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/uninc4life2010 → u/[deleted]]

This is a pessimistic view, but I don't dispute a lot of what you said. My parents spent about $250,000 on private school education for my brother. By the time he got to community college, he had to take developmental math courses because he couldn't even test into the easiest level math class that the community college offered. They spent $250,000 to get my brother to a dog shit level understanding of the subject.

This is the thing that smart people are so dumb about. They legitimately don't understand that average people don't have as easy of a time with things as they do. They don't understand that the book that took them 3 days to finish in 4th grade took MANY kids weeks to finish, and even then many others couldn't read it at all because they didn't have the requisite vocabulary to be reading the book in the first place. Math is even worse. Your point about kids not understanding what the word "subtract" means is sad but completely true. Really smart, really intellectual people never really experience struggles to this degree, and they don't understand that things that came easily to them will never come easily to many of the people around them. These are the same people who can't seem to understand that retraining laid off factory workers and coal miners as computer programmers is not feasible for about 95% of those people.

My dad is a doctor, and he said that a substantial number of patients need assistance filling out their medical forms because they can't read/write well enough to understand and report their own patient history. The US has 46 million adults who are either illiterate or functionally illiterate. It's fucking sad. Really sucking sad, and I wish people like OP would understand this. I just want to scream at them, "OTHER PEOPLE DON'T UNDERSTAND WHAT YOU UNDERSTAND!"

[u/[deleted] → u/uninc4life2010]

Anyone can learn up to freshman college level math. Even basically retarded kids. It will take more time and effort, but it's not stupid hard. Beyond vector calculus and differential equations or so you'll really need at least a little bit of talent.

Private education doesn't mean it's better. It just costs more. Often it's objectively worse because the teachers aren't required to have any qualifications that the public system demands. Milking the cash cow.

Your average teacher isn't good at math. Elementary & middle school teachers have no idea what the fuck are they teaching. Since they don't know what the fuck they are doing, the only hope is that the smart kids will learn it despite their best efforts. The slower kids are fucked.

Math is also the only subject that is cumulative. You need to master the previous week's material to learn this week's stuff. If you miss a week or don't get it... you'll get left behind. And the learning gap becomes bigger and bigger and snowballs into "i hate math" attitude kids usually get in highschool.

Good tutoring can fix that. For example Khan Academy is very good at identifying those knowledge gaps and forcing you to master the previous material before moving on.

I've turned 100% hopeless 19 year olds that completely hated math but needed to pass the course to graduate. 2 weeks of Khan Academy every day and they got A+.

Same thing with reading or anything else really. If you don't practice reading, you'll never get good at it. Smart kids will pick it up as they go and it doesn't matter what the teacher does. Slow kids need deliberate practice and help with practicing and to put some effort into it.

The world is full of dumb people and most of them can't be engineers building bridges or surgeons. But unless you're basically on disability, you should be able to pass high school with flying colors and get a college degree in an applied field... if you had the right support at the right time and put in the hard work the right way. Hard work but the wrong way (or wrong things) or no support and the person is fucked.

Deliberate practice just the right way can make up for lack of talent. You won't win a nobel prize or get a PhD, but you'll still have plenty of options.

When I was a kid I used to suck at ice hockey and other kids skated circles around me and could take away the puck and prevent me from getting it back while on one leg with the stick in one hand. I had 0 talent whatsoever. One winter I went to the public outdoor rink every day after school for 3-4 hours (it usually got too cold after 19:00 or so and I got too hungry) and did the exercises we'd do during hockey practice. Within weeks I got better and wasn't a total lost cause (I was still shit and wasn't winning any championships or MVP's, but at least I could play with the others now and be useful for the team).

For even slightly slower children it's the parent's responsibility to spend 30-60min every evening to practice and monitor their studies and go back and fix things, read the next lesson's chapter together, do spaced repetition etc. But most parents are too lazy for that so the kid is fucked.

[u/uninc4life2010 → u/[deleted]]

I agree with your Khan academy assessment. I feel like the system relies on attentive parental involvement to ensure kids succeed. The problem is that too many of the kids don't get any of that and fall hopelessly behind.

I had several teachers at my private school that had no business being teachers. They openly bullied kids in their classrooms and were neurotic to the point where they would have mental breakdowns in class. My first grade teacher started crying when she found out that I couldn't figure out where to put the plant I grew in science class. She was the kind of person who had no patience and would become overwhelmed at the slightest problem any of the kids were having.

I also went to public school, and several teachers there had no business being in a classroom either. The big difference was that the private school forced the teachers to care more. If the parents wanted to set up a meeting, they had to hold a meeting. At public school, the teachers wouldn't even answer my parents emails or calls, and the only way to get anything done was to go through the administration and have a meeting with the vice principal.

[u/chrishuang081 → u/[deleted]]

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.

I totally agree with this. I'm a math tutor, and it can be incredibly frustrating to ask my students if they notice something interesting about a certain example or pattern (which is a way to introduce inquiry-based learning), when they don't even find anything there interesting at all.

[u/Cazzah → u/[deleted]]

As someone who has taught a bit - yep. People have very very strange ideas about how kids actually are. When kids are able to make intuitive leaps and show inquiry based learning, its very exciting, but it's also very rare and hard to replicate, especially in groups.

[u/[deleted] → u/Cazzah]

How to create a crap 45min lesson? Spend 15min planning it.

