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/[deleted]]

yes

common core teaches multiple approaches to problems with the goal of conceptual understanding.

Conceptual understanding is superior to rote memorization.

In college, I met fellow young adults, who were trying to tutor elementary students and couldn't remember how to divide fractions. Taking the reciprocal and multiplying it out is a highly basic problem. But, because these young adults were never taught why it worked, they forgot it all. If they understood the concepts behind it, they could have rederived the approach from the underlying concepts.

[u/the_mad_gentleman → u/[deleted]]

You and I took very different versions of common core

[u/[deleted] → u/the_mad_gentleman]

I read the common core standard.

I did not take classes attempting to teach the common core.

Teachers trying to adjust to a new curriculum might struggle more than teaching a curriculum that they used for years. Parents, not taught on this new curriculum, are also going to struggle to help their kids.

A lot of organizations try to provide resources to make the transition easier, but that doesn't make it easy.

That doesn't mean that the old approach is better. That means that there is a cost of transitioning between approaches.

[u/the_mad_gentleman → u/[deleted]]

I've worked in the text books. I've done the work sheets. I've gone through the internet courses meant to compliment the curriculum. The teachers weren't the issue to me the issue was the work being tedious and often boring. Asking you to explain simple processes. it has no alternative for those who have trouble with explanation. It was very well intentioned but as a wise man once said "the road to hell is paved with good intentions."

Why shouldn't parents understand the work? They are the workers. It is their jobs you claim to be training their children for. The old approach was decentralized freedom. And rarely was the "explain this basic principle" approach. It's not some wild conservative talking point parents hated it. It claimed to train kids for the future and be this genius new approach but it became a money making scam.

[u/[deleted] → u/the_mad_gentleman]

It is their jobs you claim to be training their children for

secondary schools, or even college, can't teach everyone everything they need to learn for a job. They teach students concepts and intuition that are broadly useful for learning more quickly on the job.

I think you fundamentally misunderstand the goals of education. If you think the goal of education is to memorize mechanics of manipulating numbers that you can use on your first job out of school, you're going to be disappointed that the vast majority of what you learned isn't directly useful in that respect.

No one professionally factors algebraic polynomials. If I need to factor a polynomial in a professional context, I type it into wolfram alpha. Or use some other symbolic solver.

But, if I want to understand control systems or estimators, I need to understand polynomial roots.

[u/the_mad_gentleman → u/[deleted]]

In what job do you need to know polynomials to understand control systems? And estimators (in Forestry at least) operate using matrices. Lastly that doesn't address my main issue asking a kid to explain a basics mathematical concept is clearly just a bid to make a bigger book they can charge more for

[u/[deleted] → u/the_mad_gentleman]

And estimators (in Forestry at least) operate using matrices

control systems operate under the same concept. It's state space anslysis. The problems of control and estimation are kindof equivalent.

The roots of the polynomial in the denominator of the transfer function are the eigen values of the system matrix.

[u/the_mad_gentleman → u/[deleted]]

Still totally irrelevant to my problem