Shortcuts are a necessary part of math. If you are an efficient problem solver, you are likely using shortcuts that you have learned. The approach to shortcuts is what we must examine.

Are we showing students all the shortcuts without allowing time for them to understand why they work?

If we are showing students shortcuts, students are likely memorizing them in order to get an answer that day or pass a quiz that week. Memorization without understanding causes problems later. Without the conceptual understanding of what is happening, students forget. They apply the shortcuts at the wrong time, and they cannot extend them to other concepts. And it sends the message that math makes no sense, which may be the most worrisome outcome of all.

Read on for commonly misused shortcuts and what to do instead.