Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Math education: It’s not about numbers, it’s about learning how to think

nwaonline.com

Post reply on HN
Print view View original

171–180 of 343 posts

Re: Math education: It’s not about numbers, it’s about learning how to think

#171

Post by greenmana »

d3ckard wrote: post #19

Maybe I'm wrong, but I have always believed that if you want people to be good at math, it's their first years of education which are important, not the last ones. In other worlds, push for STEM should be present in kindergartens and elementary schools. By the time people go to high school it is to late. I never had any problems with math until I went to university, so I was merely a passive observer of everyday stru…

If I was to review (CS-related) math after a break of many years, what would be a good starting point? High school math? Discrete math? What are the foundations and the path like for the stuff more closely related to algorithms and core CS stuff?

Re: Math education: It’s not about numbers, it’s about learning how to think

#172

Post by calebm »

I agree, but have a small caveat: math does typically strongly involve numbers, so in a way, it is about numbers, though it's definitely not about just memorizing things or blindly applying formulas.

It just bugs me sometimes when people make hyperbolic statements like that. I remember coworkers saying things like "software consulting isn't about programming". Yes it is! The primary skill involved is programming, even programming is not the ONLY required skill.

Re: Math education: It’s not about numbers, it’s about learning how to think

#173

Post by wruza »

kungito wrote: post #43
d3ckard wrote: post #19

Maybe I'm wrong, but I have always believed that if you want people to be good at math, it's their first years of education which are important, not the last ones. In other worlds, push for STEM should be present in kindergartens and elementary schools. By the time people go to high school it is to late. I never had any problems with math until I went to university, so I was merely a passive observer of everyday stru…

To this point, I have been doing a plenty of 1on1 lessons with kids trying to catch up with Math in high school/college/matura exams and one this I have noticed is that things which are problematic to these people are things which were covered quite well already in elementary school. Later the curriculum only expands on these problems so it's even harder and harder to catch up. I have been working with college freshm…

>calculate the price after the discount

It is the discount they care about, not the price. These have no calculations, only gut feelings, which are perfectly exploited.

Btw, how many world-ruling decisions are made this way?

Re: Math education: It’s not about numbers, it’s about learning how to think

#174

Post by watwut »

jharger wrote: post #50
Ntrails wrote: post #49

Earlier quoted context omitted.

> I never had any problems with math until I went to university So, here's the thing. Did I have no problems with math until uni because I'm smart? Because I have a specific type of brain? Because of my upbringing? Because I had very good education in my early years? Some combination of the above? I struggle to believe that people can't do algebra. I am convinced that with some thought and help they'd find it trivial…

I saw what looked like this sort of thing with my daughter. She struggled in her high-school algebra 1 class, but whenever I would sit down with her and she would work out problems, she had no trouble (but she also had no confidence that she could do it).. She ended up having to repeat the class, which ruined her confidence even more, and she hated it even more the second time through. At the start of middle school,…

Maybe she found easier math boring, therefore did low effort, therefore had bad results. It is a cycle, happen to kids that have aptitude but are in easy class. The teacher might have been right.

I used to have bad grades from classes I considered easy.

Re: Math education: It’s not about numbers, it’s about learning how to think

#175

Post by shas3 »

Merovius wrote: post #159
d3ckard wrote: post #19

Maybe I'm wrong, but I have always believed that if you want people to be good at math, it's their first years of education which are important, not the last ones. In other worlds, push for STEM should be present in kindergartens and elementary schools. By the time people go to high school it is to late. I never had any problems with math until I went to university, so I was merely a passive observer of everyday stru…

> Maybe I'm wrong, but I have always believed that if you want people to be good at math, it's their first years of education which are important, not the last ones. In other worlds, push for STEM should be present in kindergartens and elementary schools. By the time people go to high school it is to late. I indeed believe you are wrong. I started getting interested in STEM when I was 16 and now have a masters in mat…

> Honestly, the whole "you need to get them when they are young" idea never convinced me very much. It's never too late to learn a thing and often you need a certain age to actually appreciate something. You don't have to be a childhood prodigy to be good at something.

While starting early is neither necessary nor sufficient for success, the question should be: do the benefits of starting early outweigh risks? Like the parent comment, I think they do, if done correctly and gently, but it should be decided case-by-case for each child. The only risk I can think of is: if you push too hard, it can have the opposite effect of making the child hate it. So, one has to do it with utmost sensitivity and by responding to cues and feedback from the pupil.

