[imgabe]

Do other disciplines ask similar questions?

How should physics be taught to non-physicists?

How should writing be taught to non-writers?

How should car maintenance be taught to non-mechanics?

I guess my point is, why should we teach mathematics any differently to "non-mathematicians" than we do to "mathematicians"? I mean, at the point when you're first teaching someone, how do you even know if they're a "non-mathematician" or a "mathematician"? After all, they haven't learned enough yet to know if they'd want to continue in that field of study.

[tikhonj]

Yes, all the time. I've heard it for physics, I've heard it for CS and I've heard it for programming, all with good reason: the way you teach somebody deeply invested in your field is different than the way you teach somebody deeply invested in a different field, learning yours as a supplement. Or maybe a better way of putting it is that the way you teach somebody interested in a field in and of itself is different than the way you teach somebody who has other interests and motivations, but still needs to learn.

And hey, maybe before college, almost everyone is a non-mathematician. There's the small majority of students who'd love learning group theory because it's fun and beautiful, and then there's everyone else who need practical applications and real-world examples. But the way you teach them is ultimately just like the way you'd teach non-mathematicians in college or further on in life, when there's a clearer delineation.

[Spivak]

This situation actually started a pretty nasty divide at my university. Engineering and Math are in separate organizational units which gives each a degree of independence. The politics worked out that most of the operational budget of the Math department came from teaching students from other disciplines. Over the years Engineering was dissatisfied that after going through the prerequisite Math courses their students had plenty of theoretical knowledge but couldn't actually do the Math -- even those that took the applied variants. So after Engineering came into more money they hired engineers to teach "Calculus/LinAlg/DiffEq For Engineers" courses that focused on application and topics that more directly applied to their other curriculum.

It was a success overall for the Engineers but Math wasn't happy. The engineers working on advanced coursework needed higher level math courses that were only available in Math. Not only were they constantly failing which angered Engineering but the professors teaching them had to devote more time to the Engineering students which took away from the math students and angered Math.

The sort of uneasy truce that they eventually came to was Engineering students take the regular Math courses and their Physics/Engineering curriculum supplements what they're taught in Math. This annoys double major Math/Eng students because there's far too much repeated material in their curriculum but it's the best they could do.

[kkylin]

Absolutely agree with this comment. If you get beyond the title, what Gowers is talking about specifically is "If everyone were compelled to take 2 more years of mathematics, what should it be?" It is very different from what we would teach undergraduates getting engineering degrees; it would also be very different from what we would teach math majors. If we were to replace "mathematics" by, say, "programming," it would also not be surprising that one might come up with a list of topics differing from what we would want an aspiring computer scientist to know.

I did not find anything really surprising in the first part of Gowers's essay, but I thought the list of questions was great, independent of whether or not it is really appropriate for a required course.

[godelski]

When I was in school I taught a physics lab to non-physicists, and this was a conversation professors and I had. Granted this was at university level so most people had an idea about whether they (thought they) were a math person or not. I went in with a completely different philosophy to that class than with physicists. Because here's the thing, a physicist will care about different things than the non-physicist.

What I focused on was less of the physics and mathematics and more on making sure they gained an intuition about how nature works and how to think critically. These people didn't need the same toolbox as the ones trying to get a degree in physics or engineering. I could care less if these students knew the equations for Newton's laws, but I did care if they had an intuition. I didn't care if they had Bernoulli's principle memorized, but I did care if they could analyze an experiment.

The difference is that these people needed different skills in their lives. You must know it is popular to say things like "School taught me the Pythagorean theorem but not how to do my taxes." These people aren't realizing that math is giving them a toolbox that can help them do their taxes and other things. I teach my young nephews math whenever I visit them. They don't care about it in school but they like what I teach them because I make it fun and challenging. You can get a lot of topics covered and a lot of ideas and principles conveyed if you aren't worried about them being able to do every case. An example of this being that the basic principles of calculus can be used in your daily life and could benefit everyone (thinking about things like rates of change, tangents, series, limits, and squeeze theorem), but they won't need to be able to take the derivative of a function unless they are going into a job that requires that.

So I guess what I'm getting at is that there is a lot of benefit from math to the average person without actually requiring them to be fluent in the language. Think about this like being a moderate speaker in a second language but not being able to write or hold a deep conversation. They have a lot of advantages over someone who might know more about the written language and grammar, but don't know many words. I think the same argument of learning basic phrases in a second language would apply here as well. Most people don't need to be fluent, but we are teaching them like they are.

[blahblah3]

Maybe this is an unpopular view, but I think there is something unnatural about mathematics for most people. It tends to be much more abstract than other subjects. I say this as someone who has always enjoyed math and majored in it.

And it does make sense to have "math for mathematicians" or "physics for physicists" classes. You see this a lot in college (often intro classes are divided into different "levels"). This allows some students to accelerate and others to still learn relevant materials but at a more appropriate pace.

[zengid]

Usually mathematics is taught in a progression, and layers are built upon more basic layers. A 'non-mathematician' is someone who does not consider it their life's goal to solidify their expertise in mathematics, so they may choose other disciplines to obsess over, or no disciplines at all. Either way, a teacher of a class for 'non-mathematicians' who wants to explore depth in a certain area of mathematics cannot assume that this population of 'non-maths' will understand jargon or any concepts that aren't specifically explained within the scope of the class. Thus they must proceed axiomatically, being sure to avoid using concepts that haven't previously been defined.

Conversely, a class for "mathematicians" would be one with some background that can be used to begin from, depending on the average grade-level or prior education of the students.

So in a nutshell to teach deep math concepts to 'non-maths', one has to start from the beginning and define each concept in order, ignoring wider scope for the sake of reaching the goal. 'Math' students can start at a middle-depth, depending on their background.

[ordu]

I agree with "we should teach mathematics to non-mathematicians in the same way we do to mathematicians". But I do not agree with teaching mathematicians the same way as we do to non-maths. I personally was taught like non-math. And it was a pain. It was boring. Every year I finished reading through math textbooks in a month, it was fun. But then the rest of the year it was a total boredom. I hated math classes for this. Literature classes was much more fun, than maths, despite I didn't like all those stupid discussions about stupid books of stupid authors.

[spion]

> How should writing be taught to non-writers?

Sort of: http://paulgraham.com/essay.html

[danarmak]

People keep asking this about programming all the time. There are many movements that aim to teach everyone (kids or adults) to program.