I decided to start a CS undergrad degree 15 years after finishing my first undergrad degree.

The university had a math placement test. I didn’t remember almost at math, but spent about 3 weeks going through the placement test review materials for 30 min to an hour a day. Got almost perfect score on the placement test.

I did retake calculus 1 and 2 by my own choice since I wanted to know it quite well, and much of that seemed completely unfamiliar.

So it’s much much easier to learn a topic the second time around even if it’s forgotten. To get up to speed on it, you could use the placement test materials—collegeboard has some standard tests and materials to review for those tests, or your local university might have review materials for an in-house test.

I will say, I completed calc 2 a year ago now, and I already feel it slipping away again due to disuse. Now I’m onto new math topics I never took the first time around, like linear algebra and higher levels of calculus.

I have a sneaking suspicion that there's something fundamentally wrong with how we approach math in school, given that:

1) It's presented as the most important thing in the world, pretty much, and

2) I've forgotten most of it past the first semester of algebra 1 in high school but that's mostly because... it wasn't important, at all, for me. And I think that's overwhelmingly the typical experience.

Honesty, I struggle to even talk fluently about early grade school math. "You can flip around the terms in a multiplication problem and the result's the same, because of the... uh... transitive property? Maybe? I think that's the name?"

Meanwhile, aside from when I'm trying to help my kids with math, life goes on just fine.

Everybody says it's important, but for the wrong reasons. It's treated like a contest, to get "ahead," get high test scores, get into a desired college, and hopefully major in STEM. Then it can be safely forgotten.

I know adults from the countries that are supposed to have wonderful math education (high test scores), and they forget their math too.

I think the people who remain good at math in adulthood were the ones who developed a genuine interest in math as an end unto itself, and figured out a way to keep up with it after college.

I have a hard time to conceptualize mathematics because of the teaching methods and how they presents the information.

1) Math teachers loves to gave out their own shortcuts, I mean they will tell us to use it every chance they gets. Then in next mathematics level, they warned that method is old and shouldn't be using it at all. Then the new teacher taught their own shortcuts. This method made it difficult to solve problems because some of the formula wasn't taught how to properly solve without shortcuts. 2) "Why? How?", lots of mathematics teachers during my education times have struggled to give out the explanation of how it get to that answer and why it is that answer. Their response is simply just nodding and "That is how I taught, so it is the answer".

It is hard for me to be able to solve mathematics because I can't conceptualize it well and struggled a lot without using technologies to help me. I do love math, I just can't enjoy math because of my past teachers have failed to educate me. And I failed myself.

Math is a skill, just like playing an instrument. Just like an instrument, if you don't practice regularly you lose the skill. People have no problem accepting this when it comes to a musical instrument, but for some some reason our schools seem to teach people that math doesn't require ongoing practice.

As for being presented as "the most important thing" - well for students it is one of the most important things at that time in their lives because it opens so many career paths.

But once you are out of school and on a career path that doesn't require math (or requires just certain subset of math) it really isn't important anymore.

This is just like music. If you hope of become a professional musician mastering your instrument and music theory is pretty much the most important thing it the world for you. But if you end up becoming a programmer and don't play for 20 years - you can't pick it up and play without a lot of practice and catch up - and nobody is surprised by that.

We need to teach math a little more like we teach music.

But should it open up so many career paths? We treat math at the same importance as it was in 70 years ago before computers and whatnot.

Should someone genuinely bad at math or disinterested in math be precluded from a CS degree and the opportunities it provides?

I find it very similar to primary education language classes. Unless you use it as an adult after school, you’re not going to retain the knowledge for very long. And most people aren’t going to be using either set of skills in their adult lives after school.

I took several years of Latin in both high school and college but outside of those academic environments I never had cause to use it and while I remember a lot of aspects of it structurally, my Latin vocabulary is almost all gone. I have at times pulled out my old textbooks just to try and see what I can do, and I can certainly work through that material a lot faster than the first time around, but I’m still needing to start at a rudimentary level to get anywhere.

Nice thing about language classes is that being bad at a language (or just not being interested) doesn't preclude many career paths. Math on the other hand is a clear gate, which doesn't make sense since you can literally forget and still do well in your career (as the parent poster mentioned).

> Nice thing about language classes is that being bad at a language (or just not being interested) doesn't preclude many career paths.

