One of my goals is to be an agile teacher. I also want that for my students. Often students arrive in my class preferring to work with one method that works for every problem of a certain type. I want them to flexible and use the most efficient solution depending on the particular problem.
Case in point – quadratic equations. Students who have seen this material before want to use only the quadratic formula, as they know it can be applied to any quadratic equation. However, it is not always the most efficient approach.
- I encourage my students to begin with the 10-second rule: If they can factor in 10 seconds or less, they should factor.
- Some equations, such as (3x-7)^2 + 21 = -11, are easier to solve by extracting square roots than they are by squaring 3x-7/rewriting the equation in standard form/using the quadratic formula.
- For certain equations (leading coefficient of 1, b is even) completing the square can be more efficient than using the quadratic formula. It will always be easier to simplify the solutions.
After finishing with the quadratic formula this week, my class will take a quiz where they have to solve four equations using the four techniques (factoring, extracting square roots, completing the square, and quadratic formula). But here’s the catch – they can only use each technique once. They will have to think about the most efficient strategy for each equation. Hopefully it will help them to develop some intuition about when to use techniques other than the quadratic formula.
The same strategy can be used for graphing lines (intercepts vs slope), solving systems of equations (substitution vs addition), and many more problem types. I’d encourage you to try an assessment like this, and I’d love to hear back from you about how it goes.
TeachBetterTuesday (TBT) is a weekly blog series I am writing this semester. If you have a topic you want me to cover or a strategy you want to share, reach out to me on Twitter or leave a comment below. – George