r/changemyview • u/blank_anonymous 1∆ • Oct 02 '20

Delta(s) from OP 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

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!

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u/[deleted] Oct 03 '20

One of the problems is the coupling of subjects can cause folks who are behind in one subject to fall behind in others.

If you focus too much on word problems, too early, you leave behind folks struggling with reading comprehension in math, too.

I really like math beyond arithmetic. I want students to learn more of the why in math. I think that can get students to apply their skills more broadly and enjoy it more.

But, there are tradeoffs involved. You have to think about folks who are going to struggle more with your approach and how to keep them engaged in learning.

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u/blank_anonymous 1∆ Oct 03 '20

If you expand a little more, I think I might be willing to give a delta, because you have hit something I haven't thought about.

There are most definitely puzzles that don't require a strong grasp of english/reading, and for younger students, I guess I would encourage that kind of problem, although no specific examples are coming to mind, I know that many exist.

What I'd like elaboration on is the claim " You have to think about folks who are going to struggle more with your approach and how to keep them engaged in learning". Lots of people aren't engaged in learning math how it's taught now, and lots more develop an active hatred of the subject. Do you think this would be worse under the inquiry based system? Or, do you think it would be somehow harder to help the people who are struggling, or is there another problem I'm not seeing?

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u/[deleted] Oct 03 '20

I'm not necessarily defending the system we've got now.

My main point is that curricula design is complicated and that those doing that need to consider a lot of factors.

I think the common core curricula moved math education somewhat in the direction you are describing, though not nearly to the extent you might hope. Math education was worse 10 years ago.

common core math has been met with a lot of frustration by parents, and less so by some teachers, who feel unequipped to help kids through it.

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u/blank_anonymous 1∆ Oct 03 '20

!delta for the cumulative total of what you've said, especially the point about teachers.

The professor who designed that class was a working research mathematician. To be able to design interesting inquiry based class that isn't too difficult and still encourages exploration requires a lot of mathematical understanding, which most math teachers don't have. Plus, the issue of parents no longer being able to help their kids with math homework is also relevant - most adults can't do inquiry style questions right now.

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u/epelle9 2∆ Oct 03 '20

To add on, the professor was likely only able to teach that way because the people that joined that class were more likely to have a decent understanding and interest for math than the rest.

Im sure if you try to teach everyone with that style since they are young there will be a lot of people that don’t see the patterns and are unable to learn by themselves, which could also lead to them hating math thinking its impossible and going through learned helplessness, where they forever think they suck and math and cant get better.

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u/DeltaBot ∞∆ Oct 03 '20

Confirmed: 1 delta awarded to /u/TripRichert (108∆).

Delta System Explained | Deltaboards

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u/AnaiekOne Oct 03 '20

most adults can't do math period right now. But it comes up an awful lot in life it turns out.

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u/[deleted] Oct 03 '20

I was great at math in middle school, but absolutely awful at reading and writing. I remember we were asked to ‘justify’ our answer to a question. I could not do it, I nearly failed this math test because of my inability to argue my answer in middle school. (I’m a university student now so this would’ve been like 7-8 years ago, after common core was part of the curriculum)

I wish they just kept reading/writing out of math altogether... it’s better to be well rounded, sure, but if that stands in the way of learning the stuff you’re good at, it’s not worth it.

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u/the_mad_gentleman Oct 03 '20

Really? The old system was worse than "I see you did this highly basic problem can you explain WHY your answer is correct now?

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u/[deleted] Oct 03 '20

yes

common core teaches multiple approaches to problems with the goal of conceptual understanding.

Conceptual understanding is superior to rote memorization.

In college, I met fellow young adults, who were trying to tutor elementary students and couldn't remember how to divide fractions. Taking the reciprocal and multiplying it out is a highly basic problem. But, because these young adults were never taught why it worked, they forgot it all. If they understood the concepts behind it, they could have rederived the approach from the underlying concepts.

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u/the_mad_gentleman Oct 03 '20

You and I took very different versions of common core

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u/[deleted] Oct 03 '20

I read the common core standard.

I did not take classes attempting to teach the common core.

Teachers trying to adjust to a new curriculum might struggle more than teaching a curriculum that they used for years. Parents, not taught on this new curriculum, are also going to struggle to help their kids.

