Math education: It’s not about numbers, it’s about learning how to think • Hacker News Board

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

#221

Post by justicezyx » Tue, Jul 11, 2017, 8:49 PM UTC

baq wrote: post #214

justicezyx wrote: post #121

Earlier quoted context omitted.

> I think the idea of focusing on concepts over computation 100% in the right spot Concepts of what? Without intuitive understanding of basic computation procedures, what concepts can anyone build out of nothing? Math is concrete. It's from observation of actual quantitative phenomenon.

And yet it's completely abstract as sets and numbers don't need a universe like ours to exists, they only need axioms. Modeling the world is a job that math the tool was created for, but it certainly isn't concrete just because the world that needed it was or is.

You forcefully disintegrate concepts and physical world. All concepts have certain degree of abstractness for human understanding. It's not unique to Math. And it's not necessary that abstractions automatically alienate something from concreteness.

To split them, and think that, just because there is abstraction, and it's OK to develop the concept without the concrete substrates of actual experience is trying to make dream come true.

And I argue that no one should live in a dream. And it's obvious that only those dreams that have a strong connection with the real world have realistic chance of being made real.

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

#222

Post by d3ckard » Tue, Jul 11, 2017, 8:55 PM UTC

Verdex_2 wrote: post #202

d3ckard wrote: post #189

Earlier quoted context omitted.

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…

> 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. If you knew it's not what they meant then why did you start off saying that's what they meant? If you thought they we…

To better illustrate the point. I actually started with that, decided that it sounds too aggressive and added that paragraph to make that clear.

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

#223

Post by munchbunny » Tue, Jul 11, 2017, 9:15 PM UTC

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 disagree that you have to get them young... but I do think that math classes need to start involving proof-based work rather than calculation-based work by the time students hit middle school because it's such an explicit exercise of critical thinking muscles.

Recalling my own experiences with middle school and high school, I saw my peers frequently fall into the trap of trying to memorize pipelines of steps while we were learning algebra, geometry, trig, pre-calc, and then calculus. The ones who "didn't get it" would fall apart to varying degrees when confronted with problems where you had to think in terms of combining toolboxes of strategies to unfamiliar but analogous patterns, but I don't necessarily think it was their fault, because they didn't know better and rote memorization had worked consistently until this point.

I often feel a bit sad about it because I did a ton of proof based stuff outside of class (as a mathlete), and that was a HUGE part of my development in logical reasoning, intellectual rigor, and critical thinking.

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

#224

Post by throwawayjava » Tue, Jul 11, 2017, 9:19 PM UTC

watwut wrote: post #165

bitwize wrote: post #98

Earlier quoted context omitted.

> I think math education needs to be reworked from top to bottom to focus more on building blocks. E.g. I'm not sure there's enough focus on what multiplication is before you're expected to memorize the times tables. This was tried. It was called "New Math". Spectacular failure. Do you want to know what worked? Memorizing times tables. There's just no way around the fact that drilling is key to early mathematical lea…

Memorizing time tables and similar rote learnign means that precisely kids who could be good at math hate it. Meanwhile, those who have good memory and sux at problem solving think they are good at it. People who were taught by memorising go into outrage a new type of exercise is introduced. Suddenly thinking is needed and that is bad in their eyes. Not exactly success. Meanwhile, you can memorize time tables in late…

I think this is a very astute observation. I know a lot of people who develop problem solving skills later in life after realizing that their mathematics education in high school was woefully inadequate. I don't know anyone who memorized a multiplication table by choice, and I know several professional mathematicians/engineers who haven't memorized their 10x10 or 12x12 multiplication table.

Once people see what they need out of mathematics for success in life, they never choose to memorize multiplication tables. But they do often learn new problem solving techniques.

That should tell us something about which is more important.

(But of course, we don't have to choose between the two either.)

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

#225

Post by sjg007 » Tue, Jul 11, 2017, 9:20 PM UTC

BeenThere888 wrote: post #60

throwawayjava wrote: post #53

Earlier quoted context omitted.

Encourage her to give it another try when she gets to late high school or college. I know a lot of math phds who fell out of love with math around middle school and then fell back in love during their first proof-based course in college.

Yeah, this. I hated math in middle-school and early high-school. It was boring and rote. But proofs based math, and learning how to think of math as a language, instead of a collection of overly specific "solutions" crammed into my head by teachers, was the key.

I never got proofs. I wish I did.

