe it's true then that teachers have to first progress through traditional pedagogy as they build up their depth of content knowledge before they can start to incorporate more problem-based or project-based learning. Would love some pushback on this though :)</li>
</ul>
Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com2tag:blogger.com,1999:blog-8537494321067959493.post-71466086179757223442016-09-01T22:27:00.003-07:002016-09-01T22:28:26.905-07:00Habits of Mind Unit - Math 1We've had four whirlwind days of school so far - I'm really enjoying starting with a Habits of Mind unit in each of my classes as it means students are working on tasks and learning the routines of the class every time we meet and I am getting to know them and the flow of the new year.<br />
<br />
In Math 1, we have been working on several different tasks, each of which is related to combinatorics, the first unit that we'll be officially starting next week. In each task, students start with an introductory question and then each group creates an extension to pursue next. The three tasks we've done so far are below. I'm still tweaking the fourth one and will post it when I'm done (hint: this is one of the things I need help deciding).<br />
<br />
Task 1: How many paths from A to B if you can only travel down and to the right?<br />
Extensions created by students: generalize for a grid of any size, allow travel up and to the left (without crossing over), allow traveling diagonally<br />
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgInMZ9GGpufomoq2oukB4-e8dV6uKLdvCU_R3pNxplQaxYz0y8TbpkWAxewYZ_TEjWhb7EzYn5RSxwDFM0b6o2OscRlKvHMqRT0AYHiV8OVACQdxWbb7ypXr43OdaqfNIvSS49cI6HGMM/s1600/Screen+Shot+2016-08-29+at+8.55.41+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="193" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgInMZ9GGpufomoq2oukB4-e8dV6uKLdvCU_R3pNxplQaxYz0y8TbpkWAxewYZ_TEjWhb7EzYn5RSxwDFM0b6o2OscRlKvHMqRT0AYHiV8OVACQdxWbb7ypXr43OdaqfNIvSS49cI6HGMM/s200/Screen+Shot+2016-08-29+at+8.55.41+AM.png" width="200" /></a></div>
<br />
<br />
Task 2: Consider a game in which you flip a coin four times. At the beginning of the game, your score is 0. Each time you get heads, you get a point. Each time you get tails, you lose a point. What are the different scores that are possible and how likely is each of these scores?<br />
Extensions created by students: generalize for n flips, what about dice that have 4, 5, 6, etc sides?<br />
<br />
<br />
Task 3: How many different monetary values can you make from these bills?<br />
No extensions created yet, will have more time on this next week<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjRaqEJNy311MW9GyCC7KItudH4JCzaHr603jFnYhTDPNz0-LtMauGQhG-zd2gH0dl5ZDWSztWyB9Xgc1FbFeSAsXq9ylYa8PEVvbsBezYym8DYADifDuBJI7zav_LoVMhBDs4NnZeOWM/s1600/Screen+Shot+2016-09-01+at+9.05.08+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="262" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjRaqEJNy311MW9GyCC7KItudH4JCzaHr603jFnYhTDPNz0-LtMauGQhG-zd2gH0dl5ZDWSztWyB9Xgc1FbFeSAsXq9ylYa8PEVvbsBezYym8DYADifDuBJI7zav_LoVMhBDs4NnZeOWM/s320/Screen+Shot+2016-09-01+at+9.05.08+PM.png" width="320" /></a></div>
<br />
<br />
Scroll down for the presentations from class for each of the investigations, which include slides about group/class norms.<br />
<br />
Two big questions with which I'm wrestling in doing these tasks are:<br />
<br />
<ol>
<li>How much, if any, content teaching should there be? Students are practically begging for more efficient methods than just listing out all of the options, but should this unit really be about helping students get better at exploring their own thinking or is it better to teach some content while they're hooked and eager rather than coming back to it when it actually comes up in the unit? For those who incorporate student-driven investigations along with teacher-led instruction, when do you do the latter? </li>
<li>Relatedly, how much should I be pushing students to make the connections between these problems more explicit? I feel like I've been dropping some (subtle) hints and revisiting student work from previous problems in the hopes that some students will point out the underlying connections, but no such luck. Again, is it better to show these connections now, even if it means they will mostly be teacher-driven, or better to wait until later and let these problems simmer for a while longer?</li>
</ol>
<div>
<br /></div>
<div>
My current thinking on these two questions is that I will require each student to work on generalizing one of the tasks and then have students present their generalizations and ask more explicitly about connections between them at that time. I have to now choose a fourth task that I hope will make the connection more obvious... suggestions? What are some tasks/problems you've liked for hooking students on combinations?</div>
<br />
<br />
P.S. I am super happy with how group norms and vertical whiteboarding is going so far this year. Using the same routine with a new math task each day so far has created a really nice flow and students are interacting well and starting to independently leave their groups to find out what other groups are doing to bring those ideas back. It was definitely worth taking a few days out of the content rush to set things up.<br />
<div style="display: block; font-family: helvetica, arial, sans-serif; font-size: 14px; font-stretch: normal; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; line-height: normal; margin: 12px auto 6px;">
<b>Presentations from class</b></div>
<div style="display: block; font-family: "helvetica" , "arial" , sans-serif; font-size: 14px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 12px auto 6px auto;">
<a href="https://www.scribd.com/presentation/322806045/Math-1-Problem-Solving-Unit-Day-1#from_embed" style="text-decoration: underline;" title="View Math 1 Problem Solving Unit Day 1 on Scribd">Math 1 Problem Solving Unit Day 1</a></div>
<iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_61310" scrolling="no" src="https://www.scribd.com/embeds/322806045/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br />
<br />
<div style="display: block; font-family: "helvetica" , "arial" , sans-serif; font-size: 14px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 12px auto 6px auto;">
<a href="https://www.scribd.com/presentation/322806063/Math-1-Problem-Solving-Unit-Day-2#from_embed" style="text-decoration: underline;" title="View Math 1 Problem Solving Unit Day 2 on Scribd">Math 1 Problem Solving Unit Day 2</a></div>
<iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_38040" scrolling="no" src="https://www.scribd.com/embeds/322806063/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br />
<br />
<div style="display: block; font-family: "helvetica" , "arial" , sans-serif; font-size: 14px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 12px auto 6px auto;">
<a href="https://www.scribd.com/presentation/322806069/Math-1-Problem-Solving-Unit-Day-3#from_embed" style="text-decoration: underline;" title="View Math 1 Problem Solving Unit Day 3 on Scribd">Math 1 Problem Solving Unit Day 3</a></div>
<iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_83503" scrolling="no" src="https://www.scribd.com/embeds/322806069/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe>Anna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.com2