#TMC16 Recap

I certainly didn’t need another TMC conference to remind myself of the power and specialness of the #MTBoS, but it didn’t hurt either. I think that this year, I needed the professional rejuvenation of seeing everyone in person just a bit more than usual after a difficult year. So my first and foremost task in this blog post is to convey my gratitude to everyone at the conference who made time for me to vent, invited me out to dinner, came to and participated in my session, gave me amazing advice, and was a source of support. It’s amazingly powerful to have a common starting point with a group of people, to pick up where we left off, either from last year, at other conferences, or Internet conversations. There’s no need to explain, to get our bearings, to wade through small talk and establish common ground and trust – these people get me, we’re on the same team, and it’s effin’ going places. There were so many friends with whom I didn’t have a chance to reconnect, unfortunately, but huge shout outs to @davidwees, @park_star, @jaz_math, @MrJanesMath, @AlexOverwijk, @normabgordon, @JamiDanielle, and @crstn85 for helping me unpack the challenges of this year and get excited about the year to come.

Even though the power of the TMC for me is in the relationships, not the workshops, I have to give huge props to @davidwees for completely challenging my notions of professional development for teachers. I have always been of the camp that the less structure, the better, and that our work together should be about discussing best practices, research, and ideas. Let individual teachers determine how to tweak and interpret these ideas for their particular classrooms, on which they are the experts. It turns out, tightly structured practice with specific strategies, seeing and debriefing them from different angles, and trying to do them yourself while getting feedback is pretty damn powerful. I can’t do a three-day morning session justice here, but check out the materials available about two of their instructional routines here, and I really hope that there are videos available for people who were not able to attend since this is really the kind of thing that needs to be experienced to be understood.

On a meta level, I was surprised by how much practice and feedback we (who were mostly very experienced teachers) needed to get halfway decent at a single routine. We saw it demonstrated several times and debriefed these examples, which is generally as good as it gets in PD. But once we tried implementing it ourselves, new issues and questions surfaced and were addressed. David’s focus on improving teaching practice, not individual teachers, was instrumental here to allow us to be vulnerable and know that we were working together to learn how to do something new and not to be judged (either positively or negatively) by our colleagues. Going to internalize the heck out of this and bring this thinking to my work with other teachers in my department and in the PD that I lead.

I feel like I learned several key points about instructional routines themselves from David and his awesome colleagues (yay Jasper and Kaitlin!):

• Having a good routine frees us to dig deep into the learning, which is extremely counterintuitive for me as my tendency was to assume that structure is limiting and restricting. Nope! Having good guidelines (which can certainly be tweaked for tasks that would benefit from that) means that our cognitive energy is directed solely at learning and the intellectual work at hand rather than trying to figure out expectations and how that learning should proceed. The routine allows students to do more challenging work. It is nothing like the mindless-recipe-following that I imagined.
• A quick pace and keeping the focus on what we can learn about patterns/shortcuts/whatever the purpose of the routine is makes the activity engaging and mediates students’ relationship with math in a way that honors their thinking, but pushes them to go deeper, see connections, and understand other methods and representations. This allows all students, not just those who intuitively know how to learn math, to access the learning.
• A routine is not the time to teach something new. Its purpose is to explore students’ thinking, bring out and connect their ideas, and help them represent and synthesize key mathematical ideas. I can certainly “teach” something in a more traditional sense after the routine, but genuinely focusing it on student thinking keeps it engaging and powerful.

Finally (longest blog post everrrrrrr, bless you if you’ve stuck with me for this long), I loved David’s suggestion of using instructional routines as a focal point for lesson study rather than the traditional use of lesson study to develop a content topic. Different teachers working together can develop different lessons around the same instructional routine and then observe each other, give feedback, and improve the routine in their work together, improving their teaching along the way and creating programmatic change, not change on the individual level.

I am planning on working out my own instructional routines for doing guided and open investigations (similar to Exeter problems and Interactive Math Program tasks) since these form the backbone of my class, but could see separate routines being developed for Open Middle problems (paging @math8_teacher), Would You Rather, Estimation180, or Which One Doesn’t Belong. Contemplate then Calculate was basically created with @fawnpnguyen’s VisualPatterns in mind and it feels like @ddmeyer has already created a 3Act routine, so those two are all set. Any others?

