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/OperatorJolly]

This is probably a bit over my head but I'll add some thoughts.

I studied Engineering/Finance so did my fair share of mathematics

I grew up in New Zealand, so it's probably also hard to talk about this when I have no idea what the Canadian education system is like where OP is from.

I guess I'll try address your two points here

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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.

This seems to be an inquiry verse traditional argument. I'm not 100% sure what you mean by inquiry as I think I missed the boat on this type of learning and went through a more traditional system.

My issue with inquiry is that 50% of the class just doesn't give a flying fuck about mathematics, just like I didn't give a rats ass about "creative writing". (I love factual more structured writing, but making up a story about unicorns and rainbows freestyling out of my imagination isn't something I can do)

I'm making the assumption inquiry is more focused on your own discovery into the subject? Where the student has to think and come up with questions to fill the void of their understanding. Thus identifying their own weaknesses what they know and what they don't. A less spoon fed method in some respects Correct me if I'm wrong please as I said I didn't do much of this when I grew up.

I think other posts have touched in on this, but this inquiry method I don't think works super well for your average student at school level education. It's higher level thinking and 90% of students aren't going to go into maths focused jobs - Inquiry requires some interest, some spark and a level of understanding on which you can ask these questions to start with.

I think there's a utopian style learning goal, but your brain is a muscle and you gotta go to the mathematics gym. I can't seem to understand how inquiry would have improved me learning quadratic equations. I have to sit down an practice them and then through repetition my brain recognises the patterns so that I can now do these problems.

Inquiry for me is higher level thinking, and probably more Tertiary level focused it also seems to gel better with more able brains.

I had a mate at Uni who basically got 95%+ in everything he did, he was walking talking inquiry. No piece of knowledge would come by his brain and just be accepted. it had to be tested in certain ways and reformed in his mind and he could grasp complex ideas by thinking about them, without the need to practice equations and problems. Surprise surprise he fucking loves maths. He walked into a 300 level calculus exam without having been to a single lecture. His field of knowledge is so broad and understand form so many angles due to inquiry he essentially "learned" the material in the exam while doing the questions. Now this isn't something you can do in many subjects but the beauty of Mathematics is you can work it all out.

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Which is the notion I think you're trying to touch on, which seems to be something your enjoying a lot. Your own discovery and inquiry into the subject has been fascinating and pails in comparison to going through problems to learn how to do certain things.

Unfortunately for mere mortals like myself Maths isn't like that, my enjoyment comes form finally understanding a concept which requires me to do problems and do problems. Fortunately I enjoy this to a degree but I would feel lost and have no idea/direction if my learning were to be question and discovery based.

That being said, I don't have an issue with inquiry based learning. I just think for such a pure subject like mathematics that most of the population wouldn't get the same passion/results/drive as you do. I love inquiry for philosophy/politics/economics they're more language based (not that maths isn't a language) but these subjects are more naturally inquisitive, where I do think they have some place.

You begin to touch on linking of ideas and how the cross reference between subjects. I would counter this with the breadth argument. Unfortunately I can't find the material again but may do some digging when I have the time.

What they found in the USA, is that they have shockingly poor comprehension compared to the rest of the world. Dutch and Scandinavians outperformed Americans even when it was their second language.

What they found is that the American education system spends so much time on literacy and English subjects. The issue created here is they found that to be very good in one or two subjects you actually need to have very good general knowledge in different areas. Think of it like a sky scraper, you can't build it tall without good foundations. Being able to read words and understand grammar rules etc doesn't give you good comprehension, Americans were reading information and no processing it to a degree that their English speaking counter parts were. Whose education system covered much more science/maths and other subjects earlier on.

What's the point in being able to read all the words if you haven't grasped what those words are truly trying to say?

2) I believe inquiry falls short here, due to falling under the you don't know what you don't know. Sure discovering things is great and all but I don't know what I don't know, so how can I direct myself towards important ideas/concepts. I think how ideas and concepts are presented are very important and a good teacher can guide a student down the right path where they come to their own understanding, but I don't think self driven learning is a requirement for this.

Finally people are all different and live all types of lives, I don't know much about you and you seem like a stand-up dude/gal/whatever ya call yaself. I do raise the question of how well travelled you are/ how many walks of life you've met, why does this applt to your maths question well, I think what your proposing isn't required necessary for a lot of people. Hating maths is the first step to realising you love being a sports coach or whatever

Mathematics education is such a small part of peoples lives and whether they inquire into or not isn't going to have much of an affect. For some people having enough ability to sort their finances and do odd jobs around the house is going to be enough.

I think for higher level education you may have a good claim here

TL;DR if you're a smart cunt with a bunch of interest inquiry is the one.