Answers:
It is important because the different interpretations will be encountered as they try to apply their knowledge. It's like teaching the use of a comma in a sentence is to separate a list, but then leave out the other uses of a comma. Just knowing how to multiply isn't enough to get an understanding of when to multiply.
So much of school and math in particular is sets of seemingly aribitrary rules. But one of the main points of math is that the rules are, in fact, logical and not arbitrary. So, if students learn that the mathetical operations are aribitrary rules and not steeped in a logical base, it gets very difficult for them to understand math at all. That is to say that teaching more than one interpretation of mathematical operations can allow the students to see the logic behind the operation as opposed to memorizing the "hows"
If I understand this correctly...
- to enable the child to develop a relational understanding of the problem rather than just an instrumental one.
- to empower the child with different methods for solving a problem so that they can choose the best methods from a variety in future.
The Numeracy Strategy is a great example of this. I have to explain to parents why we teach so many methods. They think that it confuses the kids.
If done properly it enables the kids to juggle with numbers in a way that most parents would envy. They tend to understand the problems and choose the methods to solve them that they are comfortable with. Anything that gives them the confidence to tackle a problem rather than pull the shutters down and think - I can't do this - has to be a good thing, don't you think?
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