It does outside the English-speaking world. In many non-English-speaking countries—including Japan, where I live—English education is similar to mathematics education: All children have to study it and ability at school English is treated as an indicator of overall academic ability, but many children struggle with it and by adulthood most people have forgotten most of what they learned.

In Japan, school English education is also affected by problems similar to those mentioned in other comments on this page, including English teachers who themselves are not skilled at the language, educational policies that require that all children study the same material at the same age, and, sometimes, an overemphasis on rote memorization and teaching-to-the-test.

There’s a huge industry in Japan serving adults who have forgotten most of their school English—or didn’t learn much in the first place—and who now want to get better at it in order to advance their careers.

If you can forget math, it means that you memorized it. I don't think one can ununderstand math.

Oftentimes math is taught as a set of rules. Do these steps in order to get the answer. Works well to pass the test with minimum effort, does not help much long term.

It's definitely possible—common, even—to forget things you didn't learn by memorization.

I use math often, but most of the time it's basic math. Simple things like ratios when trying to calculate per-unit costs in a grocery store when two things are displayed with different units, or converting between Fahrenheit and Celsius. Basic multiplication for tip calculation.

The most complex was when I used some trig to calculate the angle at which I had to wrap a square column with christmas lights to ensure I covered the column from top to bottom with a single string and no excess.

For finance and stuff like that I don't even bother trying and just use calculators.

Oh, yeah, to be clear I use math (well, I apply mathematical algorithms and formulas) many times a day. But the ROI for my time spent on formal math eduction peaks somewhere around 3rd grade and declines fast after that.

I (genuinely) wonder how much that is attributable to having no actual use for other math, vs

1. not having been taught math early enough for it to be second nature

2. not having been taught useful every day applications of the math so as to keep practicing it

I've also forgotten quite a bit of math, but I also frequently encounter scenarios where I acknowledge that having a better handle on it would be advantageous to myself or others. For example, a better understanding of statistics and probability would certainly help political discourse in our society.

>The most complex was when I used some trig to calculate the angle at which I had to wrap a square column with christmas lights to ensure I covered the column from top to bottom with a single string and no excess.

that doesn't seem trivial at all.. wonder how that's done.

The length l of the Christmas lights is the hypothenuse of a rectangular triangle of height h, the height of the column. So, if the slope angle is α, we have sin(α) = h/l, or α = arcsin(h/l).

Soundness check: that doesn’t have a solution if h > l. Looks good.

does this assume the xmas tree is shaped like a column or a cone?

edit: ah, i re-read the original problem and it does mention column. i thought it was a xmas tree that was being wrapped.

That would be harder, yes. Reading https://en.wikipedia.org/wiki/Conical_spiral#Slope, you want a logarithmic spiral (you need a constant angle to make the problem make sense)

Luckily, arc length isn’t too gnarly for those (same Wikipedia page), but you still have one equation with two variables.

I would have to think hard about whether those give you a unique solution.

I also doubt that spiral would give you uniform coverage of the cone (and that probably, is the real requirement, not constant angles), but again, I would have to do some thinking.

oh, interesting variation for uniform coverage! that is indeed what i'd want for the tree. in building a road around a cone, a constant angle would be more desirable.

Suppose you’ve got a 16 foot strand of lights and an 8 foot column. If you unwrap the column in your mind, you can see you’ve got a right triangle with a hypotenuse of 16 and vertical leg of 8. What’s the angle that the hypotenuse makes with the floor? It’s the angle whose sine is opposite/hypotenuse = 8/16 = 1/2. That’s 30 degrees. So wrap the lights around the column at a 30 degree angle and it’ll be close (with a bit of slop thanks to rounding corners on the column).

my xmas isn't shaped like a column, it's a cone.

edit: ahh, the original question was for a column. i misread it and thought it was for a xmas tree.

If you unwrap a cone you get a circular sector. Similar idea.

Years ago I had to correct a Bridge design I was tasked with writing a program to draw out the complex curved shape.

The engineer had used 2d instead of the 3d formulae :-)

I have been working through the Art of Problem Solving Volume 1. I was a competent, though by no means excellent, maths student 20 years ago. AOPS was exactly the refresher needed to find those neurons again. Everything came back. However, had I jumped right into Trigonometry, I too would have been feeling like part of my mind was erased.

The math will come back, but you need to sit down and give yourself a structured program and, most importantly, time to actually do some exercises.

