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

181–190 of 343 posts

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

#181

Post by gdfer »

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…

I wouldn't make math/STEM a special emphasis when they're young.

It's more important to foster an positive learning environment and encourage/draw out curiosity and creativity at this age. Help them become curious about the world, fascinated with what they're learning and find enjoyment in learning.

In terms of subjects, aim for a strong reading focus at an early age as it will pay dividends in all other subjects (even math) if they can read/comprehend well.

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

#182

Post by alexandercrohde »

Enough "I" statements already. It's ironic how many people seem to think their personal experience is somehow relevant on a post about "critical thinking."

The ONLY sane way to answer these questions: - Does math increase critical thinking? - Does critical thinking lead to more career earnings/happiness/etc? - When does math education increase critical thinking most? - What kind of math education increases critical thinking?

Is with a large-scale research study that defines an objective way to measure critical thinking and controls for relevant variables.

Meaning you don't get an anecdotal opinion on the matter on your study-of-1 no-control-group no-objective-measure personal experience.

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

#183

Post by dahart »

Jtsummers wrote: post #167
dahart wrote: post #145

Earlier quoted context omitted.

I could use alpha - a as in add. I could use sigma - s as in subtract. I could use iota - I as in integrate. Of course it's arbitrary.

You claimed the symbols were arbitrary, they are (often) not. What you demonstrate here is not that the symbols are arbitrary, but that the concept (sound as abbreviation) maps to more than one potential meaning and the choice of which one is standard or convention is arbitrary. That is correct, but at this point it is standard to see sigma as summation (or in some other contexts as set or space, but it's also clear…

You're conflating choice with canon/convention. The choice was made arbitrarily by someone. There was no convention at the time the arbitrary choice was made. The choice to use alliteration was as arbitrary as the choice of which Greek letters to use. There are other equally arbitrary possibilities.

Also don't confuse arbitrary with random. Having a reason doesn't mean a choice isn't arbitrary.

Bigger picture, maybe I'm misinterpreting you, but I feel like the logical conclusion of your argument is that nothing can change now, because canon. And yet basic math notations have changed throughout history.

It would take a lot of effort to change the summation symbol from sigma to something else. But if something else made learning math faster, the canon is exactly the part that needs to go, not an excuse to stop improving.

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

#184

Post by acjohnson55 »

mathperson wrote: post #115
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…

Not even wrong. You think New Math refers to the current modifications of common core. New Math actually refers to a series of cold war changes made in response to perceived russian scientific dominance. https://en.wikipedia.org/wiki/New_Math

Oops! Forgot about that. I assumed the OP was griping about Common Core.

BTW, "not even wrong" is a rather rude way to point out a misunderstanding.

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

#185

Post by sekou »

gdfer wrote: post #181
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…

I wouldn't make math/STEM a special emphasis when they're young. It's more important to foster an positive learning environment and encourage/draw out curiosity and creativity at this age. Help them become curious about the world, fascinated with what they're learning and find enjoyment in learning. In terms of subjects, aim for a strong reading focus at an early age as it will pay dividends in all other subjects (ev…

Salman Khan's One World Schoolhouse does a good job exploring this topic I think. On the one hand many students struggle with what he calls a "swiss cheese" understanding of math: lacking mastery of fundamental concepts that leads them to struggle as they grow older. On the other hand he advocates for a more holistic approach to learning overall from the beginning, exposing children to various subjects and exploring how everything is connected.

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

#186

Post by ghettoCoder »

gnaritas wrote: post #179
ghettoCoder wrote: post #131

Earlier quoted context omitted.

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.

I know. I was replying to the comment and using the his/her terminology. It's actually a blended common core/discovery math hybrid.

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

#187

Post by acjohnson55 »

ebola1717 wrote: post #120
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…

idk, I studied higher level math very seriously, and even there, practicing computations is pretty key to understanding the underlying concepts. Concepts and abstractions are important, but they don't stick without practice.

I agree that it's an important part of the process, but I think it works best when it's connected with actual application, and not just a worksheet full of disembodied computations. I saw way too much of that as a student and as a teacher.

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

#188

Post by k__ »

I always had the feeling I failed to grasp math because I never got good at mid level things.

It took me reeeally long to grasp things like linear algebra and calculus and I never was any good at it.

It was a struggle to get my CS degree.

Funny thing is, I'm really good at the low level elementary school stuff so most people think I'm good at math...

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

#189

Post by d3ckard »

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…

So basically you're saying that it is a preferred solution to teach kids math poorly, let them develop insecurity and aversion towards it and then spent a lot of money to let them overcome it than just do it right in the first place?

Yeah, I know that's not what you mean, but you're missing a point. The premise of the article is that US has a STEM problem. I merely suggested that they're allocating resources wrong to fix it. I didn't mean they should introduce rigor and discipline or increase hours - I said that the best way to achieve results in teaching math is to fix it early, when it's most commonly broken (in my experience).

It actually helps you if you decide to switch interests, because you got the basics right, which in this case is the ability to think in an abstract way.

If you don't agree with me, you should have provided arguments that math problems do not arise early in education system, but they are introduced later.

One last thought - timing _does_ matter. That's why almost every professional athlete starts as a child. The question is how much you gain for starting early and I agree, that it is usually unreasonable to put too much pressure on kids. Pressure is not necessary to fix the system as far as I see it, though.

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

#190

Post by mathperson »

acjohnson55 wrote: post #184
mathperson wrote: post #115

Earlier quoted context omitted.

Not even wrong. You think New Math refers to the current modifications of common core. New Math actually refers to a series of cold war changes made in response to perceived russian scientific dominance. https://en.wikipedia.org/wiki/New_Math

Oops! Forgot about that. I assumed the OP was griping about Common Core. BTW, "not even wrong" is a rather rude way to point out a misunderstanding.

yeah it is a bit rude..sorry! I just get very few opportunities to say it- and I was like yo- this is a good chance. Are you familiar with the history of the term? with pauli?
Post reply on HN