A few weeks ago I was presenting a session called "High School Math for Junior High Math Teachers" at the Calgary Teachers' Convention. The goals of this session were:
- Identify concepts and skills taught in junior high that form a foundation for high school math
- Solve high school problems that are direct extensions of these foundation skills / concepts
- Reflect on your teaching practice to see if your teaching methods and explanations can easily be extended to high school problems
So where does the swearing come in? At the end of the session I was told that junior high teachers would prefer it if elementary teachers didn't let students use calculators. Then I was asked what high school teachers would prefer junior high teachers not do. One of my responses was "cross multiply".
When students say to cross multiply, I tell them not to swear in my math class, even if it will give a correct answer. Why? Because in my experience, most students don't know why it works or when to use it. Students typically want to "cross multiply" whenever they see fractions, such as below:
Perhaps even more important, though, is that "cross multiply "obscures what's happening mathematically: multiplying both sides by each denominator. Even more fundamental, is that we're performing the same operation to both sides of an equation. And that's the basis of solving high school equations, isn't it?