Allowing our students to talk to each other about mathematics is very important in today’s educational culture. Gone are the days when students sat in rows quietly working on repetitive worksheets. Instead, we want to hear what students are thinking. How are they processing information? What do they see as important? What solution pathways are they following? Are they able to generalize and take what they learn from one situation, and apply it to a new situation? Students learn from hearing each other’s unique perspectives in solving problems.
Here is the best part… we as teachers learn a lot as well! As we listen in on those same conversations where students are changing one another’s perspectives, we get an insight that we never had before. Our students are learning to verbalize their thinking and we get to take full advantage of that through our professional noticing.
I thought of this as I listened to a 3rd grade student explain her thinking on a subtraction problem she had solved incorrectly. The problem was 70 – 36, which she solved as:
70 – 36 = 46
I have to tell you that when I saw the solution, I assumed that she hadn’t been sure how to subtract the ones place. It can be confusing to regroup with zero in the ones place for students. I thought she had subtracted up: 6 – 0 = 6 in the ones place, and down 7 – 3 in the tens place. But I was wrong! As I listened to her explanation she said,
“I knew seventy take away thirty was forty, but then I thought I needed to add the six to the forty. Now I see that I needed to take away the six from the forty, so the right answer is thirty-four.”
I was blown away by her thought process. This brilliant little girl had broken the number apart in her head and had subtracted (and added) the number in parts! Once she was able to talk it through with her partner, she had even analyzed her own mistake. I couldn’t help but think how little I would have learned if I had just seen the problem and solution on paper. I realize now how much more conversation I want to have with this student, now that I had the opportunity to hear her thinking.
As we attend to our students’ problem solving abilities, it is a gift to get to hear their thinking out loud. It helps us to interpret where they are in their journey through the mathematical curriculum and better enables us to decide where we want to take them next.