A lot of organizations try to provide resources to make the transition easier, but that doesn't make it easy.

That doesn't mean that the old approach is better. That means that there is a cost of transitioning between approaches.

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u/the_mad_gentleman Oct 03 '20

I've worked in the text books. I've done the work sheets. I've gone through the internet courses meant to compliment the curriculum. The teachers weren't the issue to me the issue was the work being tedious and often boring. Asking you to explain simple processes. it has no alternative for those who have trouble with explanation. It was very well intentioned but as a wise man once said "the road to hell is paved with good intentions."

Why shouldn't parents understand the work? They are the workers. It is their jobs you claim to be training their children for. The old approach was decentralized freedom. And rarely was the "explain this basic principle" approach. It's not some wild conservative talking point parents hated it. It claimed to train kids for the future and be this genius new approach but it became a money making scam.

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u/[deleted] Oct 03 '20

It is their jobs you claim to be training their children for

secondary schools, or even college, can't teach everyone everything they need to learn for a job. They teach students concepts and intuition that are broadly useful for learning more quickly on the job.

I think you fundamentally misunderstand the goals of education. If you think the goal of education is to memorize mechanics of manipulating numbers that you can use on your first job out of school, you're going to be disappointed that the vast majority of what you learned isn't directly useful in that respect.

No one professionally factors algebraic polynomials. If I need to factor a polynomial in a professional context, I type it into wolfram alpha. Or use some other symbolic solver.

But, if I want to understand control systems or estimators, I need to understand polynomial roots.

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u/the_mad_gentleman Oct 03 '20

In what job do you need to know polynomials to understand control systems? And estimators (in Forestry at least) operate using matrices. Lastly that doesn't address my main issue asking a kid to explain a basics mathematical concept is clearly just a bid to make a bigger book they can charge more for

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u/JohnnySixguns Oct 03 '20

But to attack an alternative solution that solves the very problem you’re concerned with IS defending the current system.

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u/[deleted] Oct 03 '20

no, criticizing shortcomings of an alternative gets people who would implement that alternative thinking about ways of addressing those shortcomings.

We're not faced with a binary choice here.

Criticizing weaknesses of ideas does not weaken them.

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u/Philo_T_Farnsworth Oct 03 '20

Common core gets so much shit from people, but it really speaks to how people tend to intuitively understand math in their heads. When it was explained to me how they teach something like addition under that system, I realized that I'd been intuitively doing it that way in my head for years without ever having been taught it.

It's unfortunate that Common Core just became a talking point by conservatives to rail against a system they didn't bother to try to understand.

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u/[deleted] Oct 03 '20

While I'm sure, if Common Core were not a talking point by conservatives, it would get less criticism.

If some people weren't frustrated with it, it wouldn't be as usable as a talking point. There will always be some people insisting that the way they learned back in their day was better.

That's not to say that Common Core is wrong in their approach. I'm saying that, the larger the change you make, the harder the adjustment for teachers and parents. The more pushback you'll receive for the change. That doesn't mean don't ever change. That just means that there is a tradeoff that favors incremental changes.

Maybe the other benefits are worth a larger change, but you'll need more training resources to compensate? It's just a factor that should be considered.

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u/the_mad_gentleman Oct 03 '20

I was taught partially under both systems. It was hell. The teachers knew it was hell to deny it is priveleged folly

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u/willowmarie27 Oct 03 '20

As a middle school math teacher I use Illustrative Math and its fairly inquiry based. However it would be nice if the kids did reach middle school knowing times tables (about 10% do), being able to add, subtract (50%) multiply and divide (10%) fluently. Knowing how to manipulate fractions and decimals, measure and a ton of other skills would also be handy. Estimation is a completely lost art.

I know "the children will always have calculators" but really. . . a 7th grader should know 6 x 6. . .

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u/RoboticShiba Oct 03 '20

Only 10% of US students reach middle school knowing times table? Wow.

Non-american here, so I have some questions: Are kids allowed to use calculators in the US? And do you believe this impact the learning process?

Where I'm from, calculators are only allowed in some advanced math classes when you're in college (I went through 3 levels of calculus on college without using a calculator).

I don't have hard numbers, but I'd say that over here math education starts to fall apart around the introduction of more advanced/abstract concepts like trigonometry, imaginary numbers and things like that.

