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

#281

Post by webmaven » Wed, Jul 12, 2017, 4:04 AM UTC

hinkley wrote: post #230

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…

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 term…

> 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

That's quite insightful! I can think of a few related approaches that could round it out, like frugality (eg. only buy the paint/bugspray/lumber/etc. you actually need for your project), and laziness (do the least amount of work possible that still gets the job done).

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

#282

Post by sanderjd » Wed, Jul 12, 2017, 4:09 AM UTC

Jtsummers wrote: post #198

sanderjd wrote: post #42

Earlier quoted context omitted.

Learning multiple different highly abstract concepts at the same time does not seem like a solution to the difficulty of learning a single highly abstract concept.

My experience with this comes from college, but I disagree. I added a math major late into my education (I was one course from a minor, then 4 more from a major so why not?). I ended up in several math courses at once that were often taken separately, but specifically abstract algebra and a higher level (4xxx) linear algebra course. I pretty much aced both, though I probably would have gotten an A in them taken separ…

Maybe! I just don't think programming (even in Haskell!) is similar enough to algebra for this to be effective, no matter how much we all want it to be. Programming still requires a mental model of how machines compute, which is a good thing to learn about but not (in my opinion!) a strong complement to learning math.

Don't get me wrong though, I learned programming and calculus at the same time, I'm not saying you can't learn both at once, I just don't think one helps much in learning the other, for a novice in both.

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

#283

Post by zbobet2012 » Wed, Jul 12, 2017, 4:14 AM UTC

kenjackson wrote: post #133

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…

I was a proponent of "New Math" types of philosophies before I had a kid. It was only when I tried to teach concepts did I realize how important it was to be able to be able to arithmetic quickly off the top of your head. Its hard to explain, or even to grasp, how fundamental basic arithmetic is to almost everything in math. For us arithmetic is as simple as thinking a thought -- but only when I tried to actually exp…

I never memorized my times tables and do just fine with graduate level mathematics.

If you ask me 9 * 7 I still do 10 * 7 = 70 - 7 = 63 in my head; but, I seem to handle spectral graph theory just fine.

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

#284

Post by kayoone » Wed, Jul 12, 2017, 4:15 AM UTC

mindcrime wrote: post #258

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…

But once I needed to use math, it was trivially easy. This is close to my experience as well. Math, for me, wasn't super difficult, but it didn't necessarily come naturally either, and I got really bored with the tedious, mechanical aspects of it in algebra, college algebra, trig, etc. Geometry and Calc I were mildly interesting, but I was handicapped a bit in Calc I because my basic algebra skills weren't as strong…

I am in kind of a similar situation. Was never really good or into math during school, been a software developer for 10+ years (mostly backend and web stuff) and at 34 am now working on my calculus and linear algebra after spending some months brushing up my basic algebra skills (which i still do on the side to keep "fit"). I am actually toying with the idea of going back to college to do a Masters in Data Science because i got so fascinated with Machine Learning and AI as well. Soo, you rock, keep it up!

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

#285

Post by toomanybeersies » Wed, Jul 12, 2017, 4:18 AM UTC

kamaal wrote: post #279

toomanybeersies wrote: post #275

Earlier quoted context omitted.

Trig and Simultaneous equations are probably the two parts of high school maths that I actually use on a regular basis. I don't think it matters what ethnicity or race you are, it's good to be able to actually get things the right length. And it's a lot easier to do it on paper than run around for half a day with a tape measure.

Where do you use simultaneous equations on a regular basis?

Last I used one was for mixing paint. I will admit it's not super regular, but I use them once or twice a year.

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

#286

Post by taneq » Wed, Jul 12, 2017, 4:39 AM UTC

lordnacho wrote: post #142

jack_h wrote: post #99

Earlier quoted context omitted.

As someone who went to university for mathematics (and computer science) I can tell you this is the most common misconception. People think that I spent years studying how to become a calculator. I love talking about both subjects I went to university for actually and both can be difficult to get people interested in. There are massive misconceptions about both.

Yes, this is one of the most annoying things about people who don't know anything about math. - They see a shopping bill or a phone number and ask you if you can add them. - They see random equations, often in the background, and ask you if you understand what it means.

It's like when you study mechanical engineering and suddenly everyone wants you to fix their car.

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

#287

Post by nippples » Wed, Jul 12, 2017, 5:04 AM 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…

> 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 without first explaining how it's calculated?

If we're waiting until children are capable to derive those equations before we get them to use those a bit, then we're waiting for very long. And if you just keep telling them to add numbers and multiply numbers together for many years in a row without giving them any interesting problems to go with it, there'll be no one interested in math by the time they'd usually have the abstract maturity to deal with the more foundational modern math problems.

We don't ask Computer Science students to write an OS before using one, we don't ask carpentry students to build a hammer and cast nails before using them.

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

#288

Post by a-saleh » Wed, Jul 12, 2017, 5:27 AM UTC

hinkley wrote: post #232

brightball wrote: post #216

Earlier quoted context omitted.

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 was so pissed in college when I found out that all of those equations we had to memorize in physics were just the integrals. Why did I have to memorize all that shit if there's a simple way to derive the formula? Jesus.

I remember the day in my last year in high school, when my physics teacher looked at us with a frustrated face and asked:

"So, you still didn't have derivation in math class?"

We explained, that we will have it in the final month of the school year, if we are lucky. Her reaction was:

"But we kinda need it already. But I should be able to teach you that in 20 minutes."

And she did. And then she spent the rest of the lesson going through some old equations that she might have spent hours explaining: "Remember how long it took us to get to i.e: equation relating gass pressure and temperature? We always used that finicky helper variable. I think I even named it delta. In reality, you just derive this base form, and do a simple substitution."

Ok, my memory is a bit hazy. But she went on and on, through stuff we have been ehm, deriving without calculus for hours, that took with calculus around 3-4 steps.

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

#289

Post by bigger_cheese » Wed, Jul 12, 2017, 5:45 AM UTC

kamaal wrote: post #279

toomanybeersies wrote: post #275

Earlier quoted context omitted.

Trig and Simultaneous equations are probably the two parts of high school maths that I actually use on a regular basis. I don't think it matters what ethnicity or race you are, it's good to be able to actually get things the right length. And it's a lot easier to do it on paper than run around for half a day with a tape measure.

Where do you use simultaneous equations on a regular basis?

I'm an engineer at an industrial plant simultaneous equations are very common in engineering problems. Just about any "optimization" problem can be represented as a system of simultaneous equations even very complex non-linear dependencies are modeled like this.

i.e a common problem such as calculating the optimal blend of fuel in a reactor is done based on solving a system of linear equations with constraints such as Loss on ignition, maximum allowable ash content, minimum specific energy etc.

Industrial design as well uses simultaneous equations extensively. Do you want to build your aircraft wing out of CFRP or a titanium alloy? One way is to use a constraint based selection method something like strength to weight ratio vs cost.

edit: I should add 99% of the time these are solved programmatically with the aid of a computer. You do not solve these problems "high school math style".

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

#290

Post by katdev » Wed, Jul 12, 2017, 5:46 AM UTC

You know what helps kids (and adults) learn math? The abacus/soroban. Yes, automaticity with math facts/basic math is important but what's really important is being able to represent the base-10 system mentally.

The abacus is an amazing tool that's been successful in creating math savants - here's the world champion adding 10 four-digit numbers in 1.7 seconds using mental math https://www.theguardian.com/science/alexs-adventures-in-numb...

Students are actually taught how to think of numbers in groups of tens, fives, ones in Common Core math -- however, most are not given the abacus as a tool/manipulative.