I am super, super, super excited about this as creating routines is something that I think I’m decent at (as opposed to creating creative problems/lessons, which I’m absolutely not) and it’s something that can fundamentally improve our practice in a way that sharing one-off “clever lessons” doesn’t (thanks Dylan… such a valuable point). I’ve already committed our department to doing lesson study this year, and we’re in the midst of building a new program and integrating a number of teachers new to the school so this couldn’t have come at a better time. If there are other teachers out there who would like to give feedback on my ideas or collaborate on creating and tweaking instructional routines around guided/open investigations, I would love to hear from you.

So there you have it… my #1TMCthing is to develop two instructional routines and get as many people as I can to collaborate and give me feedback. Ready, set, go!

Co-teaching and the start of semester 2

Welp, it's been a month or so since we've been in the full swing of things, and "intense" would be the understatement of the year. As a department, we rolled out a co-teaching model for almost all of the core Math courses this semester, which has created many new opportunities and also, challenges. Here's a quick summary of how we're approaching co-teaching, pros, cons, and next steps/thoughts/questions.

Summary of approach:
The core Math courses we offer follow a Math 1 --> Math 2 --> Math 3 sequence, after which many students will take Calculus (as a new school, we have not yet firmed up all the elective options we would like to eventually offer students concurrently or after the core sequence, but that's a whole other blog post). The way that co-teaching is working this semester is that two classes of the same level are scheduled at the same time in two rooms that have a divider down the middle that can be lowered or raised. There are about 26 - 36 students in each co-taught class with two Math teachers. Each of the rooms has a projector and an Apple TV so that a single computer can project to both classrooms, if desired.

The two or three teachers who teach the same prep meet during a joint planning period for two long blocks and one short block each week. Most of us have two preps, so are attending multiple co-teaching meetings. We also try to carve out a few hours once a month or so for all of the co-teaching teachers to meet and discuss how co-teaching is going overall.

Pros:
Many more grouping options are now possible than were available in a traditional classroom setting. We have had some success with differentiated groupings based on support level needed (either student-selected or teacher-assigned) and would like to explore other groupings (theoretical vs. applied, review vs. extension, project topic selected, or just interest in a topic... for example, we recently had a class where students could either be audience members for fellow students presenting on their projects or help generate a proof for an earlier topic we hadn't had time to delve into in depth). We like the idea that students can potentially learn in different ways from different teachers and have more options for who to see outside of class for help as well as choice in their groupings. Peer-peer interactions can also be more rich when there are more options of students with whom to interact and there can be a cohort rather than one or two students with a particular need. Curricula are also much more aligned than they were when classes were taught individually since we're planning so much together.

Cons:
Mainly, the cons are in figuring out how to make the best use of all of the new choices available to us and time to do all of this well. All of the pros above in terms of coordinated planning and differentiated groupings can only be realized with very thoughtful and intentional implementation, which translates into lots of time together... time discussing content/process goals, creating lesson plans, reflecting on those plans, thinking about what work various students did that day and how they received feedback on that work, and how all of these things will inform the next day/week/month.

Next steps/thoughts/questions:

There are so many things left to work out. A big one are the different responsibilities that co-teachers now have and that need to be partitioned: Who will do what during class? Who will take the lead on a particular lesson or do all lessons need to be jointly planned? Who will be responsible for giving feedback to which students and then communicating to the other teacher those student needs and what has been done so far? Who will help to make sure that the administrative stuff necessary for running a class is being done? How will we reflect on co-teaching as a practice systematically in order to learn from this semester and make it better for next year? How will co-teachers interact with each other during class, communicate about changes to the lesson plan, or give each other feedback about the lesson/teaching? And where is all of this time going to magically come from?

One area of huge support has been the hiring of an assistant teacher into our program a few weeks ago. She has already made a huge difference in the level of overwhelmingness we were feeling initially and has been instrumental in being an extra pair of eyes in the classroom, both for student learning and feedback on the lesson, as well as in helping with some of the grading and administrative work. I now understand why co-teaching often involves removing a prep or class from each teacher involved - there is so much more to do now. Trying to do it in addition to full loads for both co-teachers was perhaps a bit rash, and we're so glad to have the extra help now.

Next steps are to make progress in answering some of the questions above, as well as in continuing to play with the various possible groupings to try to harness more of co-teaching's power. It will also be important to get more student input into the process - how do they see this improving their learning and what ideas do they have for creative/new ways of organizing a classroom?

I would love any feedback, suggestions of literature that might be helpful for us, or questions!

