I am always thinking about new ways my students can develop a growth mindset in the mathematics classroom. A safe learning community is by far, a non-negotiable in my classroom. Students are not put on the spot or randomly called on. Solutions, given by willing participants, are dealt with carefully and respectfully, without me calling out the error in front of the large group. As such, as I was reading different math blogs last weekend, I came across the interview grid.

In the interview grid students are asked to develop a thought around a math problem/practice. Then they interview and record two other students in the classroom. As they re-tell their thoughts to another person, they can keep evolving their own ideas based off of what they are hearing. After the two interviews, they return to their own thoughts and write their current thoughts around the question.

I absolutely loved this idea and wondered how it could be used and what problems it would naturally lend itself to? I knew I needed a question that was short enough to interview in a few minutes and also had deep enough conversation for my 6th graders. As I was teaching decimal division, I came across Illustrative Mathematics’s task: Reasoning about Multiplication and Division.

This was an important task to me because during number talks, I have been noticing that my students often use faulty reasoning. For example: 210 divided by 3. They will say, “I took away the 0 from 210 and made it 21. I divided 21 by 3 and got 7. Then I added the 0.” Though they clearly got the correct numerical answer, their reasoning was not mathematically sound. I wanted to focus on precision of language and focusing on identifying the math.

During this task, students used the equation 13 x 17 = 221 to decide upon solutions for related expressions. As a class, we began with 13 x 1.7 I asked students to do the following:

- Provide a solution
- Tell how the current expression connected (mathematically) to the originial expression
- Use the above to justify the solution posed.

Eventually, after interviewing,etc. We started to get examples like this (Minus the peer interviews but with before and after thought):

What I noticed was after the interviews not only did many students ideas transform based upon the convincing arguments by their peers, but they also were using much clearer language. I also started hearing students speak using mathematical terms rather than hiding the math with learned procedures and algorithms.

Finally, I noticed that the level of engagement was incredibly high. Students were very willing to share and evolve their ideas based on logical arguments. They enjoyed the opportunity to interview others and write down their ideas without judging them or trying to change their statements. The point was only to share one’s ideas not to question the ideas.

The only con to this task was how time consuming it was. In one period we got through two rounds of interviews. I wondered how students’ ideas would develop for the other questions posed in the task and knew that I didn’t have enough time for students to go through this process will all tasks. Stay tuned for Day 2 (next week) to see how I wrapped up the thinking.

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