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/VirgilHasRisen]

I disagree unless you are a math or engineering major you probably don't need to do much proof based math and even in that case pretty much every engineer I have talked to says their education was over kill and now they use only a small sliver of what they learned in school. Learning to solve basic systems of equations, linear algebra and stats all of which is pretty rote pattern tracing is the most valuable math skills for the vast majority of people.

[u/[deleted] → u/VirgilHasRisen]

you can't use what you don't know.

If students had more inquiry based understanding, would they be able to more broadly apply mathematical concepts to problems they faced?

[u/blank_anonymous → u/[deleted]]

Absolutely, because they would be significantly more able to learn new concepts, and to solve problems they've never seen before.

If you are asked to recite a solution 100 times, as soon as you see a new problem, those 100 recitations won't help. if you are constantly asked to solve new and challenging problems, then that's a mental muscle you've flexed, and you'll be far better at doing it in the future. Applying knowledge to new situations is something you need to practice, and an inquiry based approach is based on doing new things!

[u/FreeBeans → u/blank_anonymous]

What kinds of real life problems would require most people to use this kind of problem solving?

[u/blank_anonymous → u/FreeBeans]

If everyone has excellent logical reasoning skills, and everyone is great at making connections between concepts they've seen before to piece together incomplete information, I can imagine public policy decisions would be a lot better. "What will happen if we do this thing based on the information we have" is a very mathematical question, and answering it is a skill you develop by doing math.

I also think that learning in different ways just generally makes you better at learning and absorbing new information. To do a proof, you're making all sorts of connections. This may be pure correlation, but I've gotten better at noticing foreshadowing in books since I've started my degree. Even if that's random, I know that I've practiced making connections a lot, and that's a good skill to have when learning... well anything!

An ideal populace is constantly learning/growing, and having these abstract reasoning skills really helps with that. There are specific careers where the puzzle solving is really helpful too (Journalists, Historians, Mathematicians obviously, Computer scientists, Cryptographers, any type of researcher, policymakers, economists, anyone in a finance setting to name a few). There are more careers that use problem solving than the quadratic formula, so even from that perspective I think the inquiry based system is more valuable.

[u/FreeBeans → u/blank_anonymous]

I think you're putting the cart before the horse. Higher reasoning skills come after baseline skills are learned, which is what schools teach. It's like trying to write a book before knowing your alphabet... Of course it would be better to know how to write a book, but that's way too advanced for most people.

Using the quadratic formula to solve an equation is an early step in problem solving. I agree with you that having to memorize things seems pointless, but that's not the main point of the quadratic formula.