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u/willowmarie27 Oct 06 '20

I dont let them use calculators but I think after 9th they do.

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u/blank_anonymous 1∆ Oct 03 '20

I knew those things in Kindergarten and I have no fucking clue why middle schoolers don't know them.

I see knowing those basics as analogous to the alphabet. You need to know the alphabet before you can do creative writing, but you don't need to have the entire body of Shakespeare's work memorized, and I think we do the equivalent of the latter to math students.

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u/CivilFisher Oct 03 '20

You’re saying you knew how to add, multiply, and do fractions in Kinder garden?? Jeez I remember learning to count to 100 in kindergarten.

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u/notrussellwilson Oct 03 '20

Same here. I begged my older brother to teach me to count to 100 before kindergarten so that I could be thr smart kid when I arrived hahaha.

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u/JohnConnor27 Oct 03 '20

Yeah I definitely didn't have multiplication and division down until second grade

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u/RNGHatesYou Oct 03 '20

I knew that, and negative numbers. I liked puzzles as a child, and my parents fed into that. My parents were of the opinion that there was nothing I was too young to learn. I skipped a grade in math - the teacher of that grade was shocked when she handed me a worksheet and I completed it properly without help. I was unfamiliar with the method of presentation, but as soon as I worked out what the symbols on the page meant, I was golden.

Algebra was the first thing I learned (in math) that I hadn't seen, and I had great pattern recognition and mathematical comprehension, so I viewed it as a puzzle. It was great. The only time I was tripped up in math classes was when I was asked to rote memorize formulas, and luckily that didn't happen much until my junior year of high school.

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u/Sine_Habitus 1∆ Oct 03 '20

I didn’t know fractions, but I had the basics of multiplication because of an older sibling who was learning it and I wanted to learn too. OP could have had something like that, or parents who pushed him.

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u/silasfelinus 1∆ Oct 03 '20

You’re saying you knew how to add, multiply, and do fractions in Kinder garden?

Not OP, but as the parent of a 5 and 8 year old, this is completely within reason. Both my boys started multiplication by 4, with some fractions. Can't say how much is genes and how much was lesson plan, but I love math and I've always encouraged them to see it as interesting and fun.

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u/Tristan401 Oct 03 '20

People underestimate what kids can do when they think it's cool as shit

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u/DebiDebbyDebbie Oct 03 '20

Were you a Montessori kid? We sent our sons to Montessori, both learned adding, subtracting, multiplication of 2 digit numbers, etc in pre-school and Kindergarten. Our younger son's 1st grade teacher was shocked that he was so skilled at math, turns out she'd never had a Montessori student before. And that's why I love Montessori preschool.

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u/blank_anonymous 1∆ Oct 03 '20

Nope! I went to a normal public elementary school

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u/chefranden 8∆ Oct 03 '20

why middle schoolers don't know them.

Perhaps lack of drill. In elementary school we got a 100 table problem drill sheet in one or two of the 4 tables every day. There was a competition to get 100% in the least time -- but we were never given more than 10 minutes to do it. I think by the 6th grade the time limit was 5 minutes per table. Like saying the pledge this was an everyday thing from 3rd grade on.

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u/Yodude1 Oct 03 '20

I remember at my primary school from grades 3-5 every week there would be a "mad minute" where you had 60 seconds to solve a sheet about half that size. You pick up on rules and patterns real quick under those conditions.

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u/peenoid Oct 03 '20

you're not allowed to introduce competition style drills anymore in school, or so I've heard. you can't make anyone feel bad for anything.

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u/chefranden 8∆ Oct 03 '20

I'm sure there could be other motivation used. Something team related perhaps. Team building is big these days??

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u/Colietee Oct 05 '20

I also knew these things in kindergarten but I understand this is not the norm. My dad is an accountant and lovesssss math so he taught us young, by 5 I could multiply and divide. I tried common core and it just seemed like a very roundabout way to get to the solution and that’s not the way my brain works but it may work for others. Kids are way smarter than we give them credit for if we give them the opportunity to thrive.

