Hacker News Reader

Comment by bedobi | Hacker News Reader

I’m no mathematician, so I only took basic school math, but I hated every moment of it. Mostly because overwhelmingly there was never any context or justification for learning any of it. Why does this exist? What actual real world problems does it solve? How did folks come up with and it, prove it works and start using it? Crickets. Just learn this formula, then that. The first time I heard the ancients calculated the distance to and size of the moon with trigonometry I was floored. Oh ok so that’s the kind of cool shit they came up with it for. Now I’m listening.

View on HN

I’ve been teaching mathematics for decades. Know how many students like the cool applications at the time they are taking the class? Very, very few. Usually, it’s later on in one’s journey through life that appreciation for the cool applications occur. At the time of taking the class doing cool applications inspires 1, pisses off 50 because it’s too hard, and leaves 49 rolling their yes.

imo this is largely because of the incentives around the game of school and testing.

If you must wait 20yrs before you can do interesting stuff and you’re evaluated primarily on your ability to maximize your grade then anything that gets in the way of that is an annoying distraction for most at best.

Even if you’re a student predisposed to find applications and the narrative of the discovery interesting you still have to focus on guessing what the test questions will be and just doing those, spending mental cycles on other stuff is a “waste” in that environment.

Once you’re finally free of school only then can you actually learn based on where your curiosity takes you, though at that point most choose not to - the curiosity having been driven out of them.

Makes me think a little bit about the movie the lives of others:

> “Did you know that there are just five types of artists Your guy, Dreyman, is a Type 4, a "hysterical anthropocentrist." Can't bear being alone, always talking, needing friends. That type should never be brought to trial. They thrive on that. Temporary detention is the best way to deal with them. Complete isolation and no set release date. No human contact the whole time, not even with the guards. Good treatment, no harassment, no abuse, no scandals, nothing they could write about later. After 10 months, we release. Suddenly, that guy won't cause us any more trouble.

“Know what the best part is? Most type 4s we've processed in this way never write anything again. Or paint anything, or whatever artists do. And that without any use of force. Just like that. Kind of like a present.”

For the vast majority of the students the curiosity, as you put it, isn’t really there. Understanding is very hard work and most people don’t want to put in the work to acquire understanding.

Perhaps, but it isn’t helped that spending effort to understand is often in direct conflict with the work required to get a good grade.

You’re not tested on understanding how stuff is derived or how it’s used, you’re tested on grinding problems, particularly ones that are easy for teachers to put on a test and easy to grade (if they even bother with that, my worst teachers didn’t create their own tests or grade them, machines did both). In English or humanities you’re tested on predicting whatever bullshit your teacher believes and then crafting an essay that leans into their cognitive bias.

I got very good at school and it was mostly by trying to model the minds of my mostly bad teachers and getting good at predicting what they want to hear and what they’d ask on the exam. With that down I could focus personal time on the stuff I was truly interested in (which ironically is what actually had market value).

At least in the US public school system this is further hurt by public school teachers often barely knowing the material themselves and that’s if they’re not also outwardly hostile/condescending to the kids (there are always great teachers, but they’re the exception to the rule).

The system isn’t selecting for the right things and those with enough money know this and work around it.

At university level not insignificant amount of students are there because they have to. The course is mandatory. And they might only want to pass. They are not getting degree because they want education, but because it is perceived as needed in society. Now should these be ignored or not is a discussion to have.

If you look at the comments in khan academy there are tonnes of people asking for real life applications—that said, they’re given in most of the material there.

Inspiring students (and showing the material can help them in their lives additionally) is one of the most important but difficult parts of teaching: good explanations falling on uninspired ears rarely settle.

And I’d argue the onus is on the teacher to inspire but it’s not something I can say is an easy skill to master.

Succinct explanations can be hammered out but fostering inspiration is a soft skill rarely taught—-and rarely deemed important in the already inspired.

I imagine - but have no data to back me up on this - that a lot of those comments you mentioned on Khan Academy come from two types of people. Those who are relearning the subject and are amenable to applications and those who say they want the cool problems but when they are actually done fall into the 99 category I mentioned above.

It sounds to me like you haven’t taught much. I could be wrong.

That 1 will go and actually do amazing things with it. maybe invent a new application of the mathematics or invent new mathematics. The other 49 will forget it as soon as its no longer something to learn on an exam.

Haven't thought is for decades, but was my environments favourite math tutor, because I managed to ground everything in people's reality and rell them a compelling fiction in which knowing how to do the thing was actually a super-power.

