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Notes for Session 9, Part A

Note 2

In this session, we'll be exploring a structural approach to algebra. When we begin to think about properties of operations rather than of numbers, we're moving from arithmetic to algebra, in a structural sense. You may recall that in Session 3 we looked at algorithms through the lens of "doing and undoing." A focus on "what undoes what" often marks the beginning of reasoning about operations. In this session, we'll continue to examine algorithms, as well as other systems that represent a structural approach to algebra.

Spend some time thinking through the following exercise.

Groups: You may want to put this on an overhead.

One hallmark of a move to algebra as structure is a focus on undoing, or inverting, processes; another is comparing them.

A simple case of this is the following:

Is adding 3 to 2 the same as adding 2 to 3?

Is subtracting 3 from 2 the same as subtracting 2 from 3?

Thinking about properties rather than individual numbers indicates a move to a structural point of view. Keep this in mind as you work on Problems A1 and A2.

<< back to Part A: Comparing Operations


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