This is why math teaching pedagogy is important. I'm a fan of first principals and pattern finding for learning math (see Mathematician's Lament by Lockhart [0]).

Most kids in the US are historically taught memorization tricks. You have a kid who can't recall if x^1 = 0 or 1 or if it was x^0 = 1 or 0. They can't _remember_ some fact like a needle in a haystack of thoughts. However, the student who understands that x^3 = x * x * x and x^2 = x * x, will quickly know that x^1 must be x, and if each step is "divide by x", then x^0 must be 1.

I'm curious where the current math education trends will take us on this path, but I do like that they seem to focus more on understanding rather than rote memorization.

For sin, cos, and tan, they are much more re-discoverable if you are familiar with the unit circle's basics.

[0]: https://www.maa.org/sites/default/files/pdf/devlin/Lockharts...

A person taught his son about sine and cosine. He himself got introduced to them as ratios of side lengths in a right triangle, but he didn't like the idea of changing definition when angles become more than 90 degrees, so he defined those functions as abscissa and ordinate of a point on a circle of unit radius, centered at origin.

I think this is not perfect. Education is more of "progressing towards lesser and lesser lies", and changing definitions is an important part. The student might face it when he'll wonder about equation sin x = 2 , which will get to complex numbers.

Similarly, here getting a one less power of x might correspond to "divide by x". But might sometimes not - choosing that it actually does correspond to "divide by x" is a choice. Often obvious, but sometimes not - which is seen in Gelfand's explanation of why "negative multiplied by negative makes positive", or similarly, why 0^0 is 1.

Just saying that "x to one lesser power is the same divided by x" can also be seen as a convention (e.g. for some objects division can be not defined). And if it's a convention, not universal truth... then to somebody who's studying the subject this convention should be justified.

Yes, but in my experience, it helps to thoroughly understand (down to first principles if you want to), and then memorize anyway.

I quickly figured out that even if I've deeply spent time with a subject, understanding every step and derivation of some equation, if I can just quickly pop up equations (and other facts) in my head to "look" at them, it not only helps with application, but also with further understanding.

Being able to quickly recite the Taylor Series or an Inverse Fourier Transform in my head to apply in a problem beats stuff like "oh I remember understanding how it was derived, but I'd need to look it up", because all the details I otherwise once understood but did not bother memorizing might be important.

x⁰ is generally a matter of definition and not a fact reasonably accessed from deeper underlying fundamentals. It just so happens that the definition fits this story that you have for reasons of convenience. Also, you know, 0⁰.

Knowledge atrophy is real. I've even talked to math PhDs who have forgotten areas of math they have definitely learned and excelled at but hadn't been using actively.

But I think your brain still subconsciously possesses knowledge of these supposed forgotten math skills. This is the reason why relearning these concepts will take way less time than learning them the first time. So I think just don't be afraid to relearn it.

Lots of good courses on Coursera and edX. Khan Academy is good too. I particularly recommend the A-level prep sequence from Imperial College London on edX

But if you really want to maintain and maybe even further develop your math skills after getting back up to speed, I think the best long term strategy is to do personal creative and/or commercial projects in domains that interest you and that make heavy use of math. E.g. low level 3D graphics programming, etc

Same - I was a straight A student, loved solving math problems, but now I don’t remember a thing. I think it’s just how our brain works - it gets rid of knowledge that we don’t use any longer. Muscle memory like swimming or riding bicycle stays, but seems like language and math skills don’t retain unless they are being practiced.

I don't think so. The feeling described here is familiar to me with certain areas of maths, ones that I definitely knew and have then forgotten seemingly entirely, but when I had to get back into them it was nowhere near having to relearn them.

It's true that you forget without regular usage, but it seems the "concept" sticks around, and all you need is some refresher to be able to access it again.

The information isn't erased - it's just that the retrieval synapses haven't been reinforced. It is relatively easy to do that.

Yes, and I believe that still existing but somewhat inaccessible information isn't just what was learned on the surface, but also includes the hard-earned intuition that was formed on the topic.

When I help kids with math homework I usually skim their textbook to see how they learned how to do it. This both refreshes my own memory and also makes sure that I am teaching it the same way they learned it (I can show them other methods after they master the way the teacher wants them to do it).

If you don't use something you are at risk of not retaining it at all.

