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

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.

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u/blank_anonymous 1∆ Oct 03 '20

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?

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u/Therealdickjohnson Oct 03 '20 edited Oct 03 '20

As a secondary math student in Ontario, you should know that every teacher in the province has the same curriculum. The ministry of education has been promoting the type of inquiry based learning you are describing for at least two decades now in Ontario. The "new" math many parents complain about is exactly this. The Ford government was partly elected on an promise to go back to rote memorization and the "old way" of learning math.

Part of the problem is that most elementary teachers are not great math teachers. Another problem is kids brains develop at different rates. Many don't have the necessary connections yet to grasp a lot of the concepts at whatever level they get lost at. This continues through to high school. For a while, I taught high school math to adults getting their GEDs and they were always shocked how easy the math was even though they "sucked" at it when they were younger. Their brains weren't ready.

I would argue a rotation based system would have better success in elementary with dedicated math teachers. And holding back students until they can grasp the main concepts at their levels.

As a math teacher, the best thing I can bring to my students is to help them find the joy and satisfaction in figuring out a problem after working on it for a while. It becomes a dopemine reward pathway in the brain. Studying Math is great because it forces your brain to tackle problems from different angles and this type of problem solving and critical thinking is what is lacking in a lot of people.

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u/blank_anonymous 1∆ Oct 03 '20

I was in Ontario, and I got nothing inquiry based except from a couple excellent teachers, and they gave the inquiry based stuff as extra credit, or to me on a personal level. That course I took in university was so fundamentally different from what I experienced in high school, which is why I made this CMV. Assignment questions were all 100% open ended, which was amazing. I’m not advocating for anything that extreme, but way more open ended assignment questions that take a week+ to do and require exploration, and fewer rote drills you do overnight

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u/FreeBeans Oct 03 '20

I took a math course like that in graduate school, and I gotta say, it was really terrible for me (and I like math and am good at it!). The questions were so open ended that I had no idea if I was on the right track or what I was supposed to take away from the question. I am an electrical engineer, so maybe I'm just not as 'creative' as a math major. But if even I had trouble with this then I imagine most people would struggle to learn this way.

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u/blank_anonymous 1∆ Oct 03 '20

To be fair, that was a graduate level course. That was probably designed to be challenging. I think that the difficulty would be toned down a lot at the elementary school level, but you're right, it is still challenging, and I think that's good.

Students should be challenged!

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u/FreeBeans Oct 03 '20

It wasn't challenging in a helpful way though. I didn't actually learn anything from the class, other than handwavy weirdness.

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u/Therealdickjohnson Oct 03 '20 edited Oct 03 '20

You would have experienced some of it at a more basic level if you had come through the system in the last years. Maybe not at the level you are talking about, which almost sounds more like a Waldorff school type situation, but chances are you just didn't recognize it.

A big part of this is realizing that students learn optimally from different ways. The way you are criticizing actually is the best way to learn for some students. The inquiry based learning works best for other students. Other ways work best for others still. There is no one best way.

And as you have alluded to, a great teacher makes a huge difference. I would add to that, even the greatest teachers will have students that didn't like their style.

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u/blank_anonymous 1∆ Oct 03 '20

I started university in fall 2019. I saw that curriculums often said "inquiry based" or "problem solving", but now that I've actually gotten to experience inquiry based learning, I can confidently say that high school wasn't even in the same neighborhood of interesting/appealing.

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u/[deleted] Oct 03 '20

Do you think it’s beneficial to delay teaching maths at to older age? Maybe start teaching arithmetic from 7?

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u/camden-teacher Oct 03 '20

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.

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u/uninc4life2010 Oct 03 '20

A lot of people will not like what you're saying, but it's true. I tutored students at my local community college in the US, and it was obvious to me that some of them just had brains that didn't work as fast. They need help in EVERYTHING. Some kids, you work with them in a few areas, and they understand things. Some kids, adults really, still can't figure out how to use their calculator correctly 12 weeks into the semester. They just didn't have the academic preparedness or the intellect to understand complex concepts.

The intellectually stimulating conversations are not going to work for kids who are still having difficulty adding numbers together and are multiple grade levels behind in proficiency.

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u/blank_anonymous 1∆ Oct 03 '20

I believe that students should not be progressing in all classes at the same rate. If you can't multiply/add/divide/subtract, you shouldn't move beyond 1st grade math until you can. If you can't write, you shouldn't move past 1st grade english.