Reflecting on yearly goals & moving forward

I've set yearly goals a number of times, but feel like this is really the first year that I went back and reread my plans and made adjustments to actually try to reach them before the end of the year. Partly, this was due to blogging about them, as well as knowing that someone was going to check in with me in October to see how I was doing. Because the online accountability didn't end up being as ongoing as I thought it would be, I want to consciously reflect on my goals and think through what I want to continue doing or change for the rest of the year.

Recap of goals for this year (full post here):

Grading/feedback

• Give back quizzes with feedback only, share the grade later.
• I've been doing this and it's going well. Keep it up! Need to give more time in class to process and correct assessments, discuss with me and others.
• Students must correct original quiz and demonstrate evidence of work/learning done in order to reassess. They may not reassess on the same day. 
• I have not been as strict as I should be on this one. I basically tell them they need to do this, but don't actually check very rigorously. I have way fewer students reassessing this year though so it's not been a lot of work to manage. 
• Teach students how to use feedback effectively. 
• Sort of doing this... in-person meetings with students have been instrumental in my giving of feedback this year. I did a few peer feedback assignments and written reflections responding to my feedback, but need to do it more. 
• Have students self-assess their practices via a portfolio.
• Haven't done this yet, but plan to at the end of the semester. Need to check in with @crstn85, who's having her students self-assess their work on the mathematical practices and provide evidence for each one. 
• Get homework and projects graded more quickly.
• In-person meetings, describe here, have been really helpful with this. I discuss students' recent work with them in person so I am staying pretty current with grading. Definitely way more current with projects, which languished on my desk reproachfully for interminable periods of time last year.

Class culture

• Continue using Visible Random Groupings and whiteboarding.
• Done and done. I merged this with a goal for strengthening student-student relationships by having each daily random group go around answering a question (such as: if you could go anywhere in the world, where would you go? what is your spirit animal? what has been your favorite class this year? when were you last a good friend to someone? what is your favorite movie? etc) Students often give ideas for questions - it's been a great way to get to know students and to build trust and relationships in the classroom.
• Continue my policy of having students volunteer to participate in class discussions, with the caveat that each person must participate at least once or they must start the next day's discussion. In addition, when groups report out, I can call on any member of the group.
• Yep, still doing this and still prefer this over calling on random students. Everyone has to participate at some point, but they can choose when and how, which I think is important for communicating my beliefs about classroom culture and that contributions should be about learning, not for punitive or classroom management purposes.
• Introduce talking points and exploratory talk ideas into class discussions and teach language of argumentation and mathematical discourse.
• Uh, this one I've definitely failed to implement and not sure that I have the bandwidth to add another thing into the mix right now. I'll look over the list before the start of the next semester and plan out some actual activities rather than the vague idea to do this somehow somewhere.
• Continue assigning bi-weekly reflections; include metacognitive questions as well as questions about mathematics and thinking routines/student learning. 
• I have not been assigning longer metacognitive reflections as often as I did last year, but including a few reflection questions on most daily assignments. Definitely doing more questions that ask students to restate concepts in their own words, look for connections, and explain errors or discrepancies more frequently. I haven't really addressed the issue of thinking routines and how they are impacting student learning, other than asking students to reflect on their learning for bigger projects/write-ups. Need to balance the benefits of reflection with students not feeling like they are reflecting all. the. time.

Homework

• Be more intentional about homework: assign fewer problems, spiral it in more intentional ways, and always provide answers in advance and worked solutions from students' own work after we discuss homework in class. Organize homework into Review, Reflect, and Reach. 
• I'm much, much happier with how homework is going this year. I am lagging assignments, which allows class to be more flexible and not feel like it needs to cover a certain amount in order for homework to make sense. There is also more time for students to process and make connections in class before they are asked to do independent work on the topic. I am also seeing more retention since every assignment includes review that intentionally brings in topics that are related or that I think students could use more time with. I would like to assign fewer problems as we are still sometimes spending a lot of time going over questions, but they are good problems to be discussing.
• Ask students to give themselves feedback on their homework. Continue assigning a catch-up day every 2 weeks.
• I have had students give themselves feedback once, need to do it again. I have not had any catch-up days this year because students are able to complete assignments by the original due date since the work load has been more manageable and because they are getting feedback in person. Should definitely have at least one or few times that I ask students to pick an earlier assignment and revise it though.
• I will continue having students turn in pictures of their homework digitally while keeping an organized notebook. 
• I need to put more effort/teaching into students' notetaking. I would like students to take notes and write down questions/ideas/connections. This is especially important since we don't have textbooks so notes are students' only record of what we are learning. I also want to have students write down questions, conjectures, tests, and conclusions more formally - it will be really helpful to show models of actual student work so that students have a better idea of what this looks like. I am giving students time at the end of class to write down summary statements and examples, but need to do this at a few intervals instead of just at the end and give students more tips and feedback on how to do this better. I am providing a rubric for all assignments, but it would be great to have links in the rubric to samples of student work so that students have more specific models. I also need to provide students with models of what formal write-ups look like as well as what an "exemplary" (which is our highest level in the standards based grading rubric) level for each mathematical practice looks like. 

