BOX 5-3
Engaging Students’ Problem-Solving Strategies

The following example of a classroom discussion shows how second-grade students can explain their methods rather than simply performing steps in a memorized procedure. It also shows how to make student thinking visible. After several months of teaching and learning, the students reached the point illustrated below. The students’ methods are shown in Box 5-2.


Maria, can you please explain to your friends in the class how you solved the problem?


Six is bigger than 4, so I can’t subtract here [pointing] in the ones.

So I have to get more ones. But I have to be fair when I get more ones, so I add ten to both my numbers. I add a ten here in the top of the ones place [pointing] to change the 4 to a 14, and I add a ten here in the bottom in the tens place, so I write another ten by my 5.

So now I count up from 6 to 14, and I get 8 ones [demonstrating by counting “6, 7, 8, 9, 10, 11, 12, 13, 14” while raising a finger for each word from 7 to 14]. And I know my doubles, so 6 plus 6 is 12, so I have 6 tens left. [She thought, “1 + 5 = 6 tens and 6 + ? = 12 tens. Oh, I know 6 + 6 = 12, so my answer is 6 tens.”]


I don’t see the other 6 in your tens. I only see one 6 in your answer.


The other 6 is from adding my 1 ten to the 5 tens to get 6 tens. I didn’t write it down.


But you’re changing the problem. How do you get the right answer?


If I make both numbers bigger by the same amount, the difference will stay the same. Remember we looked at that on drawings last week and on the meter stick.


Why did you count up?


Counting down is too hard, and my mother taught me to count up to subtract in first grade.

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