You know like the survival tricks certain preppers learn and never use — that, but with math. Even if the examples were sometimes over the top, involved flaming moats and other xkcd-like freakiness I got students where their teachers told me it is hopeless sitting there participating with glowing eyes.

Meanwhile in my own math education I had a teacher who made us do integrals for what felt like a year without telling us once what the hell it is needed for. I had to figure that out on my own.

My colleagues who didn't care just learned it by hard and forgot it immediately after. But I guess they got thought all the material and got ok grades so their education was a success.

What bullshit. Now, 15 years later I relearn a lot of those thinga because school made it sound boring only for me to later discover it is one of the most exiting things your brain can do. But that is about thinking on solutions to actual things not learning steps and doing them and getting punished for making one mistep.

This is precisely what I was referring to about people who come back at a later time and relearn the stuff. They want applications. At the time a class is taken very few actually want to dive into applications. The subject has been taught the way it is taught for a reason.

I am in education and what you claim here is in contradiction with both my experience and the direct feedback of the people I educated — most of which would say they dislike math or say they are bad at it. The argument that it is like it is for a reason can be made, but it has probably more to do with the historical role of school as an institution that is meant to produce obidient workers than with school as a place that is meant to produce people able to analyze nature and the world around them with the tools of mathematics. Ever student that got a bad grade because they solved the problem, but did so using the "wrong" way can testament to this.

Back when I was in school I had the luck to also have a lot of maths both physics and mechanics classes, so I had above average exposure to mathematical applications. This is what made me the most wanted maths-helper among my friends who went to other schools with a "purely theoretical"-maths approach: I could finally show them how the stuff they had a hard time with connects to the actual real world and nature around them — which contrary to your statement really their ability to grasp it.

If we think about how one would go about teaching any subject in a way that creates the maximum disinterest in the field it would be done dry theory only while keeping real world connections and story telling to a minimum. Sure, you could do that and there would always be a small number of students who would excell at that anyways because their brains are wired for abstract things — but that isn't a healthy approach to to take in general education.

Sometimes my feeling is that mathematicians, like many other nerds want to gatekeep and shroud their own field in an overly opaque mysticism, because they can derive a higher self value from that. So things get explained over complicated and they tell you, that you would never understand (because you are the wrong kind of person).

I like to instead believe that if explained right you can nearly explain everything to everyone — provided you manage to spark their interest, keep their interest and provide a good way into the matter. This is why Feynmanns lectures are so famous. He was really good at this.

Feynman’s lectures demonstrate my point. From Wikipedia on the lectures:

As a result, some physics students find the lectures more valuable after they have obtained a good grasp of physics by studying more traditional texts, and the books are sometimes seen as more helpful for teachers than for students.[5]

It does not sound to me that you have much experience with actual teaching.

Hard to meet everyone where they are and at the same time give them a relevant practical application for their own life. Good learners just soak it up and look for the application later. But that also doesn’t fit all. It’s hard to even write a pop song that everyone likes so math education that appeals to all is almost impossible

It's really this. I was a "good" student so I got pretty far in college math; and none of it has stuck with me without a real life application. At ALL.

What's kind of killing me now, as my kids go through algebra et al, is that now we have a VERY OBVIOUS way to make this interesting and we're severely underutilizing it, which is video games. "Draw a rainbow in Minecraft" or "Figure out the trajectory of that frag grenade" seems just gobsmackingly obvious as a path here.

That is a consistent problem with the education system no matter what the topic is with few exceptions.

I'm pretty sure math is the most poorly taught subject out of all of them. Social studies, current events, history, literature arts are mostly skills most people use everyday.

Math is important so every school is required to teach it however not many schools can. The issue with math is there are never going to be very many good math teachers as that would require many more people who know math. How many adults even know math beyond basic arithmetic?

Even the basic content from textbook is not real mathematics. the daily work of mathematician is very different to calculate some interesting things.

I think the economic returns to "decent understanding of X plus decent communication skills" are much higher when X is math than when X is art or language or history, so you need a greater passion for teaching to select it in spite of that fact, and this shrinks the pool of good math teachers relative to other subjects.

I did a (not fully third party reviewed for errors, watch out) project to record all the math related "cool shit I'm glad to have discovered": https://github.com/EternityForest/AnyoneCanDoIt/blob/master/...

Did you not have a physics class around the same time you learned calculus and linear algebra? That makes it obvious what the application is.

This is completely asinine.

