The reason for the critical need of a definition of similarity is that a working knowledge of similar triangles is absolutely essential for students to achieve algebra. Without this knowledge, they would have no hope of understanding the interplay between a linear equation of two variables and its graph, which is a major topic in beginning algebra.

So, why do you think that is?

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## 5 comments:

I think that similar triangles and slopes of lines are closely related, but that there is no intrinsic reason to believe that one must be learned before the other.

What do you suppose Wu is getting at, then?

I think Wu speaks like many mathematicians who think that K-12 math should be taught like graduate mathematics. Instead of doing mathematics like mathematicians do math. Looking at examples of similar figures and non-similar figures will lead to informal descriptions. Solving problems will lead to the nead of a more robust definition. Thinking like mathematicians will lead to forging a precise definition.

To me, slope is related through the power of ratio. Since both similarity and slope are examples of the extraordinary power of a constant ratio, you can set up many examples where the ideas overlap.

I'm curious as well to the connection. Could you email him? I clicked on one of his references in the handbook and got to his homepage,

http://math.berkeley.edu/~wu/

, which lists his email. Or if you're really daring, you could CALL him.

I double dog dare you.

Paul Hawking

Blog:

The Challenge of Teaching Math

Latest post:

Teaching factoring quadratics when a>1

http://challenge-of-teaching-math.blogspot.com/2011/03/teaching-factoring-quadratics-when.html

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