I discover a lack of number sense is really a lack of base-10 understanding.
At the end of our last session, I decided that I wanted to find out more about what the children understood about groups of 10 and base-10 concepts. I had a hunch that what seemed like a lack of number sense for some of them was in fact little to no understanding of base-10 concepts. Each of the problems for this session was designed to assess and help develop base-10 understanding.
Most central to base-10 concepts is understanding 10 as a unit. Children who understand 10 as a unit find the Valentine’s Day problem easy; those who do not, find this problem just as difficult as any other grouping problem (e.g., they would solve 4 groups of 7 in the same way as they would solve 4 groups of 10).
Emilio’s thinking about the Valentine’s Day problem — in contrast to his strategy last week — showed no base-10 understanding. First he interpreted the context to mean he should add 10 and 4 to get 14 rolls altogether. After questioning him, unsuccesfully, about why he added, I described a context where he was the candy maker and had to put 10 candies into each of 4 boxes. The librarian helpfully handed us a roll of sweet tarts to help Emilio visualize the 10 candies to 1 roll relationship. I then left him to solve the problem and he solved it by modeling each box with cubes (arranged in a squarish shape) with 10 single cubes on the interior of each. He counted his answer by twos and got 40.
Success, of a limited sort then: he used his knowledge of the context to construct a solution. But he didn’t use any of the knowledge of 10s that was in evidence last week.
The other children performed similarly. I have a hunch that much of their current difficulties in math may be traced to under-developed knowledge of 10 as a unit. I decide that we will focus on developing this understanding over the next few weeks. At the same time, because of the nature of my work with them, these children will also be working on developing strategic competence and productive dispositions towards math.
Posted in Case Study: Four Second Graders, Emilio, Uncategorized | Comments (0)
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