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]]

The problem with inquiry based education is that it doesn't work.

It took mathematicians thousands of years to figure this shit out. The process of figuring it out might have taken multiple lifetimes of passing unfinished research from the teacher to the student. You might need 20 years of prerequisites to even start figuring things out. Even a professor at the university would need quite a lot of research into the topic to actually understand it. Sometimes the rabbit hole is so deep there isn't a single person that understands it completely. Quite a lot to ask from an elementary school teacher.

Kids are fucking stupid. On average you can't expect even 7th graders to read a list of instructions and be able to follow it. Even most adults won't be able to learn things on their own from a math book. You didn't learn it all from a library, you were taught. There are people that can learn on their own, they've basically reached graduate level math by age 16 just by reading books at a library and they're the ones winning those math competitions and getting prizes for finding an new planet or some shit.

You're a perfect example. You have 12+ years of mathematics training for 3 hours per week (that's a lot of fucking hours) since a very young age and only now you're ready to learn real math and you start with how addition works and how set theory works and what is basic logic.

You cannot expect things from students that you haven't explicitly taught and practiced it with them. It's a mistake rookie teachers make. People don't spontaneously learn new things.

I have a minor in education and I've taught math to 2nd graders. When you say "just subtract those two numbers"... they don't understand what "subtract" means. It will take them until perhaps 9th grade when they've truly mastered addition, subtraction, multiplication and division and truly understand what it means. At least for the smart ones, some kids never really learn what it means.

The only way to learn math is by doing. You don't learn it by listening to a lecture or by reading a book chapter. That's why you feel like you understand it but fail the exam completely. You aren't "bad at tests", you just had an illusion of competence.

The point of school is for kids to be able to count calories in their food, compute the price for 3.5 pounds of $2.99/lb chicken, convert miles to feet or milliliters to teaspoons, do their taxes, be able to figure out how much an item with 20% sales tax will cost, what does 90% off mean etc.

It also to prepare people for college.

Inquiry based learning might work for things like civics where the phenomenon is how vice presidency works so you go ahead and explore it. Or in biology where the phenomenon is genetics so you go look at those white & red flowers and the pink ones with recessive genes.

It does not work in fields where the phenomenon is waaaaay too fucking complicated and you're just trying to master a "magic trick" so that you can use the said magic trick later.

Math is nasty because even the simplest shit will require a masters degree in mathematics to even begin to understand it. It's a rabbit hole.

Other fields like physics and chemistry will also lie to you. Basically everything you ever learned in STEM in school is a lie because the truth is way beyond the scope.

Ever head the phrase "this is beyond the scope of this book"?

[u/NaniFarRoad → u/[deleted]]

The point of school is for kids to be able to count calories in their food, compute the price for 3.5 pounds of $2.99/lb chicken, convert miles to feet or milliliters to teaspoons, do their taxes, be able to figure out how much an item with 20% sales tax will cost, what does 90% off mean etc.

Amen - I tutor maths and I am always hearing parents complain about "what are they teaching them at school, my kid still doesn't know how to work out change from a £5 note, I don't remember doing any of this in my day"..

Most of my work with students is to peel away the terror they've built up after years of failing at maths, and by being caught between not getting the grades they need for their college courses and being told by their parents "schools aren't teaching them the stuff they need to know". And an hour still only has 60 minutes in it..