About 10 years after I got my masters degree I browsed through some notes made during my studies. I was very surprised to find out that it's not that I don't remember some things, I didn't remember if I ever learned them.

Not sure why Physics, Chemistry and Biology stuck with you. I'm sure I don't remember 90% of history, geography, literature and many, many things.

What stuck for me are things that I was learning myself anyways. Math, physics, chemistry, a bit of biology. Same way I retained a bit of electronics even though school never attempted to teach me that. The rest went to hell and I don't regret a single thing forgotten from primary school and high school.

Curriculum for such young humans is aimed at keeping little buggers from annoying their parent for x hours a day, not for usability and future retention.

Kids don't even need decades to forget this stuff. I vividly remember coming back to school after summer break and knowing I forgot everything I learned last year and feeling safe because I'll most likely have no use for that information this year or later (except for math because it's the only thing in school that can be learned only on the foundation of simpler math that you need to learn earlier and retain).

I realized a few years after school I had mostly forgotten elementary calculus.

I still had my textbooks (Apostol volumes I and II) and re-read them. Things were again right with the universe--I could do elementary calculus.

A few years later, I realized I had again forgotten it. I decided for variety to buy Spivak's "Calculus" and read that instead of reading Apostol for a third time. Yet again, I could do elementary calculus.

The next time I realized I had forgotten elementary calculus, I re-read Apostol again (although just Volume I). To try to make it stick, I did every exercise in the book.

I of course have since forgotten elementary calculus. I'm not sure if doing all the exercises made it last longer or if I forget it as quickly as I usually do.

The next time I decide to relearn elementary calculus, I think I shall first make sure I have a long supply of problems covering the entire subject, and then after I finish the textbook I'll do a few random problems a week so that I have to actually use the stuff.

I've been helping one of my kids with some online high school classes, and we just read through the course material together and work the problems. Despite my having taken those subjects before, all of the material is new to me. I have no memory of learning that stuff in high school, despite graduating with AP classes.

It's nice because I get to learn new things, so I'd recommend that rather than teaching yourself before teaching your child that instead you just learn the material together. If you point out the stuff that is confusing to you and how you find the answer then your kids can learn that process as well.

And I can never remember the formulas for sin, cos, and tangent either so I just keep a graphics book handy.

This is like riding a bike isn't it? First few steps are a bit shaky but then you're back pretty soon.

Also keep in mind modern media has an explanation for everything online, there's not much below graduate level that isn't explained in several ways by several people.

Same issue/question. I was a pro until I stopped actively using it 10+ years ago and now, well, my math is embarrassing compared to teenage me.

I'm pretty sure the only way to pull that knowledge back into "actively useable" would be to start studying a la college again. I imagine it'd be a lot easier since we would be revisiting it instead of learning for the first time.

Hard to get excited about studying math relative to my other priorities :\

I learned math way better as a math teacher than I did as a student because I had to figure out how to explain it - which meant I had to learn it first. Open up your child's math textbook and read the section they're working on, get to where you understand it yourself, then teach them. The textbooks do teach the material, and as an adult I found them to be easy to understand and sufficient explanations.

A similar technique, one I use, is learning by writing summaries. The process is simple: study, summarize, link to other summaries. That said, it takes a lot of time to write a good summary!

This, and it’s hard work, no way around that.

I had similar experience, but different outcome. I also had forgotten many formulas, but was able to derive everything from basic algebra. Quadratic formula, sine and cosine of sum of angles, derivatives, etc.

Some of those things took much longer than necessary, but I made it a point to not look anything up on principle. How can I explain something if I can't do it myself?

If you look up the definitions of sin, arcsin, logarithms, etc, does it mostly come back to you? Or do you feel like you need to completely relearn? I’m wondering if in your case all you need is to take a little time for a math refresher.

sin/cos for me were quite common since I'm fond of geography and geometry. So, even though they weren't needed at all, I had areas to apply them.

I never needed any math like log/exp at work, but somehow remembered it, probably because I used to do some fast estimations of things, for instance, "how big a pool of water you need to store energy to heat a house in winter", or "how fast will energy dissipate from the pool".

And that was probably thanks our school physics teacher, who showed that such napkin calculations were easy.

I Googled what I forgot till I found text that was interesting to read, basically.

For me, once I have found something to remind me, it all went back fast.

I ran into this too. The process of relearning Math with my kids has made me much stronger than the first time around.