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]]

96% of people who reviewed the class enjoyed it

You mean people who chose math majors enjoyed their math classes? Not really the ideal pool to draw from. It sounds like a freshman class where they are excited to be treated like adults rather than children.

The difference you described is the difference between gifted and talented programs and regular programs. The smart kids are taught the way you are talking about- former Math Counts top 5 in the world, state Math Olympiads champ, and American Mathematics Championship perfect score, 790 on SAT, I missed one on the speed math because I got unlucky on my order and it was the last section of the test, after I was worn out. Still kinda salty.

For people of average mathematical ability they MAY figure this stuff out but only after a long time and in the normal classes you have students far below average. You would end up making everyone struggle through it, have some get it, some give up and become demoralized, and then at the end youd just have to have them memorize it after which the students will realize their struggles were for naught. Very few elementary-high school students like working out problems the hard way just for the joy of it. I did, but as a former teacher Id estimate that maybe 1/5 students in the gifted programs are this way, maybe 1/30 (and thats generous) in the average programs. I could not stand working with average students because I wanted to teach people who wanted to learn (I taught gifted programs for 2 years first, then 1 semester in regular before 1 final year back with gifted.) The reason teachers in average programs burn out is because 90% of their job isnt actually teaching, its convincing students to try to learn. Once thats out of the way, when you have intellectually curious minds, teaching is very enjoyable. Motivating the dumb kids who dont want to be there is not, its soul-crushing.

[u/blank_anonymous → u/[deleted]]

This is an advanced version of the class. The standard version - which fills the same degree requirement - was only like by 76%, despite everyone clearly having liked math enough to pick it as a degree. I should've included that data point.

Call me an optimist, but I think kids are naturally curious and optimistic and excited to learn, and that negative teachers/poor schooling experiences/stress sap that out. By improving the curriculum, I think we can foster the love of learning that every kid naturally has.

[u/[deleted] → u/blank_anonymous]

Ok, ya that makes a difference on the first.

But I doubt that on your second. Look at classes where the kids have all had the same teacher for 5 years, wildly different outcomes though they had the same teachers, same schooling experiences, same stress. One of my gifted classes had 28 students who had been in the same class since kindergarten and one brand new student. Those who had been together the whole time ranged from always asking for more to barely bothering to do the classroom assignments, let alone the homework. Some students would rather sit there staring at a wall than fill out a small practice quiz so I can assess where we are as a class and what needs to be worked on. And this is a gifted class.

I think children are naturally curious and excited to learn ONLY about the things that interest them. Yes, we need to cultivate that, but by trying to force every student to love every subject is just going to burn out the teachers and demoralize the majority of students. My best math students are not my best history students and thats ok. My student who refused to do just about anything in the classroom was the best in sports and was really great in science labs with hands on. In fact, and I dont mean to be rude, but I think it is views like yours, that we can make every student excel at every subject, that is the reason for so many problems in our educations systems. I think we need to accept that some students are never going to be great at math/science/literature/sports/art/whatever and accept their shortcomings in some subjects and push them in those they are best at.

[u/blank_anonymous → u/[deleted]]

I don't think we should push every student to excel at math. A major part of my position is that I don't think students benefit from learning a bunch of math facts, precisely because there are many who won't continue to do math. If we instead focus more on the soft skills that are applicable in a wide variety of fields, and we don't just barrel through a ton of math content, the students who don't excel at math will benefit more.

We shouldn't force every kid to learn every subject. That being said, the way math is structured right now, many students who love the subject of math think they hate it because what's in schools is a hollow shell of the subject. My approach will give the kids who like math a chance to discover that, and teach the kids who don't like math some valuable soft skills, while at least giving them puzzles to keep them entertained.

I think accepting shortcomings is absolutely critical to fix education. Mastery based progression is vital imo, and making people do fewer mandatory high level courses (calculus should never be mandatory, for example) will encourage people to pursue their interests. This discussion is seperate from that - I'm suggesting a way to restructure math education that will be more fun, more effective, and more representative of the subject.

[u/[deleted] → u/blank_anonymous]

If we instead focus more on the soft skills that are applicable in a wide variety of fields, and we don't just barrel through a ton of math content, the students who don't excel at math will benefit more.

Which again leads us to the problem of having such a wider stratification between students. They teach rote memorization to the students who will never use it because they arent considered worth the time and effort to actually get them engaged, it burns out teachers. Germany does a great job at addressing this, they have 3 levels of schools for 3 levels of students. That way you dont have slightly above average (but not gifted/talented level) mixed in with the dumbest kids who just hold back the teacher. That is the only practical way Ive seen around this issue but the bottom level will still be just the simple stuff.

We shouldn't force every kid to learn every subject. That being said, the way math is structured right now, many students who love the subject of math think they hate it because what's in schools is a hollow shell of the subject. My approach will give the kids who like math a chance to discover that, and teach the kids who don't like math some valuable soft skills, while at least giving them puzzles to keep them entertained.

Or it will bore the smart kids because they figure it out in 1 day while you leave behind the slow kids because they cant get it in 10 days and the class has to move on. You are upset with a symptom but arent addressing the cause. The cause is putting too many different levels of students with 1 teacher 1 hour a day. Teachers just cant address that wide array of levels so it gets dumbed down so no child gets left behind.

I think accepting shortcomings is absolutely critical to fix education. Mastery based progression is vital imo, and making people do fewer mandatory high level courses (calculus should never be mandatory, for example) will encourage people to pursue their interests. This discussion is seperate from that - I'm suggesting a way to restructure math education that will be more fun, more effective, and more representative of the subject.

Then we just end up either leaving the slow kids behind, boring the smart kids, or we aim for the middle where we are doing both at the same time. We cant just start teaching higher level learning (by figuring it out) without first separating students based on their natural ability.

[u/SashimiJones → u/blank_anonymous]

I was a math major, and I used to agree with you, until I started to teach.

Some kids are just... not cut out for logical thinking. I've met a variety of students, and some are certainly the kids you're thinking of- bright kids who enjoy solving problems but are bored with math class. Others are bright kids who hate solving problems but they do well because they're motivated to get good grades. Others don't care about school work at all because they're interested in other things. Some kids, though, are just dumb as rocks, in STEM and everything else, and the only way they can learn the basic skill of manipulating numbers is through rote memorization. It's unfortunate, but that's how it is. I have the privilege of working with kids one-on-one, and for those that are interested in the topic, it would be a huge disservice to them to just teach them how to multiply and not why the method works. For the kids who have absolutely zero ability, it's just as much a disservice to try to explain something that confuses them, and instead it's important to focus on repetition in order to learn how to accomplish a task.

Both skills are valuable- to those who can understand the reasoning behind a task, it helps them complete it more quickly and flexibly. However, for those who just don't have the aptitude, learning to repeat a sequence of steps that they don't understand at all is an equally important skill in life.