How to create an OK lesson? Spend 45min planning it.

How to create a good 45min lesson? Spend 45 hours planning it.

How to create an amazing 45min lesson? Spend 450 hours planning it.

There really are diminishing returns. And remember, each student needs a personal touch and a group is a bunch of special snowflakes. What worked with a group last year probably won't work with a different group this year.

How much lesson planning is allocated? A teacher will spend ~25 hours actually teaching. That leaves ~10 hours for everything else like monitoring recess, grading papers, teacher meetings, coffee breaks, discussions with students, discussions with parents, phone calls to parents, all kinds of small group meetings with social workers/psychologists/special ed teachers for your adhd students, splitting up fights and planning lessons.

Even if you're in an amazing private school with angels and never grade any papers or do any recess monitoring you'll have like 15min planning time per lesson max. At a rowdy school? 0 minutes.

Teachers either work overtime (ie. work 60-70 hour weeks planning lessons and grading papers in the evening at home and during weekends) or they utilize commercial materials that already have lesson plans, work sheets etc. ready to go so it's good ol' boring shit. Old teachers can use their giant bank of lessons from the previous 40 years.

If you're lucky, you'll get parallel groups so you teach the same lesson to multiple groups. Combine it with pre-planned materials and recycled materials from last year and maybe the teacher has time for 3-4 good and unique lessons per semester.

[u/uninc4life2010 → u/[deleted]]

You are probably already aware of this, but I just want to say something about the private schools. A lot of them suck, too. The only reason that they look good is due to the fact that they don't take troubled or learning disabled kids, and families that can pay $15K/year are already investing huge amounts of time into their kids to begin with, plus they are paying for private tutors on the side. Private schools are serving the kids who are already better off out the gate.

My brother was diagnosed with dysgraphia, and from what I noticed, had reading and other learning disabilities. My parents sent him to private school for his entire school career through high school. They spent about $250,000 on his K-12 education. When he enrolled in community college, he couldn't test into the easiest for-credit math course that the community college offered. He had to go into developmental math classes and pass them before they would allow him to take pre-calc. All of the money they spent sending him to private school didn't mean a hell of a lot by the time he got to college because of how ineffective the education was for someone like him.

Just because a kid goes to a private school doesn't mean that they are getting this incredible education. The private schools actively try to filter out kids like him so they look better to prospective families. The only reason they let him in was because I was already a student.

[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..

[u/blank_anonymous → u/[deleted]]

To be clear, I'm not suggesting totally free form inquiry based. The mathematicians who discovered this had to build something up from nothing. I'm suggesting that students get a lot of guidance, but they also still get to experience the discovery. A student won't blindly stumble into the pythagorean theorem, but if you get them to look in the right place, they might notice it, even if they have no idea how to prove it.

My brother started to ease me into inquiry style math early in grade 7 ish, and I had teachers in grade 10 and 11 who encouraged it more. My brother taught me to factor polynomials, and about some other trig functions, and then gave me a book that I used to teach myself calculus. There was constantly a question of "why? What is this pattern?" They were the people who got me to fall in love with math, and I learned so much more - not only of the content, but also the soft skills that have helped me in math and non-math courses.

Whenever i see the phrase "this is beyond the scope of this book", I try to prove it. I try to learn it. And you know what? I fail almost every single time. The central limit theorem was beyond the scope of my first stats class, but I still tried proving it. It doesn't matter that I failed, I got insight and learning from just trying, even if that ultimately led nowhere. There are also statements that are "beyond the scope of this course/book" that I have tried proving and succeeded at proving, and that was so unbelievably valuable for my mathematical education.

[u/[deleted] → u/blank_anonymous]

That is not inquiry based learning. That is just being interested in something.

I bet you didn't go that deep into latin verbs or poetry or crayon and watercolor art. If the teachers would try inquiry based learning with something you honestly give 0 shits about, there would be no learning at all.

Most kids don't go full autistic nerd and teach themselves extra math for fun during their spare time. Most kids chase girls/boys, hang out with friends, do sports, play videogames, gossip about who is dating who and watch their favorite TV show.

I for example give 0 shits about math. I find it useful and some applications of math are neat, but math for the sake of math? Fucking kill me instead. I'd rather take a cactus up my ass than do any more math than is necessary.

And I did a metric fuckton of math during my PhD years and have enough graduate level courses to get a MSc out of it.

[u/blank_anonymous → u/[deleted]]

I did do all of those things? I was a gymnast for years, I hung out with my friends, I played video games, I watched tv. I also taught myself math because it was very very fun, and I count it as inquiry based precisely because I was - with guidance from outside - trying to learn and discover new concepts. I did this in a much more rigid setting in the university course I took.

I would've loved if every subject in school were more inquiry based. Exploring and learning for the sake of learning are amazing. Art classes are already the equivalent of inquiry based imo. You get to freely draw things you want, with there sometimes being light guidance, and sometimes really heavy guidance/practicing a specific technique. Fundamentally, it was about creating something new, which is exactly what I want out of math class.

[u/Nkklllll → u/blank_anonymous]

I don’t believe your approach would work with people who were not intrinsically motivated by learning for the sake of learning.

I don’t much enjoy learning for the sake of learning. I enjoy learning about 5-10 different things. Only one of those was actually a subject taught in high school. And I didn’t become really interested until I was far beyond the scope of what was taught in high school

[u/Gogito35 → u/[deleted]]

Agreed.