Detracking with Building Thinking Classrooms series: All Students Can Contribute to the Learning

Students share their square pyramid, part of a non-curricular task they completed.

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.

Fully Invested in the Process

After nearly two weeks of non-curricular tasks, we introduced a curated version of Illustrative Mathematics’ seventh- and eighth-grade curricula. From our pre-assessment, we learned that students had varied exposure to math concepts (from content-forward exposure to ineptness with grade-level concepts), so we opted to include some eighth-grade concepts as extension tasks integrated into some lessons. At each grade level, IM provided tasks that adequately landed in the zone of proximal development for students to advance to a higher learning level with each lesson activity. We knew that IM’s curriculum gave students multiple entry points into the lessons, so students of all exposure levels could contribute to the learning. Each lesson’s design appealed to students because of the discovery-based problem-solving expectations and probing questions that were similar to those of the previously experienced non-curricular tasks.

Students discuss the "Unusual Baker" task.

Non-Curricular Practice Makes Perfect

Through our consistent use of IM, students learned that justifying their reasoning verbally in their triads was far more impactful than sitting in their seats and working individually. Having access to everyone’s responses on the vertical non-permanent surfaces helped us use evidence of student learning to elicit thinking, as described by NCTM’s eighth Mathematics Teaching Practice. It was another nuance that built agency, classroom culture, and trust. This also deepened understanding by giving students opportunities to observe and analyze multiple solution paths and decide which strategy aligned with their thinking or appealed to their logic. It far outweighed receiving a simple yes, no, check or “x” as feedback about misconceptions. It was differentiation in real-time.

One student shared his perspective with us, highlighting the advantages of working collaboratively:

“I love working in triads. Well, it’s much better than previous methods of learning that I’ve done in the past [where] it’s been like, teachers lecturing me…this year I get to do my own work and work with other people to try to figure out different ways of learning.

Like every day we have new people, and it’s nice to talk with different people about, like solving problems, you know. Sometimes we solve a problem but we have two different methods of doing it, so we can look at those methods and [learn] different ways of solving problems.” 

Several students "huddle," or stand together around the warm-up task, collaborating to make sense of the math.

In keeping with BTC Practice 6, When, Where, and How Tasks are Given in a Thinking Classroom, we required our students to stand or “Huddle up!” during the launch as they worked through instructional routines like “Which One Doesn’t Belong?” and “Notice/Wonder.”  After reading the learning goals of the lessons and the launch, we asked “What do you think the lesson will be about?” or asked them to look for the connections between the launch and the forthcoming lesson to further analyze the task and its intent, piquing the students’ interest.