Student Documentation Panel

Analysis:

G.'s thinking on this problem shows that he is able to add two single digit numbers. His chosen strategy is consistent with a pencil and paper direct modeling strategy, as defined by Carpenter, Fennema, Franke, Levi, and Empson (2015). After drawing his chart and counting the one's present in the problem, I asked him about bundling. We had covered bundling as a class and G. typically bundles when adding multi-digit numbers. G. circled ten on the small dots in the one's place on his chart. This tells me that G. understands bundling but does not use it as a strategy.

Analysis:

G. was not successful in solving this join change unknown problem. Instead of finding the number of toy cars Robin received, G. found the sum of the two values in the problem. The misconception seems to lie in G.'s comprehension of what the problem was asking. Upon reviewing the recording, I believe I could have done more to facilitate his understanding of the problem. At the time, I did not assist G. in comprehending the problem because I wanted to see what he can do. His inability to comprehend the problem makes me wonder about the rest of the class's ability to comprehend join change unknown problems.

Analysis:

G. also had a difficult time with this join start unknown problem. He approached the problem using an equation, which he set up correctly. He then attempted to use the tape diagram strategy he learned this year, per the Engage New York mathematics curriculum. As can be seen in G.'s work, he does not fully understand how to use tape diagram. When used correctly, a tape diagram illustrates the relationships present in the problem; making it easy for students to intuitively understand how to solve the problem. For example, a tape diagram for this problem would look similar to G.'s but have 28 in the large tape strip, and the question mark in one of the bottom tape strips. G. puzzles over the incorrectly set up tape diagram for a while before admitting he was stuck.

He next attempted to solve the problem with a direct modeling strategy. In the recording G. can be heard asking about using blocks to solve the problem. When he could not find enough blocks, I asked him to draw what he would do with the blocks. Drawing the little squares took a significant amount of time. Then G. had to decide how to take out the 16 cars Robin got for her birthday. To do this, G. chose to erase 16 squares. However, he did not count the squares before he started erasing. When he realized he had erased too many, he stated the remaining squares were the solution instead of recalculating what he had done.

While it was initially clear G. comprehended what was occurring in the story problem, he had a difficult time arriving at a solution. The class will be covering subtraction more in depth in the next couple weeks, which should help G. solve problems similar to this one.

Analysis:

This separate result unknown problem was easy for G. to solve. He utilized a direct modeling strategy, which entailed drawing squares for the initial 13 pencils and then crossing off 4 squares to symbolize the pencils given to Fred. However, as G. is in second-grade, he should no longer rely on direct modeling for subtraction problems less than 20. This work is an improvement from where G. was at the beginning of the semester, but he is still not performing at grade level.

Analysis:

This problem was also easy for G. to solve. For this problem, G. connected the relationships in the story problem to the relationships in the previous problem. G. noted the problems contained the same values, which allowed him to use the work that he had already completed.