New goals:

• Take pictures during class of work that is going on the whiteboards and post these - still need to figure out an organized way to put up this work so that students can find it easily if they need to review a specific topic and don't remember the date on which we worked on it. I currently provide a list of electronic resources for each topic we are studying - perhaps I can make a second column of links to pictures of our in-class work on that topic. I still need to think about what makes sense here - a chronological order or a topic-based order. One idea is to assign each topic to a student and put them in charge of writing a summary of the topic, including examples, and uploading this to a class online textbook.
• Keep better track of students' progress. I have been doing a lot of discussion and in-person meeting, but not a lot has been in writing or communicated more formally. I am now starting to write down a summary of our in-person meeting with specific objectives listed, such as "review binomial distribution model and reassess on it next week" and then emailing the list of feedback and to-dos to the student. I should make sure to loop in the advisor when appropriate as well.
• I need to have more regular meetings with my co-teachers. I have not been doing a great job of planning together or watching others on my team teach. I wanted to do some co-teaching and lesson study, but in the frenzy of the year, this has sort of fallen by the wayside. I'd like to recommit some time & energy to this in preparation for the second semester to figure out a regular plan for making this happen.
• I need to figure out better ways to support struggling students in my classes. I have been more focused this year on providing sufficient rigor and challenge to students who learn quickly and want to explore more topics, but haven't been addressing as much the needs of students who need more time and to sit with concepts for longer and from more perspectives in order to feel more comfortable with the material. I need to structure classwork and homework occasionally to allow for more differentiation and review/reach, as needed.

Student meetings for formative assessment

This year is going by in a blur, but I did finally squeeze out a few minutes to blog about something that I've tried this year that I'm really liking. Based on a description in the book, "Creating Cultures of Thinking," I implemented something that the book calls Individual Feedback Sessions (I just call them "regularly scheduled meetings," but sure, pick the fanciest name you think you can get away with), which were created by a teacher profiled in the book. His explanation of this strategy is here, but the gist of it is:

1. Schedule 20 minute bi-weekly meeting with each student (he recommended meeting with 2 students at the same time, which I would do if I had a more typical class load). I meet with students before school, during lunch, during their free periods (if they overlap with mine), during tutorial, and after school.
2. Discuss work that the student has turned in during the last two weeks (since the last time you've seen them). Go through their work with them in detail, giving verbal feedback. Either you or the student records a summary of the feedback (I put comments in the online gradebook and ask students to also write some notes in their notebook).
3. Discuss the student's overall progress in the class, how they're doing incorporating feedback from previous sessions, and ask for questions about the content and for feedback on what you can do to support them better. Follow up on any issues that have come up in class with that student.

I have a schedule of meetings posted on the class page so students know when we're supposed to meet. For students who need a bit of an extra reminder, I have an automated email that emails them the day before our scheduled meeting. It is more work. I do have a much busier schedule during the school day as a result with almost no "free" periods. BUT, I do virtually no grading at home (other than quizzes, which I like to grade more quickly than a 2 week window would allow) AND I feel like students understand my expectations, really hear my feedback, and develop stronger self-advocacy and ownership of their learning. 

Grading papers at home by myself vs. interacting with an actual student about their actual work...
You do the math

Doing this has made it possible for me to assign better problems. I have been using IMP Problem of the Week tasks in my teaching for a long time, but every year, after grading a few write-ups, I became quickly overwhelmed by the sheer volume of grading (how the heck do English teachers do it??) and stopped assigning them. This year, I have already assigned four Problem of the Week write-ups for every class. And graded them all with students. And seen tremendous growth in their ability to describe their process and reasoning. Yes, I do think it's a valuable skill for students to learn to interpret written feedback from teachers, and I plan to do some of this in the second semester (perhaps, I provide written feedback first, then we meet and student explains how they understood it). But in terms of actually understanding and learning from feedback, in person conversations are waaaaaay more effective. Especially when I'm asking students to do mathematical work that they are not used to doing (writing about process, explaining reasoning, providing evidence, using formal notation and clearly annotating work, etc). Overall, I do think it takes more time, but it's much more fun for me and results in more learning for students so I think it's worth it. 

