Unfortunately, many of today’s students view mathematics as a non-creative field. They’ve been told that there is only one way to solve a problem. Rather than search for solutions, they have become conditioned to waiting on their instructor to tell them what to do and how to do it.
First, students need to dispel that myth that there is only one way to solve a problem. This week I was introducing the general addition formula for finding the probability of A or B occurring. I asked students for the probability of drawing a king from a deck of cards, and they got 4/52 pretty quickly. Then I asked for the probability of drawing a heart. Again, a quick reply of 13/52 followed. When I asked for the probability of drawing a king or a heart, the initial response was 17/52, obtained by totaling the 4 kings and the 13 hearts. A student pointed out that simply counting those cards produced only 16 that were kings or hearts.
I asked them to come up with a strategy for solving these problems. Some suggested taking one group, like hearts (13), and adding the extra kings (3) to the total. Others suggested adding the kings (4) and hearts (13), then subtracting away their overlap (1). We all agreed that there was more than one way to get there, and that was OK.
Fast forward to today. I gave my students the probabilities that a student was taking math, taking English, and taking math and English. They applied the general addition rule with little difficulty. Then I proposed using a Venn diagram, and some students understood the addition rule much better after that. I then added that they could begin with the probability that a student is taking math, then add on the probability that a student is taking English but not math.
I made a big deal about how there is usually more than one way to solve problems in math, and that the best approach is to try to find your own way. I shared some of Jo Boaler’s research and they seemed more at ease with the idea of trying to find their own way to solve problems. Hopefully they continue to be creative.