Student Strategy : Student A Falls Within The ' Direct Modeling ' Framework

2413 Words Jun 11th, 2016 null Page
Student strategy: Student A starts by drawing 11 circles, which is what I saw. When asked to explain what he did, he said that he first drew 2 circles and then 9 more. He then added them together by counting them all to get 11 pennies, which is the answer. When solving the problem, he adds them by counting from 1 to 11, and he seems to have drawn 2 circles and then 9 more, following the time sequence. However, I never saw him count 2, 9, and then all of them, I only saw him count 1 to 11. Placement within Carpenter’s framework: Student A falls within the ‘direct modeling’ framework. Student A had a one to one correspondence with the circles and the numbers in the problem. He drew 2 circles to represent 2 pennies and then drew 9 circles to represent 9 pennies. He then added all the circles up starting with the first circle, showing that he does not have quotity. He also followed the time sequence of the story problem by first drawing 2 circles, then 9 circles.

Student strategy: Student B uses his fingers to count on from the larger number in the problem. After he heard the problem he mentally held the number 9 and then counted on. Using his fingers to count to 5, at the same time he counted on from 9, adding 5 more, to get to the answer of 14. Student B was double counting as he solved this problem.

Placement within Carpenter’s framework: Student B falls within the ‘counting’ framework. Student B was able to mentally hold the number 9, which shows that he has…

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