Chapter 5 shows some very diverse thinking when it comes to multiplication. When reading Eleanor’s case I found it interesting than none of the children used the standard algorithm to multiply 27x4. A lot of the strategies are very conducive to mental math. I thought it was interesting how Mark changed the problem into an addition problem by adding all of the 20’s and then four 7’s. I also thought Mika’s interpretation of 4x25=100; 2x4=8; 100+8=108. She is basically using the distributive property by solving this way. These strategies as well as using the arrays in Lauren’s case study were much easier to understand for student than using the standard algorithm as seen in Susannah’s case. Some students tried to follow a procedure rather than really understanding the math behind multiplication. An example of this is:
1
49
x 2
108
In this case the student “carried” then 1 and added 4+1 to get 5 and multiplied 5 by 2. This use of a familiar procedure proved detrimental because she made a small mistake that lead to an incorrect answer.
When reading Lauren’s case an issue came up for me. She was troubled by the language students were using when they multiplied by a multiple of 10 (4x20=60). The students would have explained that 4x2=6 and you “add a zero.” I find this language to be a bit troubling as well. I think the concept is very important, especially to doing mental math, but I wonder if there is a better way to describe the mathematical processes that are actually occurring.
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