ABSTRACT
Teachers should teach shortcuts with caution. Often students rely on the shortcut but are unable to explain why the shortcut works, such as moving a decimal point to the right to multiply by 10. However, when students discover a shortcut on their own, they tend to understand the mathematics behind it. Teachers should explicitly teach students how to recognize opportunities in word problems for using a shortcut, such as when a calculation is repeated. For example, if a word problem involves adding 5 + 5 + 5 + 5, the students should stop and discuss how it would be more efficient to count by fives or to multiply instead of writing out all of the addends. In order to find shortcuts, students have to pay attention to the details of the problem as well as be aware of the goals of the problem. In the previous example, it does not matter how the problem solver arrived at the answer of 20, but that they understand there are efficient ways to arrive at the same answer to satisfy the goal of the problem.