Re: Math education: It’s not about numbers, it’s about learning how to think

#176

Post by dahart »

eeZah7Ux wrote: post #88
yequalsx wrote: post #82

Earlier quoted context omitted.

In theory it shouldn't matter but it does. We brainwash students to think in terms of y being a function of x. y = f(x) If you give a problem with x = f(y) it really confuses people. If I label the horizontal axis y and the vertical axis x in the cartesian plane then confusion ensues. t = b(a) where t is the velocity and a is time That's confusing. I suppose it's analogous to me saying "The male, fluffy, white, large…

If this is enough to "really confuse" someone than there's a serious problem with understanding VS rota learning.

This is an enormously serious problem with humans. All humans. Cognitive biases, miscommunication, misinterpreting patterns and data and evidence, inability to differentiate what something looks like from what's inside, inability to believe statistics that contradict personal experience, the list goes on and on...

People who have learned math and are comfortable with it's symbols and abstractions are less susceptible, but all people are susceptible to this confusion.

Re: Math education: It’s not about numbers, it’s about learning how to think

#178

Post by kaitai »

mamon wrote: post #144
Jtsummers wrote: post #89

Earlier quoted context omitted.

It is a US thing. And it's because until middle school (age 11-13) your teacher is likely not that familiar with math (they have taken math courses, but likely little formal math beyond geometry and trigonometry, perhaps some courses on math pedagogy). So for them, math is all about the numbers, they barely got to the more abstract concepts. In middle school in the US you start getting teachers specialized in their t…

What kind of education is required from teachers in US? In Poland it is Bachelor's degree in relevant topic (for elementary and middle school) or Master's degree (for high schools) plus a course in pedagogy. Most teachers however get Master's degree even if not required (they get salary increase for that). It is hard for me to imagine math teacher not good in match themselves.

The sibling commenter is right re: bachelors and certifications, but due to shortages in the US often teachers with no certification in a subject are teaching. See Table 2 in [1] and find that 70% of high school math teachers have a math major and 81% are certified, while 10% of public high school math teachers have neither a math major nor a certification in math.

[1] https://nces.ed.gov/pubs2015/2015814.pdf

Re: Math education: It’s not about numbers, it’s about learning how to think

#179

Post by gnaritas »

ghettoCoder wrote: post #131
acjohnson55 wrote: post #104

Earlier quoted context omitted.

It's way too early to judge "New Math" to be a failure. I think the idea of focusing on concepts over computation 100% in the right spot. The biggest problem to its acceptance is cultural. Parents don't feel comfortable with math concepts, and in my opinion, most of the negativity is coming from that insecurity. So they demand for things to be taught the "old way", even though that's produced a generation or two of m…

I disagree. I am not uncomfortable with math in general or the "new math". What I am uncomfortable with is the fact that my kids, and everyone else's kids, are essentially lab rats in a massive experiment. The result of which is 1+ generation of kids who can't calculate tax in their head or split a restaurant bill . They can't manage more than a few number without a calculator and are missing many of the basic blocks…

You're confusing "New Math" with common core.

Re: Math education: It’s not about numbers, it’s about learning how to think

#180

Post by dsfyu404ed »

kaitai wrote: post #146
acjohnson55 wrote: post #110

Earlier quoted context omitted.

Nailed it. I remember "hitting the wall" in Honors Algebra II, when I just couldn't keep up with all the new things I was expected to compute: radicals, synthetic division, logarithms, etc. It was a major dent in my math confidence, which up until that point had be reinforced by being told I was "good at math". I didn't start regaining that confidence until Chemistry, when I learned what pH actually meant. That spark…

This is compounded in the weird American class called "precalculus," which is just a random grab bag of math crap that might maybe needed before calculus but might not. In most precalc classes I've encountered, not only is there no explanation of why the concepts will be used in calculus, but there is little attempt to relate the concepts covered in the class. Let's go from linear equations to complex numbers to pola…

>"math for liberal arts"-type classes

I took a class that met in a room used by a class like that the period prior and got to listen to the better part of it. In the one lecture the prof coaxed them into creating an algorithm for the number of moves to solve a rubix cube based on the number of cells who's configuration is known and where those cells are located on the cube. In a different lecture they were doing the math necessary to cut hypoid gears on a manual milling machine. They didn't even know what they had did until he tied it back to the underlying concept.

The quality of those courses depends on the prof.

Post reply on HN