Implementing Building Thinking Classrooms with Students with Learning Differences

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. Here's the original presentation, and now let's get into the unpacking.

Part 1: Why students with learning differences benefit from a BTC approach

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.

Part 2: Adjusting the first toolkit (what, where, and who should students work with)

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 sentence starters were helpful for getting students to work together with greater focus and engagement.

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. 

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 visual patterns, estimation 180, fraction talks, slow reveal graphs, and which one doesn’t belong. 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 thin slicing 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 worked example à la Michael Pershan 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.

Part 3: Adjusting the second toolkit (teacher moves to start and maintain flow)

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. 

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 questions to ask yourself if you're feeling stuck and I frequently refered to these when checking on progress. 

We also spent time early on practicing several of the routines from Routines for Reasoning (book, website). 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. 

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 Avery Pickford, but a quick Google search shows that a few others have blogged about it - here's 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.

To promote student autonomy, I relied heavily on collaboration rubrics 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. 

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).

Part 4: Adjusting the third toolkit (moving from collective to individual knowing)

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 whole other post on consolidation, 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. 

I also started using the 4 R's strategy from Routines for Reasoning (more here). In this strategy, a student shares an observation or summary and the teacher follows up by doing the following:

Repeat = ask someone to repeat what was shared (this helps to ensure that everyone heard)

Rephrase = ask someone to restate in their own words (this helps to ensure that everyone understood)

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

Record = annotate (add notes and vocabulary words, circle key components, and otherwise create a written record of what was shared)

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.

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. Here 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. 

I got this idea from Sara VanDerWerf, who blogged about providing reference sheets to students here. 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). 

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. 

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.

Part 5: Adjusting the fourth toolkit (grading aligned to values and to inform students)

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.

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: 

1. Turning work in on time, checking answers, and revising errors, if possible
2. Seeking out challenge, persevering, and asking for help
3. Coming to class on time and with supplies, staying engaged and participating in class activities
4. Collaborating with other students, giving constructive criticism, supporting a positive class culture

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:

1. The goal I have been working on is... 
2. I have or have not made progress on this and my evidence is... 
3. My next steps are... (continue working on previous goal or set a new goal and how you will try to reach it)
4. Pick one and delete the others:
1. Something that’s going well recently is… 
2. My teacher/parents can help me by…
3. I’d like Anna to know that…

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. 

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. 

References:

• “Teaching Mathematics Meaningfully,” Allsopp, Lovin, and van Ingen
• “Routines for Reasoning,” Kelemanik, Lucenta, and Creighton
• “Dyscalculia Pocketbook,” Hornigold
• “Can I Tell You About… Dyscalculia,” Hornigold
• “11 Effective Strategies for Teaching Math to Students Who Have Given Up on Learning,” Smith

If you got this far, kudos to you! Please feel free to connect with me on here or via Twitter or Mastodon.