Every student is capable of deep thinking and problem-solving in math. Yet, sometimes after a carefully planned lesson, I’d watch my sixth-graders file out the door and wonder, Did they get any of that?
About 18 months ago, I learned about Peter Liljedahl’s book, “Building Thinking Classrooms in Mathematics.” When I started reading it, I was amazed at how well the author’s observations in different math classrooms related to my experiences.
Liljedahl explained in a research summary: “In every classroom I visited, I saw the same thing — students not thinking in ways that went beyond mimicking the teacher. Closer investigations revealed that within a 60-minute lesson, 20% of students spent 8 to 12 minutes thinking, while 80% spent zero minutes thinking.”
That really hit home. I often implemented the “I do, we do, you do” instructional model. I realized that when students practiced on their own, most simply replicated what I did; they weren’t thinking for themselves.
As I read through Liljedahl’s 14 teaching practices to enhance learning in mathematics, I felt like they were solutions to the challenges I saw in my classroom and in the classrooms of the teachers I worked with. I appreciated that I could apply these practices right away. To me, that’s the best kind of professional learning.
Last school year, I made several changes to transform my room into a thinking classroom, and I’ve continued these practices because of the positive impacts I’ve seen.
Implement curriculum materials that support active, collaborative thinking
One change came as the result of my school district’s decision to adopt a new math curriculum. For several years, we had implemented teacher-created lessons. Even though we all used the same lessons, it was difficult to keep everyone at the same level of rigor. It was also time-consuming to differentiate for individual students.
To make math instruction more equitable and rigorous, our district reviewed several programs, piloted a few, and then adopted Carnegie Learning’s Middle School Math Solution. Even though we weren’t specifically seeking something to support the Building Thinking Classrooms approach, the curriculum’s focus on student-driven learning turned out to be a great fit.
Together, the curriculum materials and Liljedahl’s framework have allowed me to create a safe learning space where all students actively engage in collaborative work. I have immediate access to problem-solving tasks that get students curious and creative and thinking and talking about math. Using an AI platform that’s part of the program, students can also work through problems and engage in productive struggle while receiving one-to-one coaching.
Form groups to help students build conceptual understanding
In his book, Liljedahl described how forming “visibly random groups” helps students enter group work with the mindset that they will think and contribute. In my classroom, I’ve found that these groups capitalize on students’ strengths. Even struggling mathematicians shine because each learner brings something different to the table, and students can ask and answer questions to help each other grow.
For example, a student who struggles with a skill might serve as the group’s notetaker for the lesson. The notetaker will listen to their peers talk through their ideas and ask clarifying questions, such as “Is this what you mean?” or “Can you say that in a different way so I can better understand?” These interactions have worked wonders for building students’ understanding and confidence and for reinforcing their learning.
Organize the classroom to foster engagement, participation for all
I used to do the majority of my teaching from the front of the room. Students would be in their seats, often just mimicking my instruction and examples versus truly learning. In a thinking classroom, there is no “front.” In his research, Liljedahl found it was better to have students standing and working on “vertical non-permanent surfaces.”
My students now work in groups at whiteboards, which keeps them thinking and engaged. While they work, they’re expected to stay with their group, collaborate, share one marker, erase with care and ensure that everyone understands the work being done in a way that they can explain it to me.
Here’s an example of what this type of learning looks like in my classroom:
After completing a whole-group warm-up activity and reviewing expectations, I assign students to random groups and give each group a task from our math curriculum. (I like to use tasks that either build off of previous skills or allow students to create connections to further develop more complex concepts.) The task is printed on a piece of paper and hung on their whiteboard.
We have developed the algorithm for dividing fractions by creating models using real-life scenarios: Mason has two-thirds of a foot of ribbon. He needs to divide the ribbon into one-sixth-foot pieces. How many pieces can he cut from the ribbon? Create a model to represent the situation, and then answer the question.
Students discuss ways to get started and determine who will start with the marker first. As they work, they question each other, confirm ideas and evaluate reasonableness. Because they can easily erase their writing, they’re comfortable jumping in with ideas and changing problem-solving strategies as they go. I circulate to groups, ask open-ended questions to keep them thinking and engaged, and provide nudges for those who may not be as engaged. If students have a question, I answer it with another question or ask them to visit another group to gain insight. Students are each other’s best teachers!
When a group finishes, I randomly ask one student to explain what they did and ask clarifying questions to other group members. If someone can’t answer, I ask them to discuss and then come back to them. Because groups often finish at different times, I also have an extension activity or independent activity ready. When everyone is done, I then bring together the whole group to consolidate the big ideas of the lesson.
I must admit, there were some days we didn’t do vertical learning last year because I was still familiarizing myself with our new curriculum. The difference, however, was like night and day. Doing things the old way was boring. When students were working at the whiteboard, their engagement was sky-high.
Building confident, engaged mathematicians
Thanks to these changes, my students have gone from passively sitting and getting to actively taking control of their learning. They’re approaching tasks and applying their knowledge in new ways.
They also feel more comfortable taking risks. If they try something and it doesn’t work, then they’ll try something different. They’re also building grit. When they encounter a challenging problem, their walls no longer go up; they know they can work through it. As a result, my students said they felt more confident tackling problems on their state test this year.
My classroom is now driven by student discourse. Students routinely use the language of math, and their vocabulary is way beyond what I’ve seen in prior years. For example, when dividing fractions, students no longer say, “Keep, change, flip.” Instead, they say, “multiply by the reciprocal.” Or when working with ratios, they say we’re “scaling up” or “scaling down” instead of we “times-ed” or “divided.”
Because students are at the center of the learning process, I feel like some pressure has been taken off of me. Instead of spending most of the day talking, I now act as a facilitator. I also no longer have to spend hours on differentiation since students get personalized support in our curriculum program and from each other.
These positive impacts are only the beginning. This school year, all of our middle- and high-school math teachers are reading Liljedahl’s book, and we’ve begun incorporating some of the practices into our professional development. If it were up to me, I’d build thinking classrooms in all of our schools because they can benefit every student.
Opinions expressed by SmartBrief contributors are their own.
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