The algorithm is not the goal
The point is not to be on top of the mountain — the idea is to climb it. (Image by Susanne Jutzeler)
Like everyone, I see things on the Internet that I wish I hadn’t.
From red carpet gowns that look like trash bags to Instagram humblebrags that forgot the humble part, there is a cost to the never-ending quest for the new, interesting, and relevant.
Recently, I came across a statement from a high school math teacher who said that the ultimate goal of middle school math instruction in a given concept is to get students proficient with the standard algorithm.
Several other teachers agreed. I did not. But since it’s no use to argue on the Internet, I’ll share my thoughts with you.
The ultimate goal is not proficiency with the standard algorithm. That’s what we have calculators for. The goal of education, whether it’s math or art or history, is to help a human being to grow and develop. A student’s ability to perform the steps of an algorithm, bereft of an understanding of why it works, is effectively treating the student like a machine — or really, like a factory worker.
In prioritizing the algorithm over the conceptual understanding, we’re definitely not preparing the student for the real world, which presents scenarios that are even messier than the dreaded “word problems” that students can only solve if they understand the concept behind what they’re doing.
No, the only benefit would be a test. I understand that at some point, students will be tested (perhaps even with a standardized test, oh goody) on what they know and can do. If it is your job to prepare the students to take such a test within just a few weeks, it makes a certain kind of sense to teach them procedures that they can simply repeat. However, such desperation is not to be confused with education. I choose not to be a part of it.
The sad part is that teaching the algorithm — that is, teaching a procedure without the why behind it — doesn’t even work. It’s like trying to play music without hearing it, or making a sauce without tasting it. Without anything to connect the procedures to, they fall apart. It would be the same as memorizing sentences in a foreign language without the meaning. It ends up being a bunch of noise. Our brains aren’t well suited to information we can’t assign meaning to. It goes “in one ear and out the other.” As a result, students fail. They decide they hate math, believing that math is simply a series of procedures. Worst of all, they begin to believe they are stupid.
The emphasis on superficial knowledge in school may seem benign, but it is utterly toxic. Not only do students develop a distorted picture of their capabilities, they lose faith in the system and trust in the adults around them. When they’re supposed to learn something that actually does have intrinsic meaning, or material is presented in a way that actually would allow them to understand, they may be wary and uncooperative. They may go through the motions or refuse to engage at all. And if they do participate, they may be ineffective. This is because they’ve been trained to pay attention to stuff that isn’t important and take shortcuts that don’t work.
In order to transform students’ experiences, we need to set up a situation in which students have the time they need to understand a concept — and the material needs to be presented in more than one way, ideally in a hands-on format that might allow them to literally grasp it.
In the long term, school systems would do well to reevaluate their curricula and consider making space for students to learn fewer concepts more fully.
That said, I don’t have solutions for the whole world. I just know what works for my students. And I know the magic that happens when a student finally understands something that they assumed was out of reach. It’s more than just a light going on — it’s a sunrise. I believe that virtually every child can have experiences like that if we respect them enough to teach them more than algorithms.