Last week in my placement classroom students were reviewing counting with base ten blocks and bits. This particular question ask students what is the number, students were then supposed to count the number of ten blocks and then add the bits. Since this was a review many students did not have a problem with solving it. This student solved this problem in a really unique way. Unlike most of the students who counted the blocks in their head. Cindy decided to write down what she knew. When I asked her why she wrote the numbers on top of each image she said it was to help her count them all up. Cindy said she remembered that the long ones where 10 and there were 5 of them so its 50 and then since the bits are worth one she added them on to the 50.
Questions:
1. Are the base ten blocks and bits really help these students learn place holder or has this assignment just become a math problem they need to solve?
2. Could the students still solve the problem if there were a hundredth block?
3. Do the students really know why they add the tens first and then the ones, or do they just perform this action because that is what the teacher told them to do?
I would try to figure these questions out by giving the students some more challenging problems. I feel the students are given tons of problems like the one above. However, would they still know what to do if I decided to challenge them with a hundred block 12 ten blocks and 24 single blocks. This would then require regrouping. To figure out my third question I might do a little interview with a couple of students and ask them why they count the tens first then the ones. From their answer I can then tell if they understand the logic behind counting.
Another question I would ask is if students are making the connection between "regrouping" the ones into tens for convenience...or, as you say, do they simply go through this task as an exercise in counting.
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