Students Must 'Engage in Math Problem-Solving'

There is a critical issue in mathematics education that does not devote sufficient time or emphasis to making sure that students know how to solve problems using different methods. This is most prominent in high school mathematics classes where the most knowledgeable teachers of mathematics reside, but often force one particular method onto their students.

The phrase "Work Smarter, Not Harder," coined by Allen F. Morgensen in the 1930s, is very appropriate here. The first step in teaching problem solving is to look for opportunities for students to have multiple entry points or strategies for solving a problem. Spend the extra time to allow them to explore their options. Take time to discuss strategic choices. For instance, when solving an equation that has parentheses, you can start with a simple problem:

5(x+3) = 20

Students will immediately use the distributive property. They learned to do this problem using their procedural knowledge in the eighth grade by using the distributive property. However, in Algebra I, the focus should be on conceptual understanding, so ask the students to find a "shortcut." (Students love it when you give them an opportunity to "do it in their heads" instead of showing work.) If they have good conceptual understanding, they will know that this is a multiplication problem that can be solved by using the inverse, division, first.

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