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

#226

Post by WheelsAtLarge » Tue, Jul 11, 2017, 9:37 PM UTC

True, Math is ultimately about how to think but students need to memorize and grasp the basics in addition to making sure that new material is truly understood. That's where things fall apart. We are bombarded with new concepts before we ultimately know how to use what we learned. How many people use imaginary numbers in their daily life? Need I say more?

We don't communicate in Math jargon every day so it's ultimate a losing battle. We learn new concepts but we lose them since we don't use them. Additionally a large number of students get lost and frustrated and finally give up. Which ultimately makes math a poor method to teach thinking since only a few students can attain the ultimate benefits.

Yes, Math is important, and needs to be taught, but if we want to use it as away to learn how to think there are better methods. Programming is a great way. Students can learn it in one semester and can use it for life and can also expand on what they already know.

Also, exploring literature and discussing what the author tries to convey is a great way to learn how to think. All those hours in English class trying to interpret what the author meant was more about exploring your mind and your peer's thoughts than what the author actually meant. The author lost his sphere of influence once the book was publish. It's up to the readers of every generation to interpret the work. So literature is a very strong way to teach students how to think.

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

#227

Post by acjohnson55 » Tue, Jul 11, 2017, 9:42 PM UTC

mathperson wrote: post #190

acjohnson55 wrote: post #184

Earlier quoted context omitted.

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?

Yeah, I'm familiar. To be fair, it was a good opportunity. Well played :D

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

#228

Post by Balgair » Tue, Jul 11, 2017, 9:42 PM UTC

brightball wrote: post #216

Balgair wrote: post #209

Earlier quoted context omitted.

Anecdote time: I was a late bloomer in math too. From about 6th to 10th grade, I was terrible at math. I think it was because of inapplication problems. Yes, you get a word problem about Jack and Kwanzeeah trying to fill up a pail or something, it was nonsense to me. Why are they filling up a pail? Why are they using a bucket that is 173/9th's the size of the hose? Why do they have to not let it overflow? Why do I ha…

I'd agree with this completely. It's less about teaching what, how and when than it is teaching WHY you need to know this. In high school, if you can convince a single person that they need to know calculus, more power to you. 99% of people don't and it's literally a waste of time. Teach people finance though...suddenly we have math that people will know is important.

I think motivation is key. That said, I think that the engagement in the 'personal finance' section of a HS class would also be low, maybe not for graduating seniors, but definitely for freshmen. Teaching is tricky, my SO is in education and it's not easy. Kids don't tell you things like their hunger issues, romantic issues, home life, etc. They may not even know they are having an issue, young as they are. Hormones are never going to stop making them nuts. Top that all off with budget problems (most US districts have not increased funding since 2008, pop. growth and inflation be damned) and other bureaucratic stuff, and you get a heck of a mess. Staying motivated as an educator is pretty tough, let along inspiring them to be motivated. At the end of the day, the kids are responsible for themselves largely, just like most humans have always been.

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

#229

Post by steanne » Tue, Jul 11, 2017, 9:50 PM UTC

taco_emoji wrote: post #86

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 think math education needs to be reworked from top to bottom to focus more on building blocks. E.g. I'm not sure there's enough focus on what multiplication is before you're expected to memorize the times tables. Think of stuff like the quadratic equation, or formula for the surface area of a cone. How many of us were just taught these magic formulae without first deriving them? Why do we start talking about pi wit…

the beginning of the end of my math studies was eighth-grade algebra. i GOT algebra, it was easy, and i enjoyed it. ..until the quadratic equation was introduced.

"hey, that's really neat! how does it work?"

"oh, you'll learn that in calculus, which we won't allow you to take for another four years."

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

#230

Post by hinkley » Tue, Jul 11, 2017, 10:00 PM UTC

Balgair wrote: post #209

Merovius wrote: post #159

Earlier quoted context omitted.

> 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…

Anecdote time: I was a late bloomer in math too. From about 6th to 10th grade, I was terrible at math. I think it was because of inapplication problems. Yes, you get a word problem about Jack and Kwanzeeah trying to fill up a pail or something, it was nonsense to me. Why are they filling up a pail? Why are they using a bucket that is 173/9th's the size of the hose? Why do they have to not let it overflow? Why do I ha…

Doesn't Randall xkcd assert that the paramount math problem that most people need to do is how to split the bill fairly when you take your friend out for their birthday?

If you're splitting the tip and the tax, and everyone is pitching in $3 to cover the Birthday Girl, that's more complicated than a lot of those problems they use that nobody cares about.

(In fact, I think if you put all of those math problems in terms of fairness, you'd get more kids to pay attention. Nobody wants to get cheated, and that's what happens when you're bad at math and/or finance).