Teaching math through problem solving or inquiry needs a math-talk rich community of learners. A community of learners that is at ease with asking clarifying questions, advancing personal conjectures and awaiting feedback from peers. This is an idea I have advanced elsewhere.
At that point in my thinking, I believed developing a math talk community was essential so that students could freely talk about the math they are learning about. I now believe it is deeper than that. Developing norms around a ‘math-talk community’ is more than just generating discussion. It’s about addressing the ‘math smarts’ status in the classroom and a fixed mindset towards math learning (via Helen Hindle). A mindset that stunts the learner because of an ingrained belief that you are either born smart in math or not, and can’t change anything about it.
My recent thinking regarding the necessity for a rich math-talk community has been influenced by Education Professor Ilana Horn, from Vanderbilt University. Her research explains that perceived “smartness” in math is a status issue that leaves students feeling that only those who are ‘smart’ in math can understand math. Illana Horn argues, unfortunately, that most math classrooms honour the student who can quickly compute and not those who might need more time to think because they are trying to deeply understand how math ideas work and fit together. By making it normal to ‘ask questions’ during math learning, students begin to engage with math ideas as a sense maker. A mathematician.
The desire to share this learning was to provide students with broader and richer experiences with math, which include but go beyond computation. Students need to experience what it is like to be a mathematician. They need opportunity and time for conjecture, sense making, and proving their thinking.
In this post, I will share the process my colleague Ashleigh Mcintosh and I used to develop math-norms for her grade 4 class, to address this ‘status’ and fixed mindset issue. The process was heavily influenced by Illana Horn’s research. For now, a math-norm will be defined as a co-constructed and mutually accepted code of student-to-student interaction, and student-to-teacher interaction.
Please note that I am offering a process, not a procedure.
Step 1: Chart Intuitive Ideas
Talk to students about what makes them feel “happy face” and “sad face” when talking with a partner. The happy face and sad face choice was intentional because we believed it would be general enough to let students provide a more open and perhaps personal interpretation of how they feel. The words ‘happy’ or ‘sad’ might be too limiting.
Provide students an opportunity to talk in a group of three to share their thinking. Then, ask students to share what their partners talked about. Having a student report on their partner’s ideas takes the pressure of sharing ‘what you think’ away and replaces it with an accountability to listen to your partner and develop your own ideas. In time, I have noticed that students replace the “my partner shared…” prompt to a “my partner and I discussed…” prompt.
Chart thinking on a T-Chart. Slowly guide conversation towards how it feels when talking about math. The idea is to build onto students intuitive ideas of how it feels like when there is an equitable exchange of ideas.
Below is the chart of ideas developed by Ashleigh’s grade 4 class.
Step 2: Record Synthesized Math Norms
Group students in pairs to discuss what they deem important from the co-constructed list and re-write it as a statement instead of an observation.
Next, call on students to share what their partner talked about as being important. Chart the ideas on poster paper. Keep in mind that this is intended to be an initial list of norms that the class can add to as they become more experienced within a math-talk rich community.
Below are some of the initial norms Ashleigh’s grade 4 class developed.
Step 3: What do you need to work on?
Again, students talk with a partner to discuss what their own needs might be when working in a group. Refocus the discussion and have students share what they would like to work on, and what they wish a partner might do to help them learn. Chart and record new norms if needed.
Teacher then shares a norm they want to work on.
Ashleigh and I, for example, shared with the class that we as teachers need to work on Helping by asking questions because sometimes we might accidentally take learning opportunities away from our students by giving answers instead of asking questions. To emphasize our reasons, Ashleigh and I constantly referred back to our class constructed T-chart (from step 1). This helped the class and teachers understand how we could help promote discussion and develop a growth mindset in the math classroom.
Step 4: Try it out.
In our case Ashleigh and I devised, in advance, a meaningful fraction question that we would share back to the class in a 3-part lesson format. We then let students work on the problem. As a team, Ashleigh and I walked around the classroom to support students not only with the math thinking but also how to interact with each other using the norms we co-created.
There was a definite buzz to their work as the students attempted to interact with their math partners in a way that they and the class believed would help them learn better.
In one corner of the class Ashleigh and I overheard a student exclaim, “this question is hard!” and their partner quietly explain, “But that’s the point. Feeling stuck is normal so let’s just try to figure it out.”
All Ashleigh and I could do was smile.