December 2025

Transitioning to a problem-based curriculum can feel intense. I was excited when my district adopted CPM. I love the way CPM builds math concepts with rich problems, but I was also concerned with the new task of motivating students to collaborate. 

During the first year of implementing CPM, students were initially resistant to working together and expressed frustration that they were not given examples of solutions to guide them. They believed that a good math teacher is someone who explains a math problem so well that they can repeat the same process on another, similar problem. They did not understand that they weren’t really learning math, but instead memorizing steps to solve problems that looked just like the examples. Students said that they felt cheated that I wasn’t explaining the math concepts, and continually complained that I wasn’t teaching them. 

This shift in classroom expectations made students resistant to working in teams. They claimed that the problems were too difficult for them to answer without me showing them what to do. I incorporated team roles and study strategies, but still, students would not talk to each other. 

Turning on Engagement with CPM’s Thinking Problems

To increase engagement, I decided to try the first three practices from the book Building Thinking Classrooms in Mathematics by Peter Liljedahl: I had students work on thinking tasks on vertical non-permanent surfaces in random groups of three. Incorporating these practices was easy for me since every CPM lesson is full of thinking problems, and I already had enough whiteboards around my room. 

The change was instantaneous! Overnight, students who had not even tried to work were talking with their team members and answering questions. At first, I was selective about when students worked at the whiteboards, until I realized that students weren’t thinking unless they were at the boards. Their brains seemed to turn on as soon as they left their seats.

At the beginning of class, students sit in teams of four. This serves as a home base for the students and gives me a seating chart for attendance. At the beginning of the lesson, students each draw a card and join a new, randomly assigned team of three at the whiteboard. Sometimes I will introduce the lesson before I pass out the cards, other times I will wait to give directions once students are at the board. One student will grab a book and read the problems to the team, then the team will discuss the lesson problems and write the answers on the whiteboard. Teams often work at different paces; some will answer most of the questions in the lesson, while others will only answer the core problems. 

I love hearing my students discussing their work, and I can easily see their work on the whiteboards instead of continually peering over their shoulders to look at papers. On the whiteboards, students can view the same work simultaneously, enabling them to have rich discussions. Students will also look at the work on other team’s whiteboards, which helps knowledge spread. The best part of this process is that they are seeing each other as doers of math and not always looking to me to confirm their thinking. 

Keeping the Goal of the Lesson in Mind

I fully enjoyed watching my students at the whiteboards. The problem I encountered, though, was that the students did not save a record of their work. I started taking photos of their work and sharing them in our Google Classroom. However, students did not find this useful.

I watched teams solve problems, make connections, and achieve the lesson goal. However, the next day they didn’t remember what they had done in the lesson—students were forgetting what they learned. I displayed pictures of the whiteboards from the day before, but that didn’t work. I believe this happens because from the student perspective, they just worked on a bunch of problems and found answers. They didn’t know what the goal of the lesson was and they didn’t know whether they met it.

To solve this problem, I make sure that we have a quick class discussion during the last ten minutes of class. At the ten-minute mark, I have students put all supplies away and take out their note sheets. I will quickly point out interesting work I see on the whiteboards and then I will write out a problem that encompasses the goal of the lesson and ask the class to tell me how to solve it. Students are usually excited to tell me what to do because they know what to do. Students also write the problem and the steps on their note sheets. I will also highlight any vocabulary from the lesson that students should add to their notes as well. This process helps students understand the goal of the lesson, and they have an example to look at later to help trigger their memory. 

There are occasions when one class will run out of time and not have a chance to discuss the goal at the end of class. The next day, the same class will have trouble answering a warm-up question on the topic, while the other classes have no trouble answering the question. This is evidence that the process works. I find this so interesting because all classes discuss the same problems, but students won’t transfer the information into knowledge without knowing what is personally important. 

I recently read something that might explain this in Visible Learning for Mathematics. John Hattie researched the effects that different teaching influences had on learners. The teaching influence of self-reported grades and student expectations is the highest ranked influence of those investigated by the author.

“When we think about it, though, it’s hard for learners to know whether they are learning something without having some criteria against which they can measure themselves” (pg 57). 

Measuring and Maintaining the Math Learning 

Having the class work on one last problem together with me gives them a criterion to measure their learning for that day and helps them transfer the information into knowledge. 

The process of discussing a problem as a class also helps to fill in any gaps individual students might have had during the lesson. The work I see on the boards and the discussions I hear from students have been coming from the team as a collective. Just because the team can answer the questions doesn’t mean each student can. So, it’s important to give all students the chance to put all the pieces of information from the lesson together by summarizing the lesson goal. 

Something important for me to remember is that every year I must rebuild my thinking classroom. At the end of last year, classes were running smoothly, and students were doing an excellent job thinking. Now that it is November, I need to remind myself that it took a long time to build a thinking classroom last year and that students usually start to push back against working in teams in October and November, when the novelty of working at the boards starts to wear off. But, if I continue to use the Building Thinking Classrooms practices, they will continue to build their thinking skills, and eventually, I will have built the thinking classrooms I saw last year.  

Sources

Liljedahl, P. (2020). Building thinking classrooms in mathematics: 14 teaching practices for enhancing learning. Corwin. 

Hattie, J., Fisher, D., & Frey, N. (2017). Visible learning for mathematics: What works best to optimize student learning, grades K–12. Corwin.