Hacker News Reader

Comment by handrous | Hacker News Reader

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.

View on HN

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 :-)

Reply on news.ycombinator.com