As the semester winds down, I am starting to ask students to give feedback to their own work and to the work of their peers so this is definitely not my only model for feedback. And as always, I'm curious to learn more about others' approaches and ideas on this.

Back to School Night

Aaaaaaand, it's a wrap.

Back to school night felt much more chill this year than it has in recent memory. Probably because I talked a lot less and tried to run it more similarly to how I run class with students. We started with a brief intro of me because parents are really curious about that stuff, but then jumped right into a problem I've liked for a long time.



I asked parents to make a guess. Crickets. I made a guess, and that helped break the ice. Once the gridded rectangles and scissors came out, parents got into it. They were finding volumes, realizing that the cut corner had to be removed from both sides, looking for patterns, talking to each other, asking if the corner length had to be an integer, and in general, being great students. When we discussed the need to be convincing, it made sense that a general rule could help with that.

Dum, dum, dum... enter desmos:



We talked about different approaches to this problem and why it makes sense to talk, collaborate, and learn from each other in math class. I used the problem as a way to describe my most common structure for class (problem posing --> intuition --> strategies, collaboration, checking for reasonability, changing ideas --> class consensus --> formalization, showing other approaches --> application to new problem space) and made the pitch that learning that happens in this order is far superior to just skipping straight ahead to the formalization step before anyone's hands have gotten dirty, both in terms of engagement and in the depth and quality of learning that's going to take place.

We talked a bit about content and the sequence of math courses at the school since it's a weird one.

And finally, my favorite slide: what I need from parents (inspired by @fawnpnguyen's back to school night slides, available here)


I'm not sure if this what parents wanted or expected, but it was fun for me! Wish there was a way to get quick feedback from my audience, but formative assessment is severely lacking in the back to school night business. It certainly beats going through a list of content objectives and the grading policy (ahem, what I used to do).

First two weeks of school

It's been a really fun first two weeks of the school year. Yes, exhausting as well, but super exhilarating and exciting too. This year, I started the year a bit differently, focusing more on how I wanted students to work together and think mathematically than on specific content. Because it was the first year I was doing this, I could do the exact same problems with all of my classes. Here's how it went:

Day 1:

• Students came in and saw a seating chart with randomly assigned groups of 3 or 4 and were directed to one of the vertical whiteboards. I wanted to establish this as the norm from the get go.
• Students filled out Google form describing a class in the past they've enjoyed, a class they have not enjoyed, questions that they have about this class, and questions that they have about me. I used the last two prompts as ways to discuss my expectations and structure for the class and to start building some personal relationships.
• Students worked individually for a few minutes and then discussed this problem, which I stole from IMP Year 2. Our first unit will be Statistics for all classes so I thought it would be good to do a fun, but challenging problems, that related to probabilities and ways of counting events.
• Homework was to fill out a Google form asking them about themselves and to keep working on the problem above.

Day 2:

• Students were grouped randomly anew and shared their work on the Tying the Knots problem. We spent the last half of class with group presentations sharing out their progress and practicing how to present and interact with presenters.
• Homework was to write a reflection on themselves as a learner and to start writing up the process and solution for the Tying the Knots problem (I used the Problem of the Week standard categories).

Day 3:

• New random groups, and I used one of @sophgermain's activities for helping students get to know each other. Nothing huge, kids just shared one thing they did over the weekend with their group.
• New problem! This one was incredibly fun. I originally thought that we would take it into proof by induction, but after input from @woutgeo and @hpicciotto decided to stick with a more intuitive visualization of the sequence.
• I basically let students work in their groups without too much guidance from me. Most realized it gave the Fibonacci sequence pretty quickly, but were not able to explain why. Many tried to develop a closed form rule, without much success (surprise, that's actually pretty hard to do). Most groups started trying the extensions, but didn't get super far. I stopped the class a few times and asked various students to explain their group's work. One of my classes this year doesn't have as many whiteboards as I'm used to having, but our desks can be written on so I'm going with that for now.
• Homework was a reflection on their process and feelings when working on these problems and presenting/watching presentations.

