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I have tackled the challenge of implementing Illustrative Mathematics, the Department of Education’s new mandated algebra curriculum, by embracing the pedagogical practices in “Building Thinking Classrooms,” developed by Peter Liljedahl, a professor of mathematics education. “Building Thinking Classrooms in Mathematics, Grades K-12” outlines 14 transformative teaching practices, but of the 14, I’ve found the first three to be the most helpful.

Give rich tasks: Rich tasks require students to problem-solve rather than simply mimic procedures. These tasks should encourage exploration of new concepts while using appropriate math vocabulary. For example, when teaching the similarities and differences between linear and exponential equations, I use a graph of what could be either a linear or exponential function along with a linear equation and exponential equation. I ask students to determine which equation represents the graph and what more they would need to know to make an accurate decision. While some students might argue that the graph is linear “because of the shape and the y-intercept,” others might connect to prior learning by using regression to determine which equation better fits the graph. Since the task is designed to foster discussion among students, it allows all students to come up with a plausible argument without using rote memorization. With rich tasks, I also consider adding scaffolds. For this task, I might color-code the elements of the equations (for example, by making the y-intercept always blue and the slope always green).

Group students randomly in threes: The research behind “Building Thinking Classrooms” indicates that visibly random groups of three work best for collaborative learning. While pairs can be effective for younger students, groups of four should be avoided as they often lead to disengagement, with one student typically off task or hiding within the group. When students are grouped truly randomly, such as by having them draw cards, I’ve found they are more engaged than they are when I decide the groups. Random grouping also breaks down social barriers and creates a classroom culture where everyone learns with everyone. Sometimes students who don’t get along end up in the same group, but even in those cases, I preserve the integrity of random grouping.

Using vertical learning spaces: Students work more effectively when standing at a location where they can collaborate on a whiteboard I’ve hung on the wall. I use reusable whiteboard flipcharts from Wipebook that are tear-proof and have a grid for graphing. When students are standing, they know that their fellow students and I can observe them, and they must contribute to the group. I can walk around the room and analyze all students’ work at a glance. With vertical learning spaces, the level of student engagement is higher.

These three pedagogical practices empower students to be active “doers” of mathematics while positioning teachers as facilitators. They also allow me to devote more time to students who need additional support, assess students quickly and determine student work I want to spotlight.

I recommend checking out Liljedahl’s book “Building Thinking Classrooms in Mathematics, Grades K-12” for more strategies to increase engagement and boost learning.

Daniel De Sousa, a 2024 Big Apple Award winner, teaches math at Business Technology Early College HS in Queens.