Focusing on the why – Teaching students to make decisions in math

Using tools to solve problems involves two major components. The first is all about deciding why a particular tool or combination of tools applies to the situation and the second is about how we actually use the tools. When we teach mathematics we tend to focus on the second component because this subject has a lot of tools and it is important for students to learn how to use each one proficiently. We have tools for solving quadratics, manipulating algebraic equations, finding derivatives, adding fractions and everything in between. But tools are only effective when used in the appropriate situation, a dentist’s drill does wonders for a tooth with a cavity but should not be applied to a healthy one even if it is wielded with a high degree of skill. This means that we need to be explicitly teaching our students how to make decisions about why a tool is useful in the first place. This presentation will give you concrete ideas and examples for teaching students to recognize decision making points and to practice figuring out and communicating why they are applying specific math techniques.