Day 4:

• New groups and I answered some more questions about the class and about me. I continued to have them share out a few personal tidbits in their groups as they are still very much getting to know each other (especially the freshmen). Today's questions were about favorite ice cream flavors and favorite movie.
• This was a slightly more structured day. I pushed students to be able to explain why the pattern that was produced matched the Fibonacci sequence. It was helpful to project pictures of their written work and explanations and use that to get more precise and tight in our language. I felt okay adding on to their explanations as needed since there were more extensions to explore (2 by 2 by n case and 3 by n case).
• Homework was to work on the two extensions and to start an integrated review problem set.

Students' work on explaining the derivation of the recursive formula

Some work from the first day on developing a closed form. I was not sure as to whether I should discourage students from going in this direction as finding the closed form rule is extremely challenging. 

More fun student work at the beginning of the exploration.

P.S. @daveinstpaul shared a great follow-up programming project in which students need to write a program to generate all of the possible ways to tile a 2 by n rectangle and then extend it to an m by n rectangle. I'm going to check in with one of the programming teachers tomorrow to see if this might make sense as a posible extension in her class.

P.P.S. A new teacher who I think is going to be amazing visited my class today and I got completely turned around in what I was saying and did not do a great job of moderating the discussion. It's been too long since anyone has observed me, and I just didn't feel comfortable with the kids yet to laugh it off so awkwardness ensued. Bah. We need to be visiting each other's classrooms much more frequently.

Goals for 2015-2016

I find these goal-setting types of posts pretty helpful. Ideally, I will actually go back to this and reread it at some point into the school year. Maybe when we do the #1TMCthing check-in at the end of October? I just reread some of the goals that I had set in previous years and it's pretty hit and miss in terms of how much I actually accomplished. My main concern is that I have too many goals and it's maybe unrealistic that I will be able to accomplish all, but what's that terrible saying that I've seen in a bunch of classrooms that doesn't actually make any sense? Oh yes...

That literally makes no sense. The stars are farther.


Anyway, without further ado, my goals for the 2015-2016 school year!!

Grading/feedback

• Give back quizzes with feedback only, share the grade after class (we will have an SBG online gradebook this year that will hopefully make that easier), as described in this post by @mythagon.
• Students must correct original quiz and demonstrate evidence of work/learning done in order to reassess. They may not reassess on the same day. Still debating whether I want to put a limit on the number of attempts. I thought about making all of the attempts count (with a weight making the later attempts count more), but decided that this is not in the spirit of SBG.
• Teach students how to use feedback effectively. This was from @pegcagle's session at #TMC15 and is my official #1TMCthing that I have publically promised to follow up on this year. One way to do this is to give back feedback mixed up and not attached to assignments and have students in each group try to figure out which feedback should go to which person. Another idea that I want to try is to have students exchange papers and coach each other on what to do with the feedback they received. Last year, I did a bit of peer feedback prior to turning work in to me, with some success. I need to make this a more consistent part of my class.
• Incorporate homework and classwork into students' self-assessment of their practices. Last year, I asked students to do this for projects, but I would really like a portfolio each unit with self-assessment that is more global and includes homework and classwork with linked examples of their work as evidence. This idea is based on a post by @jacehan.
• I really need to get homework and projects graded more quickly so that students are getting feedback at a time when it's still useful to them. I got bogged down with grading big time last year, and I need to be better about staying on top of it. Update: after reading "Creating Cultures of Thinking" a few weeks ago, I would like to set up individual meeting times with each of my students outside of class every 2 weeks (we'll see if the schedule supports this) in order to discuss their progress in the class and go over their projects and reflections with them. One of the ideas in the book that I found really fascinating was that instead of thinking about time as the most limiting constraint, as we usually do, we can instead think about energy... what feels energizing and what feels draining. It might make sense to change something that takes less time, but is draining with something that takes longer, but energizes you. The example given was grading papers at home, which can be exchanged for in-person meetings with students with the paper graded in real time and written feedback accompanied by in-person interaction. I would like to try this model, knowing that it will mean trading off some time, but hopefully, will feel less painful than grading projects late at night.

