Updated: Feb 12, 2020
When one thinks about the math classroom, the words “community” and “leader” are probably not the first words to come to mind. It’s probably “endless practice problems” or “equations.” The purpose of math should not be about compliance or about memorizing a set of procedures. It should truly be about thinking, learning, and problem-solving.
The key to success in math learning is to demystify the often held perception that it’s a subject all about algorithms and formulas to be memorized, and instead to illuminate it as a problem-solving adventure full of opportunities to identify patterns, critique with peers, and justify your thinking. Additionally, questioning should be the foundation for math instruction.
Unfortunately for the math classroom, many times the questions originate from only the teacher in a whole group setting. This practice further exacerbates the perception that the math classroom has looked the same for decades now with the only difference being the use of slides or whiteboards to model problems instead of the overhead projector.
To make math meaningful and self-directed, students must own the math and the discourse that happens in the classroom. Instead of the teacher being the sole questioner, cold calling students to answer questions, students must be the question and conversation generators.
The teacher should only guide from the periphery of the conversation and help students clarify the thinking of others.
Student questions should revolve around the “why,” justifying and contrasting the strategies used and not just center around “what answer did you get?” Being a math leader means a student’s thinking and the thinking of their classmates are important, therefore student conversations should go beyond providing answers when asked. Math classrooms with high student leadership are evidenced by students defending, debating, and justifying their thinking with a little nudging from the teacher.
How do we create this kind of classroom, where students are shaping their own mathematical thinking?
We first begin by creating a classroom culture that’s safe, positive, and inviting.
This culture must also support students as problem solvers, questioners, innovators, and risk-takers, embracing mistakes as opportunities for growth. Building a positive math community in your classroom is ongoing and must continually be nurtured by the teacher.
Provide students with multiple opportunities to create their own visual representations.
Many students will tend to use the strategies the teacher just modeled. Remind students there are many ways to represent math visually through models and drawings, and as math leaders, they have the opportunity to describe and justify their drawings to others.
It’s also helpful to provide question stems or discourse starters for students, otherwise, students aren’t exactly sure how to lead conversations.
Below are some examples of discourse stems that generate conversations focused around shaping mathematical thinking:
- What is your interpretation of the math problem?
- Do you agree with me?
- Do you disagree with me?
- What are you wondering about?
- You arrived at the same answer but got there in a different way. Would you share your strategy?
- Can you explain that in a different way?
- Can you show me your visual representation of your strategy or solution?
- What decision do you think she or he should make?
- What is alike and what is different about your method of solution and his/hers? Why?
- How does this relate to yesterday’s lesson?
- What ideas that we have learned before were useful in solving this problem?
- What problem have we solved that is similar to this one? How are they the same? How are they different?
- What uses of math did you find in a YouTube video or TV show last night?
- What did you learn today that was new or surprising?
- How would you approach this differently next time?
Once students become accustomed to the process of student-to-student discourse, they will begin to generate their own questions.
As teachers, we’re continually supporting student conversations, listening for great examples of high cognitive level questions (like those above), and asking students to share summaries of their conversations with the rest of the class.
When students become the math leaders, they make sense of math, own their learning, and see the opportunity for creativity and fun in every math problem, task, project, or scenario.
How can we empower students in our math classrooms to ensure they are owning their learning? Please share