Years, ago, schools taught the commutative property (e.g., 4 x 3 is the same as 3 x 4) and also the associative property, both in a very abstract way. There is, of course, no real reason to have the children become familiar with these terms, but we do want to look for opportunities for them to discover the principles behind this in the context of the second grade Waldorf math classroom. For the children, 5 x 3 (i.e., five groups of three) is a very different process than 3 x 5 (i.e., three groups of five). Likewise, 2 + 6 is a different process than 6 + 2, yet both yield the same sum. This can be an exciting “aha!” moment for the students when they discover for themselves that they can switch around the two numbers being multiplied or added and the result will be the same. The above is excerpted from Making Math Meaningful: A Source Book for Teaching Math in Grades One through Five. It is important to read: “Thoughts on Teaching Math in the Lower Grades” at the beginning of the book, for important background information on Waldorf pedagogy and math.

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