Class culture

• Continue using daily random groupings and whiteboarding, as described by @AlexOverwijk to increase student participation and engagement. Based on a Twitter conversation with @fnoschese about gender balance in groups, in which he discussed the research that groups in which there are as many or more girls as boys have higher performance outcomes for girls than groups in which there are fewer girls than boys (single gender groups are okay), I will be tweaking the gender ratios in my random groups to help make them more balanced, if needed. But not always. It depends. Basically, it's on my radar, but I'm not 100% sure that gender always trumps other status issues and I really do believe in the overall benefit of visibly random groups.
• Continue my policy of having students volunteer to participate in class discussions, with the caveat that each person must participate at least once or they must start the next day's discussion. In addition, when groups report out, I can call on any member of the group.
• Introduce talking points and exploratory talk ideas into class discussions, as described by @cheesemonkeysf here and as described in a similar Visible Thinking routine called Micro Lab. Teach language of argumentation and mathematical discourse, as described in the Claim-Support-Question Visible Thinking routine.
• Continue assigning bi-weekly reflections as a way for students to reflect on their learning and also to build community and feelings of connection. Move from reflections that are only about learning and affect to reflections that also dig deeper into mathematical concepts and connections. Incorporate reflection questions into daily homework or exit tickets to have more formal processing opportunities and feedback on thinking routines and classroom structures and how they are impacting student learning. 
• Build student-student connections to strengthen class culture. I really enjoyed the activities that @sophgermain demonstrated in her session on restorative justice, which facilitate student-student connections in the classroom. Some examples:
• There are two circles of students facing each other, a question is asked and each person speaks for 1 minute on that topic (examples of questions and topics below), then one circle rotates to a new partner and another question/topic is asked.
• Making one circle for the class and popcorn or going around the whole circle sharing on a particular topic or to give appreciation to someone.
• Have students write their names on a piece of paper, then distribute randomly and each student must write something nice anonymously about the person whose paper they received. Can repeat this multiple times and then return to the original person.
• Ask students to share at the end of a task who was helpful to their learning and how. 

Homework

• Be more intentional about homework. I blogged about this here already, but I'd like to assign fewer homework problems, spiral it in more intentional ways, and always provide answers in advance and worked solutions from students' own work after we discuss homework in class. Homework will be organized into three sections: Review (questions/problems relating to old material), Reflect (processing questions relating to new material, connections between content), and Reach (deeper/harder questions from mostly old material).
• From @bowmanimal's post on homework, I'm going to ask students to give themselves feedback on their homework and emphasize it as a learning tool. I normally tell students to limit themselves to 45 minutes per assignment and then provide a day every 2 weeks that is a designated catch-up day when they are expected to go back to old assignments that were not finished and put more work into them. I will do this more explicitly this year.
• I am still playing around with how I want to handle homework questions. I tried using a Google form, as described by @z_cress, last year, and it was a bit hit or miss. Quite a few students simply didn't do it and of those that did, many filled it out too late for it to be useful in my planning of the next day. In @pegcagle's workshop, she discussed using entrance tickets as a way to assess which homework questions are worthy of discussion and to anchor that day's learning, with questions like, "Which homework problem was the hardest for you? Which homework problem was the most interesting?" I definitely like giving groups a few minutes to discuss homework questions together and asking students to present solutions to problems that many are wondering about or that are especially important, but am still working on how to do this efficiently and in a way that maximizes everyone's learning. I definitely treat homework as a vital part of class, with questions that bring out connections between topics and that preview new content or skills that will be useful in that day's learning.
• I will continue having students turn in pictures of their homework digitally while keeping an organized notebook. I really liked that students had access to all of their work and that I didn't have to track papers last year.

Other

• I would like to emphasize organization a bit more. Ideally (if I can make myself do this consistently), I would like students to create a table of contents at the front and number pages in their notebook. I was reminded of Magdalene Lampert's structures for student notebook writing in @sgnagni's post describing the sections that she had students create (Date, Problem of the Day, Experiments, and Reasoning). For my high school students, I am thinking something like:
• Date
• Questions being investigated
• Tasks/Mathematical Work
• Summary and Reasons
• I would like to continue giving students 5 or so minutes at the end of each class to organize their written work and complete the summary section of their notes. I started doing this halfway through the year last year and students felt that this was very helpful in solidifying their learning, especially if much of their work had been done on whiteboards and they wanted a record of their thinking for that day.
• I will spend more time planning tasks in anticipating student responses and how I will treat them. I did too much of this on the fly this past year, and while much of the time, it went okay, I am starting to see the benefit of spending more time on advance planning. I would also like to provide rubrics for all projects in advance. I did this sometimes and always got positive feedback when I was able to do it.