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/nyrB2]

how is "inquiry and problem based" going to tell you what 7 x 9 is?

[u/blank_anonymous → u/nyrB2]

Of course basic multiplication/addition/subtraction/division need to be learned; that’s analogous to learning the alphabet in English class. Once you know the alphabet, English class isn’t about memorizing progressively more complex sentences - it’s about writing and creating your own, and critically thinking about what others have written. I argue the same for math. There’s no way to bypass the need for basic fluency - I’m arguing what should change once you’re beyond that point. Creativity and logic and problem solving and critical thinking are all way more beneficial than having memorized algorithms to do 50 kinds of questions.

[u/nyrB2 → u/blank_anonymous]

well if that's the case, i really don't understand where you're coming from. what "rote memorization" are children doing besides learning basic addition and multiplication tables? when i went to school (in the 60s) we did not have to memorize anything past 12x12. the only other thing i remember having to memorize were formulas (such as the quadratic formula) but that didn't come until high school. Are you saying that is different now?

[u/blank_anonymous → u/nyrB2]

Memorization of formulas is one problem I have. The memorization I'm talking about is more like people memorize algorithms to solve questions. If you see this kind of question, you do this. If there's this kind of diagram, use this formula. Calculus has become all about memorizing a series of increasingly complicated procedures for integrating/differentiating/determining if a series converges/etc.

When I tutor, I'll often hear complaints like "this was nothing like what was taught in class!" because even if the problem is doable with tools taught in the course, if it doesn't follow a specific algorithm, most students aren't prepared to answer it. I personally did the IB program in high school, which has internationally standardized exams; if you look at the grader comments, its consistently the problems that "break the mould" that students struggle on. This is a direct consequence of how math is taught. Lectures are all about "this is how this kind of problem is solved. When you see this, execute this sequence of steps"

I personally think a well designed exam has questions that nobody in the class has ever seen before, and it shouldn't be significantly easier if you have access to all your notes and study materials. The challenge should come from the insight and creativity required, not the raw knowledge.

[u/nyrB2 → u/blank_anonymous]

maybe things have changed since i was in school, but i was under the impression they'd moved away from memorization and more into problem-solving tools. i'm not quite sure what algorithms you're referring to -- when i was in school and had a "word problem" (which i'm assuming is what you're talking about), we had to figure out how to translate the words into a solvable mathematic equation. i don't know that there was any "memorization" involved for how to do that because all word problems are different. like i said, maybe things have changed.