Last week we had a few sixth graders visit our elementary algebra classroom. While my students were taking their daily quiz, I put this on the board for the youngsters. I went to the back of the room and explained the question. I put 2D Boxcar on the screen for those that didn’t want to think about the problem. Fairly soon I got the answer (Done without paper and pencil b-t-w). So I changed the problem to
This was a choice. When I talk to individual youngsters about math, I try to build an argument. For example, to show that multiplying by eight is easy, I might ask this series of questions.
In the example above, I wasn’t going for the basic structure. If so, I would have asked them to solve
next. Instead I asked for the solution to
thinking that they would have to perturb the previous answer (and use fractions) or maybe try adding the right sides and dividing by two. My next problem would have been
Most of this was done unconsciously since I was handing out papers and tending to other aspects of class management.