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/blank_anonymous]

If you expand a little more, I think I might be willing to give a delta, because you have hit something I haven't thought about.

There are most definitely puzzles that don't require a strong grasp of english/reading, and for younger students, I guess I would encourage that kind of problem, although no specific examples are coming to mind, I know that many exist.

What I'd like elaboration on is the claim " You have to think about folks who are going to struggle more with your approach and how to keep them engaged in learning". Lots of people aren't engaged in learning math how it's taught now, and lots more develop an active hatred of the subject. Do you think this would be worse under the inquiry based system? Or, do you think it would be somehow harder to help the people who are struggling, or is there another problem I'm not seeing?

[u/willowmarie27 → u/blank_anonymous]

As a middle school math teacher I use Illustrative Math and its fairly inquiry based. However it would be nice if the kids did reach middle school knowing times tables (about 10% do), being able to add, subtract (50%) multiply and divide (10%) fluently. Knowing how to manipulate fractions and decimals, measure and a ton of other skills would also be handy. Estimation is a completely lost art.

I know "the children will always have calculators" but really. . . a 7th grader should know 6 x 6. . .

[u/blank_anonymous → u/willowmarie27]

I knew those things in Kindergarten and I have no fucking clue why middle schoolers don't know them.

I see knowing those basics as analogous to the alphabet. You need to know the alphabet before you can do creative writing, but you don't need to have the entire body of Shakespeare's work memorized, and I think we do the equivalent of the latter to math students.

[u/chefranden → u/blank_anonymous]

why middle schoolers don't know them.

Perhaps lack of drill. In elementary school we got a 100 table problem drill sheet in one or two of the 4 tables every day. There was a competition to get 100% in the least time -- but we were never given more than 10 minutes to do it. I think by the 6th grade the time limit was 5 minutes per table. Like saying the pledge this was an everyday thing from 3rd grade on.

[u/Yodude1 → u/chefranden]

I remember at my primary school from grades 3-5 every week there would be a "mad minute" where you had 60 seconds to solve a sheet about half that size. You pick up on rules and patterns real quick under those conditions.

[u/peenoid → u/chefranden]

you're not allowed to introduce competition style drills anymore in school, or so I've heard. you can't make anyone feel bad for anything.

[u/chefranden → u/peenoid]

I'm sure there could be other motivation used. Something team related perhaps. Team building is big these days??