Regents Recap, January 2020: Isn’t the Quadratic Formula Completing the Square?
Completing the square is one of those mathematical techniques that should be taught but probably shouldn’t be assessed on state exams.
First, when you insist that a student use a specific technique to solve a problem, you penalize flexible and creative thinking. Second, completing the square probably isn’t important enough a problem solving technique to warrant its yearly appearance on the New York State Algebra 1 exam.
Of course, the one situation in which completing the square is absolutely indispensable is in deriving the quadratic formula. Which makes this sample student response from the exam’s official scoring materials a bit puzzling.
The student lost a point because, instead of completing the square, they used the quadratic formula to solve this equation. But the whole point of the quadratic formula is that it completes the square for every trinomial. The quadratic formula is completing the square.
As I clarified in comments on Twitter, I find this more amusing than objectionable. But these little windows into the testing process often tell us more about what is valued and understood than test scores themselves.