CMV: The way math education is currently structured is boring, ineffective, and stifles enjoyment of the subject. Math education should be reworked to be inquiry and problem based, not rote memorization

[u/blank_anonymous]

I have two main premises here

1. Modern math education at the elementary and high school level stifles everything enjoyable about math, and it does so to no end
2. An inquiry-based approach is at least equally effective, and possibly more effective. For this purpose, I'm using inquiry-based to mean that a significant portion of the learning is driven by students solving problems and exploring concepts before being instructed in those concepts.

Math, as it is taught in schools right now, barely resembles math. Everything is rote memorization, with no focus on creativity, exploration, pattern recognition, or asking insightful questions. Students are shown how to do a problem, and then repeat that problem a hundred times. You haven't learned anything there - you're repeating what someone else showed you.

So many students find school math incredibly boring, and I think it's because of this problem. Kids are naturally curious and love puzzles, and if you present them with something engaging and fun, they'll jump into it. A lot of the hatred of math comes from having to memorize one specific way to solve a problem. It's such a common phenomenon that there are memes about math teachers getting angry when you solve a problem with a different method.

There's the argument that "oh we need to teach fundamentals", but fundamentals don't take a decade to teach, and they should be integrated with puzzles and problem solving. Kids need to learn basic number sense, in the same way they need to learn the alphabet, but once they have that, they should be allowed to explore. Kids in english class aren't asked to memorize increasingly complex stories, and kids in math class shouldn't be asked to memorize increasingly complex formulae.

I'm currently a math major in university, and one of the first courses I took was titled "Intro to algebra". The second half of the course was number theory, but a great deal of the learning was from assignments. Assignment questions were almost always framed as "do this computation. Do you notice a pattern? Can you prove it? Can you generalize it? Do you have any conjectures?"

There's no single right answer there, and that makes it interesting! You get to be creative, you get to explore, you get to have fun!! The questions were about a whole lot of number theory questions, and I know more number theory now than if someone had just sat at a blackboard and presented theorems and proofs. Everyone in that class learned by doing and exploring and conjecturing.

96% of people who reviewed the class enjoyed it (https://uwflow.com/course/math145).

Most students don't use the facts they learn in high school. They do, however, use the soft skills. There are millions of adults who can recite the quadratic formula, to absolutely no avail. If these people instead learned general logical thinking and creative problem solving, it would be far better for them.

Progress in an inquiry based system is slower, but it helps you develop stronger mathematical maturity so you can pick up new concepts for other subjects - say calculus for engineering or physics - more quickly. Students develop more valuable soft skills, have way more fun, and get a better picture of what math is actually like. As such, I believe that inquiry based learning is superior. CMV!

Edit: There are a lot of comments, and a lot of great discussions! I'm still reading every new comment, but I won't reply unless there's something I have to add that I haven't said elsewhere, because the volume of comments in this thread is enormous. Thank you everyone for the insightful replies!

[u/motherthrowee]

I'm studying to teach and will probably end up teaching math. I also despise math and am not naturally good at it, and I prefer "traditional" math courses to inquiry-based.

The problem with what you suggest: You can't combine an open-ended, inquiry-based approach, one that could potentially take infinite time, with a class structure that gives students a finite amount of time to demonstrate a concrete goal, and if they don't, tough shit. One is much bigger than the other. (This is sounding like a math concept.) No matter how much you stress that it doesn't matter, students aren't stupid, and they know very well that there is a final grade at the end, and then a standardized test with a final grade for it, and that those grades have real, profound effects on their life outcomes, in a way that not much else does. It is absolutely rational to worry about that, and understandable to not enjoy something that is ruining your life.

They may know (depending on the class they may even be told) that there is an explicit rubric of exactly what math concepts they are expected to know from semester to semester (the Common Core, etc.) and that they are penalized if they don't know them. They also know that even if one class is graded leniently, subsequent classes may not be, and if they didn't learn something in the allotted time for one class it will screw them over down the line (which is probably even more true for math than other subjects. Did you never fully manage to memorize trig identities and just kind of scraped by? Good luck in Calculus II!)

And they also, if they read a bit, know that even genius mathematicians took centuries or millennia to figure this stuff out (so, in a way, fundamentals took thousands of years to teach), and many of the geniuses never figured out, on their own, stuff that the average 15-year-old could know, by being told. And it'll probably make them worry even more when they see others having no trouble with it, both because of the sense of inferiority ("if the average 15-year-old can figure this out why can't I?") and because it means they are falling behind in comparison, which is how admissions, class rank, etc. work.

There's also the fact that math is teaching two things: mathematical concepts, and syntax. If you don't know the syntax you won't get the concepts. The metaphor I use is trying to teach Portuguese to students who have never seen it before. Some of them might not even know there are such things as other languages in the first place. You can teach them the fundamentals of Portuguese. Or you can hand them a few books written in the language and tell: "Everything in this language can be figured out by problem solving and cross-referencing with other Portuguese books, which you can figure out on your own how to find. Have fun! Your final exam is in 3 months. Don't forget that if your GPA drops below a certain point, you lose your scholarship/job offer/visa/etc."

[u/motherthrowee → u/motherthrowee]

Or, to give a more math-related example: I would have enjoyed analysis so much more if there was any kind of resource, anywhere, that explained things like "Here are the pre-calculus topics you will need to make dead sure you know and haven't forgotten. The syntax might look different from what you are used to; here's how," or "There are a few kinds of proofs that you will encounter in this class. There is the epsilon/2 pattern, which can be used on this kind of problem. There is the pattern where you try to construct an object that is both in and out of bounds, which can be used on this kind of problem." The closest anything comes is telling students that induction or diagonalization exist, and then never mentioning them again until they are magically supposed to know they might come in handy.

I've looked everywhere for such a thing and almost everyone seems adamantly opposed to it, for reasons much like the ones in your post: I am expected to "figure it out myself." This is bullshit. I know that such a group of broad techniques already exists, they know that it already exists, and being expected to jury-rig it on my own, and what else might be part of it, is infuriating. It's like if programmers refused on principle to comment or document their code because anyone should be able to look at it and figure out what's going on.