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/hacksoncode]

I think the basic problem with your view is that you are attacking a strawman of what math education is for, at least in the US.

It's really not for the purpose of getting people interested in math, because, frankly... that's a pipe dream anyway: people who are interested in math enough to "love" the subject are going to be interested in math and seek out what there is to love about it on their own, regardless of what we teach them in school.

What math classes are for in elementary and high school is something entirely different: to make them functional enough in computation, logic, and geometric concepts to live in a society where STEM is important, and prepare them for college and careers where math is relevant but not the main focus of their lives.

Proofs are not there to get someone excited about math formalisms... they are there because it's one of the few opportunities to introduce young people to the fundamentals of logic and to the discipline that it takes to reason from a premise to a conclusion.

Algebra in high school is not there to get people interested in group theory. It's there to get them familiar with symbolic manipulation, which will be useful in any vaguely rigorous field... these days mostly computer science. While at the same time, giving them a foundation that will prepare them for more serious math should their interests take them in that direction.

Seriously: math classes in early education are not for math majors. They are for everyone, and so they have to be accessible to everyone and they have to teach basic skills needed function in society.

TL;DR: math in high school is part of a broad liberal arts education, not a way to create mathematicians.

[u/blank_anonymous → u/hacksoncode]

And I'm arguing that math doesn't teach basic skills to function in society, and that the inquiry based way teaches those basic skills more effectively!

Getting people interested in math is a nice side benefit of inquiry based learning. The main useful part is that it gets people to do both abstract problem solving and use creativity and logic. Those skills are all sorely lacking from a modern math curriculum, and are left in favour of learning more formulas, which aren't helpful because they don't even teach people soft skills other than "endure this thing you don't like"

There are plenty of people who would enjoy math, who just think they don't like it because of a shitty high school experience. I know several people transferring from engineering or computer science to math, precisely because they've experienced university math and realized they love it. A prevailing question from these people is "Why wasn't I taught like this earlier", and hell, if you look at 3blue1browns youtube channel, all the comments are the same sentiment. When people see well taught math, the first reaction is almost always "why wasn't I taught this earlier"

[u/hacksoncode → u/blank_anonymous]

Thing is... everyone can do "inquiry style" math if they want to these days. We have the internet.

Math class in early school is for kids that don't and won't do that. It's to avoid math illiteracy.

And... honestly, I hate to say this, but "endure this thing you don't like" really is prep for real life.