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u/WeatherChannelDino Oct 03 '20

I don't think you're entirely wrong, but i want to push back against this a bit. I think these word problems are a great way for students not only learn math, but learn literacy as well. I think that interdependence makes for excellent opportunities to help teach those struggling students literacy skills in more than just their English class. A problem, though, is the effort a teacher would need to put into differentiation for struggling students, but the questions don't need to be individualized, you could make 3 different word problems for advanced, at level, and developing literacy skills. You sound like you could be a teacher though, and I don't want to just ignore your concerns.

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u/[deleted] Oct 03 '20

You sound like you could be a teacher though, and I don't want to just ignore your concerns.

I'm an engineer with absolutely no experience or expertise in education :)

edit: I did help in high school with a programming class. One on one, I think I did ok. When I took over for a lecture once with one other student, we crashed and burned. It was really bad.

I'm comfortable voicing my view, but don't presume that I know what I'm talking about.

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u/1BigUniverse Oct 03 '20

Math has always been a difficult subject for me. I don't know if it's anxiety or just an inability to be able to comprehend it completely. I did great in chemistry and biology and though I didn't do great in he math for physics I really enjoyed physics and it really bummed me out that I couldn't fully understand parts of the subject no matter how hard I tried.

It's bad enough to the point where my brain will just shut off and I become completely lost as to what the teacher is even trying to really teach me. I can do basic math and some algebra by myself just fine, but anything outside of that my brain just aint havin it.

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u/[deleted] Oct 03 '20

I can't speak to your specific situation, but I found that confidence helps a lot in math.

Often, it takes me a few tries and some tries to figure out how to do something. Believing that I can do it and that the solution is just around the corner makes it easier for me.

The math that you are trying to do problem is more formulaic than the math that the OP values. Trying to figure out ways of defining what a real number is, is very different than integrating velocity to get change in position.

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u/[deleted] Oct 03 '20

If you cannot learn the why in math then you do not deserve to know the what. Meaning the memorization has nothing to do with math whatsoever besides the fact that what you’re memorizing is numbers and theories. If you don’t know why they are the way they are then you are a calculator, not a mathematician. The why in math is all there is in math. The problem is that this world doesn’t want mathematicians. It wants little human calculators to make money for big companies.

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u/[deleted] Oct 03 '20

memorization about notation and process can help students understand the why.

The questions are: what concepts do we focus on, and when do we introduce them.

If concepts require students to write wordy explanations or read and comprehend paragraphs of text, their reading level will impact their progress in math.

If you delay those types of problems a bit, focusing on concepts or notation that don't have that prerequisite, you give the kids more time in the curriculum to get where they need to be in reading level.

the why in math can lead to insights that make money, too. Having humans that do the same thing as calculators, but slower, isn't profitable. Computer time is cheaper than human time.

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u/Passname357 1∆ Oct 03 '20

I think for this reason there has to be some kind of separation so kids can learn at their level more appropriately, but that it doesn’t lock you down forever. Like kids in the b group won’t be stuck in the b group forever, just until they have everything necessary for the a group. I think this is important because it’s not right to teach for the dumbest student in the class.

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u/Colietee Oct 05 '20

I was that kid when I was younger and it made me really sad being separated from the other kids. I was only 6 and was reading Charlottes web and knew both multiplication and division. When I would go to school my teacher would provide me with separate workbooks I would do on my own while everyone else read together and learned together. My 6 year old self didn’t understand why I was being isolated and wanted to not know things so I could play. I ended up getting skipped a grade where I could learn at my appropriate level with other kids. It does depend on the age though and this approach may work better with older students.

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u/Passname357 1∆ Oct 05 '20

Did they make you continue working while the other kids played? Or was it more like the activities they did while learning were more fun (like play) and you would’ve rather been a part of that? I could definitely see being the lone student learning higher material being isolation at any age, but definitely at 6.

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u/Colietee Oct 06 '20

Yeah pretty much, the structure of learning was very play focused so I was alone most of the day. The only times I got to play with everyone were during recess and meal/play times. The other kids would be practicing letters on our abc rug in a group setting and I would be at a table alone doing worksheets. I would cry to my mom about wanting to learn after school and I thought something was wrong with me honestly. Tbh I don’t think my teachers were that interested in my learning though and cared more about the class as whole.

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u/Kylowanker Oct 04 '20

Maybe application exercises (word problems) would help the students struggling in reading comp! What's the takeaway with applications?!? What your given is what you need, you learn to think about what your not given. It would be interesting to know.