Things students learn we didn’t realize they were learning.
What do students learn when they are taught only one way to subtract? In this discussion between two boys who are playing a trading card game and need to subtract 347 from 6000, Linda Levi muses on the things one boy learned and some opportunities involving the development of an algebraic understanding of number that were missed:
I had never thought carefully about exactly what we tell children when teaching the standard algorithm until I heard this discussion. When we teach the standard subtraction algorithm, we tell children to start with the ones. Of course, you don’t have to start with the ones when you subtract. For example, in a problem such as 5,000 – 3,002, it makes much more sense to first subtract 5,000 – 3,000 (the thousands) and then subtract 2 (the ones). We want children to know that 5,000 – 3,000 – 2 is the same as 5,000 – 2 – 3,000. Children with a strong understanding of subtraction know that they don’t need to start with the ones. Understanding how subtraction works will help students solve algebraic equations such as 3x – 48 – x = 49 or 3x – 48 = 49 – x….
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