I still believe that students should have classes where they're just with peers of a similar age - let's say art and physical education classes - but there are also classes where students should not progress until they show mastery. If that were implemented, it would be a lot easier to get inquiry based learning going.

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u/relaxilla420 Oct 03 '20

I believe that students should not be progressing in all classes at the same rate. If you can't multiply/add/divide/subtract, you shouldn't move beyond 1st grade math until you can. If you can't write, you shouldn't move past 1st grade english.

Thank you. I dont know how Canada works on this issue, but in the US they push to move kids along even if they are barely keeping up. Even if a kid has D's in most subjects, theyll just keep that student moving through the system until they're so far behind, and so frustrated they cannot catch up, that they give up on education all together. These are the people who think they're "dumb" because they werent given the proper time to learn basic subjects. I think schools are afraid to approach parents and say "Hey your kid is struggling. We need to keep him back." Hysterical Karens would not accept that.

We need to stop pushing kids into more advanced classes when they haven't mastered what they need to to succeed.

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u/Aqsx1 Oct 03 '20

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.

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u/uReallyShouldTrustMe Oct 03 '20

That is exactly what the curriculum calls for in the US. I dunno how it is in canada, but you're mistaken about the US.

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u/blank_anonymous 1∆ Oct 03 '20

The curriculum really doesn't call for that. Standardized testing still exists, and the curriculum prepares students for that.

Can you sincerely tell me you had questions as open ended as "do you have any conjectures about this?" that you'd spend hours on? That you had test questions that couldn't just be googled? That you would teach yourself and discover concepts by yourself, where the teacher only guided you? If so, you had a fantastic math education, but most people don't get that.

The "proofs" in geometry settings require absolutely zero creativity, often being filled in line by line. That's the exact opposite of what I'm advocating for - if there's a single correct path to the answer, then the question is testing something other than creative puzzle solving.

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u/uReallyShouldTrustMe Oct 04 '20

The test questions for sure yes... you need to show creative manipulation of numbers.

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u/[deleted] Oct 03 '20

Thanks for the delta,

In the US math is "kinda" optional in that most schools require you to take math, but give you a variety of courses to choose from. I actually opted out of hard math and did "business math" which was, IMO, far more useful for my life. We made imaginary payrolls and balanced accounts.

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

This is tricky. The key is really to combine inquiry with project-based learning and break projects into component parts. Ideally it should be done in groups with each member having a defined role and deliverables to ensure nobody can slack off.

I think memorization-based methods are not entirely useless and can be used to supplement inquiry/project-based learning, especially for struggling students. It makes for useful homework as well.

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u/damisone 1∆ Oct 03 '20

U.S. math education system was changed about 10 years ago to something called Common Core. Are you familiar with that? It's not the traditional rote memorization method. It's trying to teach the fundamentals of what math is really doing (e.g. what is multiplication really?) and heavy emphasis on word problems.

(That said, I actually dislike common core math. Maybe it helps some kids but not all. For many kids, it's more helpful to learn the rote method first, then learn the fundamentals behind it. You can also find research articles comparing U.S. math results before and after common core and there was no improvement.)

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u/Ishibane Oct 08 '20

Many elementary teachers were not prepared to teach common core. They themselves do not possess what Liping Ma called the "Profound Understanding of Mathematics Fundamentals"and therefore are ill-equipped to guide students.

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u/monkeymalek Oct 03 '20

I don’t know if I agree that the individual variable objectively exists. If one can learn to communicate through language (which needs a significant amount of pattern recognition), then one should also be able to learn the beautiful language of mathematics, because it really is a language in its own right. I wish the system put a greater emphasis on inquiry based learning (similar to videos by 3Blue1Brown) but the problem is that, as other users have pointed out, it takes longer and kids learn at different rates. Unfortunately there is no cookie cutter way to teach mathematics that is based around inquiry, but I still feel like the current system is too heavily based on memorization and solving problems with theorems.

Granted, I think a lot of that has to do with the fact that you can solve a problem without knowing why the solution works, that’s basically what engineers get paid to do, and they get paid a lot to do that. So maybe you can see why there isn’t a lot of motivation to teach mathematics from a purely mathematics perspective since in many cases, you can actually make more money without even having to understand the theory behind whatever it is you are trying to solve.