Footnote 1
Eva has used the fact
that 3 + (1 + 4) = (3 + 1) + 4. That fact is an example
of what is called the associative law: a + (b + c) = (a + b) + c
regardless of
what numbers a, b, and c are. I doubt that Eva has ever heard of the
associative law.
And although she certainly cannot state that law in its full
generality, it is clear that she understands it.
Word problems and model making come first. It is a mistake to first
teach children
the abstract associative law with the expectation that they will then
be able to apply the law to solving problems.
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