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Detracking with Building Thinking Classrooms series: Three Impactful Ways Students Learn Math Together
- Adrienne Baytops Paul
- Jan 24
- 3 min read
In my final year in the classroom (2021-2022), my team and I detracked pre-algebra using Peter Liljedahl's Building Thinking Classroom techniques. I was asked by Illustrative Mathematics to share our experiences in a blog post after having success with their curricula. This series shares excerpts from that blog post, which can be found here, as well as extra photos and videos from that unforgettable moment in time.
To give support to my fellow educators who are currently deep in the BTC work, I'm sharing the experience here--one part of the system at a time.
Trusting Student Collaboration
Learning by Listening
In Building Thinking Classrooms, Peter Liljedahl contends, “A thinking classroom is a classroom where students think independently and collectively.” Even before this book was published, the IM curriculum leveraged this statement’s truth by crafting tasks that invite both individual and collaborative learning to occur. The tasks regularly put the onus of the thinking on students, using prompts like “Explain,” “How do you know…,” and “Why do you think…,” which automatically remove the teacher’s ability to provide a singular, one-dimensional solution.
To amplify this type of mathematical thinking, we continued to use vertical non-permanent surfaces (Practice 3, Where Students Work). Seventh-grade students weren’t initially crazy about standing up in math class, but they got used to it! It was astounding to watch them work together, writing and explaining their thinking, and choosing the most efficient version of a solution. They were often confident enough to explain solutions in various ways by the time we would check in to hear their processes.
Learning by Looking
Just as it was described in BTC, students who were either stumped on a task or could confirm another group’s ideas took advantage of knowledge mobility. Once the students understood that they were not cheating when looking at someone else’s work, an even deeper level of mathematical discourse was ignited. Students’ confidence levels increased because their thinking was being highlighted and celebrated by their peers. One of the most meaningful ways to strengthen a community is to ensure everyone is valued and has something to contribute.
Learning Alone
Despite working in groups most of the time, there was no shortage of individual learning. Students met with us one-on-one to review concepts if necessary, and even during the triad work, individual processing occurred. I recorded one such instance: a group of three students was learning about solutions for systems of equations. All three were involved in the discussion, but I could tell one of them, “Student A,” was still uncertain. When I asked the group whether they understood the difference between the three solution types, they all said yes and Students B and C explained them.
Mrs. Paul: [To Student A], you don’t seem convinced.
Student A: I’m sure, I’m convinced. (I knew he wasn’t, however, so I stayed near the group. About 10 seconds passed, then Student A turned back toward me.]
Student A: So…if the graphs cross [he gestured], there’s one solution, if they never touch, there’s no common solution, and if the lines are the same, the answers are infinite, right?
Mrs. Paul: That’s right.
Student A: [Nods, then turns back to his group]
Student A had gleaned the concept from his partners’ drawings, collaborative learning, and took an additional moment to process and receive confirmation after he’d made sense of the concept in his own way. The BTC structure created this duality, this opportunity to consider the concept from his own perspective and his partners’ perspectives.
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