EDUC 628-Spring-08

From Phaedrus   and his reference to this  blog, where the following was stated:

For example, they studied different approaches at teaching the basic mathematical property of commutativity — that you can switch up the order of elements and still get the same answer, as in 3 + 2 or 2 + 3 equals 5.

Some students learned the concepts using generic symbols. Others were taught with concrete examples such as pictures of measuring cups  filled with liquid, or slices of pizza or tennis balls in a container.

I thought about an example that an instructor gave at a training I went to once about the associative property, and I repeated this, with my own little changes, to see if a student would understand, and this particular student did, which was exciting.

For addition and the associative property, one can tell a story, to pretend that there are three friends a,b, and c—and a can represent Alice,  or whatever name one wants to put in for the scenario, and that b represents Bobby, and c could stand for Cathy.  Well, it could be that all three are friends and that they like to hand around together, but sometimes Alice walks to lunch with Bobby, while Cathy walks behind them because the hallway is so narrow, which would be (a+b) + c, or sometimes Alice walks behind while Bobby and Cathy walk up front together, which would be a + (b+c)—but they all go to lunch together, and the answer will always be the same–a,b,and c–for addition.