Do you recognize that distinctive bit of mathematics? It’s something you probably last encountered in high school and, for some people, seeing it again now might even trigger a few nightmares.
Most American students learn the algorithmic process for deriving the quadratic formula, and how to use it to solve quadratic equations, in Algebra I. And likely forgot it not long after. It’s a process that hasn’t changed for at least several hundred years.
Maybe going back 4000 years to the Babylonians, according to a mathematician at Carnegie Mellon University who has discovered a simpler method, “one that appears to have gone unnoticed these 4,000 years”.
His process is rather clever and the professor does a good job of explaining it in a short video.1 But let’s be real: you probably don’t care. This discovery is really only something a math teacher could love. Maybe some of us former math teachers as well.
However, reading this announcement made me wonder, why we are still asking high school students (increasingly middle school students) to derive and use the quadratic formula? After all, there are more than a few smartphone apps that will do the job much faster. And they’ll create the graph as well.
But even if teachers allowed them to use their pocket computers in class, the application problems students are asked to solve are artificial at best.
Outside of classroom-ready examples, the quadratic method isn’t simple. Real examples and applications are messy, with ugly roots made of decimals or irrational numbers. As a student, it’s hard to know you’ve found the right answer.
Which gets at the primary problem with school math instruction at all levels: students are trained to expect “right” answers. In this case, two exact, very often integer, solutions to very synthetic “classroom-ready” problem.
And even incorporating a new, “easier” method for deriving the quadratic formula won’t fix the fundamentally broken way we ask students to learn mathematics. They simply spend far too much time in Algebra (and most of the rest of the curriculum) learning the mechanical processes for obtaining those “right” answers.
As a result, students miss the context necessary to understand how and why anyone in the real world uses this kind of mathematics in the first place.
1. Technology Review also has a good explainer for his method.