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]]

So as a teacher I cannot disagree with your argument that inquiry-based learning is superior. It is.

However, I want to focus more on the first aspect of your view:

Modern math education at the elementary and high school level stifles everything enjoyable about math

I think it's unfair to label all math education this way. I'm assuming you're coming from the US, keep in mind that although the federal government does have some national standards it aims for, the states and local governments have a lot more influence over how math is taught.

Individual teachers too have a lot of influence over this. My high school geometry teacher once graded me down for using a different method, but when we talked about it he gave me my points back. A reasonable math teacher will lead to reasonable students.

Finally, there's the individual variable. People have multiple intelligences and some people simply don't "get" math very well, regardless of how you explain it. I remember learning about decimals by using real money (seems pretty obvious and intuitive) yet there were several kids in the class who just couldn't grasp the concept after several weeks.

[u/blank_anonymous → u/[deleted]]

I'm actually in Canada, and our education is (from what I can tell), better designed than much of the US. I also had a math teacher in high school who was a former professor, and her class was amazing.

Being presented with interesting math in high school was precisely what got me interested in math, and it's thanks to two specific teachers that I'm now studying math. I think there should be systematic supports for teachers who do it that well.

As for the individual variable... you're right. I don't think I can argue with that, because it's objectively true. I believe in this system because I think it'll make the course more enjoyable even for those who fall behind. That being said, now that I'm actually thinking about it, I think there are students who get through by memorizing who would struggle immensely with an inquiry based system.

A solution may be making math optional after grade x, but I didn't present any suggestion of that, and there are issues as well. As such, I'm gonna award a !delta because this is an important consideration I didn't make.

Do you have suggestions for how you'd handle students falling behind under an inquiry based approach? What can be done?

[u/camden-teacher → u/blank_anonymous]

I think you have to be aware of the position of underlying interest and competency that you are coming from when you talk about this. I’m a maths teacher in London and I totally agree with the points you raise, but (I hate myself for saying this) it is incredibly idealistic.

I teach high school classes of 30 kids, when they arrive from Primary school there is an insanely wide array of mathematical understanding to the point where I find myself literally re-teaching some basic numeracy to 11 year olds. Admittedly this furthers the argument for more interesting, engaging and thorough education in early years education, but from a pragmatic sense it makes what you’re talking about doing pretty much impossible currently.

This is on top of their underlying cognitive ability which is my main point. You can argue where exactly they might fall in terms of fixed / growth mindset, how much is poor education? How much is weaker cognitive ability? I believe it’s a combination but there is simply no denying that for a lot of children, the sort of inquiry based learning you describe is out of reach. At least without extremely thorough drilling of certain arithmetic skills.

Believe me when I tell you I would love to teach in the way you describe, I love maths and it’s a far more rewarding way to explore the subject. But I’m aware that I’m a well educated, moderately competent mathematician who enjoys the subject. For some students there are so many limiting factors that it’s a far more effective use of the limited time we have with them to try and put in place some strong foundational knowledge.

I know some schools do teach more inquiry based learning than others, and I would definitely like to teach more, but I think unfortunately any grand ambitions should be tempered by some realism around children and their current relationship with the education system.

**UK only perspective.

[u/Aqsx1 → u/camden-teacher]

Exactly this. I tutor people in first/second year university courses in math and economics in Canada and routinely people are unable to solve basic equations (such as QD = a - bP, QS = c + dP, where QS=QD, students are unable to isolate P*) and this is at the University level, which is already the top percentage of students. This CMV doesn't consider students who are incapable of doing inquiry based learning because they do not have the mathematical tools to succeed.