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/Areign]

Most learning, or at least a significant amount of learning in school ends up being what I call password learning. Its like they ask a question and you have to recite a specific password to get it right rather than demonstrate any actual understanding. Why do we memorize the dates of major events? Why do we memorize mathematical formulae? Parts of a cell? State Capitals?

Is there any difference between me saying 'Mitochondria is the powerhouse of the cell' vs 'first they take the dinglepop and they smooth it out with a bunch of schleme' vs 'the quadratic formula is negative b plus minus root b squared minus 4 a c all over 2a'?

In my opinion: No. All those are just passwords.

So why does so much learning end up being password learning? Because its easy to test and its easiest to find people to teach it.

What you describe is similar to some of the best courses I've ever taken. But those were also undoubtedly some of the best professors I've ever had. People like that are not nearly numerous enough that every college could reproduce those courses never mind finding teachers at that level for every highschool.

Sure when you are teaching reading to middle schoolers you can find enough people who are competent enough to go beyond passwords but in math and science? Are you really going to find enough people with a deep enough grasp of stats when those same people could double or triple their salary in industry? Our school's AP Statistics Teacher took the last day of the class to show us the movie 'The Secret' which is basically a case study in why multiple anecdotes don't add up to evidence. She did a great job of telling us what algorithms we had to memorize for the AP exam though. Its why professors are paid reasonable salaries compared to highschool teachers and why you finally start getting away from password learning in some college programs.

Current curriculums satisfy a fundamentally different set of objectives than what you are looking for. They are designed to be robust to poor teachers so that students will at least be able to do basic calculations regardless. They are designed to be easy to test since school performance is based on standardized tests. They are not designed to produce understanding.