Digging for Student Understanding

[By the way, welcome. I’m trying my hand at blogging again. I have a semi-defunct reading blog (A Need to Read) but these days I find myself itching to share my math teacher life. Here it goes.]

I’m a devout math-teacher-blog reader. I recently read this post by Joe Schwartz, which is mostly about looking for the truth of what students DON’T understand. I think it works the other way too… looking deeply into student work that is, or looks, incorrect to see if there are truths that students DO understand.

Check out this photo. It was breakfast time and I said, “Do something useful with your brain.” Kids were reading, using wrap-ups to practice multiplication facts, and working on compare/contrast essay revisions from last week. One little guy decided to do some desktop multiplication.


At first glance, I thought – he clearly missed our lesson on using the associative property to make 5 x 90 into (5 x 9) x 10. But then I looked closer, and asked him to explain.


He explained that he knew there were groups of 10 inside 90. So he decided to do 5 x 10 and then count that amount 9 times. Can you follow his work? (Hint: look for his numbering of the groups… the small 1 at the top, the 3 next to 100 + 50. Also read his columns from right to left.)

Do we have some work to do around organizing our work? Absolutely. (Probably also writing numbers neatly because those squiggles to the left of 300 and 350 say “6” and “7.”) But does this student understand base ten, the idea of multiplication, and how to solve a problem using multiple strategies? Absolutely.

Here’s another one that took some digging. Different kid. Check out his work.

img_7706Again, we have some work to do around showing our thinking clearly. But look at what he knows. Can you figure out the strategy he used? (Sorry I cut off his answer to 10 x 12. That’s where the 120 in his subtraction equation comes from.)

As my math coach friend says, “KIDS CAN THINK.”

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