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