What you say applies to every subject in school. I interpreted poetry, learned ancient history and dead language. Yet somehow the single most useful tool of thought humans have developed needs to justify itself so that you will learn it?

> How did folks come up with and it, prove it works and start using it

I mean, anything at the university level should include proofs on why it works. I would go as far as to say you aren't really doing math if there are no proofs.

elementary level too! Humans crave understanding. This is what we finally have with modern materials like Eureka.

Sounds like you had crappy teachers.

Establish why its "crappy teacher" and not "crappy student". I've seen far more of the latter than the former.

I don't think its hard to find something interesting about math either, and it is immediately applicable, even with what I think is extremely stupid in the form of common core as presented in the USA, you are literally being presented story problems about common every day occurrences and activities.

As someone who routinely teaches (Non-STEM) university students practical applications of math I can assure you that none of the students that told me "I am bad at maths" went out of my class without an understanding of the topics we talked about.

Yet I routinely hear a: "Wow, if they told it to me this way during school I might have cared!" or "It really made my head smoke, but it felt good."

Step 1 is believing that every person that doesn't have cognitive problems can understand an abstract concept if it is explained well and they got the motivation to understand it. Then you need to create a situation which motivates them to understand it and now you only need to explain it well.

Many math teachers fail already at step 1. They believe 90% of their students are too stupid to understand things, while this is just a convinient explaination for their own failures. I once was convinced of being that student.

I met one kid that I couldn't teach anything because he would forget things I told him 15 minutes befoee. He was a refugee from Afghanistan and severely traumatized.

The truth is that we should look to the best when teaching and we would be stupid if we didn't. And the best are people like 3blue1brown. If your class falls significantly below such a level of clarity and engagement it will suck. During my own math education I had teachers that left out the most fundamental applications. E.g. something like an integral has clear applications, it is a new super power with which you can solve new problems — yet all we did was learning a receipe and solving abstract problems. The fact that it was a super power was something I had to figure out myself, later.

And this was common. I even was lucky because I had a good physics teacher who managed to being up a lot of what we learned in math and give it a more practical feel, but most of my friends from other schools were not so lucky.

This is exactly how my education went. Oh you're not engaged with my shitty teaching and forcing you to do endless abstract nonsensical formulae with zero contextualization or application? Then you're the problem - you have cognitive defects, you are plain dumb and stupid, you are disinterested, you don't care about your education etc etc so I cannot help you. Now let me spend my time on "teaching" the kids who mostly already know what I'm "teaching".

> This is exactly how my education went.

No it didn't. I am very confident it did not. All students that make it past grade school go through nearly the exact same sequence and motivating examples beginning from geometry, high school algebra, and then some introduction to calculus if not calculus outright.

And the motivating example has always been how to calculate area, and if advanced enough, volume, for all kinds of shapes, regular or otherwise. This is not a recent development, its been the motivating example and the entire purpose for calculus having been invented.

I am so confident in this that I am here to call you a terrible student and that, yes, you likely were a terrible student, especially since your characterization is the exact standard excuse I hear from terrible students.

So now I have to drill - what was "nonsensical"? What had "zero context"? You immediately have lost the claim of "zero application", so we don't have to go there.

If your claim is beyond K-12 math and into university, then I would be too upset to even argue with you if that is your actual position. Making these claims after more than a decade of learning math tells me you have trained yourself to forget all you learned.

Interesting form of confidence. I didn't write the comment you replied to, but I wrote the original comment.

The first fact I want to have written down is that there are bad math teachers. And sadly it is not uncommon for them to be bad, as I mentioned most of my collegues from other classes and schools had bad math teachers and some of them were people that liked math.

Now as an educator I am aware that students are quick to blame other people or the system for their own deficiencies, but I can tell you for a fact that our math teacher failed to explain us what an integral was actually for in an parsable way, even after multiple times of asking. She just knew how to do the formula stuff, she never used it herself on real applications. And when she did explain things, she always did it once, much too briefly in the beginning, so that by the point at which we started doing her always decidedly abstract examples nobody knew what the fuck this was for. As I said, our physics and mechanica teachers were better math teachers than her. As for the integral I had to go and look it up myself, the internet was still young and there weren't many grown ups who knew how to look such a thing up and when I saw the explainations I wondered why nobody ever told us..?

I understand btw. why it can be an advantage to understand math in purely abstract ways, but in her case she just didn't want to talk much and stick to the examples. And that is bad teaching. Ah and before we get into a discussion about specifics, like many on this site I grew up and live happily outside of the US, so educational plans etc. might differ.

Reply on news.ycombinator.com