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

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

#331

Post by Merovius »

shas3 wrote: post #321
Merovius wrote: post #295

Earlier quoted context omitted.

I find that a pretty strange approach to parenting. IMO you should optimize for happiness of your child, not for carefully manipulating them into the path you laid out for them. My perception of a good parent is to encourage your child to discover and pursue their own passions, even if they contradict yours. You can open doors, but they need to walk through it by themselves. YMMV.

Huh? Learning can be fun, last I heard. In any case, that's what I meant when I said 'feedback'. Further, there are some skills that are absolutely necessary to learn to function in society, basic math, basic language skills, etc. More important are skills like perseverance, managing one's own emotional well-being, self-control, delaying gratification, etc. It is one's responsibility to at least attempt to teach thes…

I was referring to this sentence:

> 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.

That seems like a weird "risk".

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

#332

Post by cr0sh »

kayoone wrote: post #284
mindcrime wrote: post #258

Earlier quoted context omitted.

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 be…

Seems like both of you are doing what I plan to do once I finish my Udacity SDC Nanodegree course. I've known for a while (ever since AI Class and ML Class in 2011) that I need a refresher and more on math, because ML. This Udacity course just drove it home.

I'm tired of hearing about "take the derivative" and "perform the integral" (or whatever), and not quite understanding it. Heck, just what I wrote probably indicates I don't quite get it!

Also, my intuition on probabilities and statistics isn't there either, so I want to do something to fix that as well. So, when I finally get done - that's my next goal (after a bit of a break).

It isn't that I'm terrible at math, I just never used much beyond basic linear algebra after leaving high school. I never went much beyond high school: I got an associates from a tech school (worthless, since the school is long defunct), and I've taken a few community college courses, plus my online MOOC stuff that's more recent.

I'm not hurting career-wise; in fact, that's never been an issue as a software engineer (started when I was 18, and just kept going, earning more over time and having fun). I'm not doing bad right now, living in Phoenix. It ain't SV - but then again, it doesn't have the downsides of it, either (not that there aren't certain downsides).

Now - after having done MOOCs in ML/AI - I am finding that I need more understanding and intuition about calculus and other mathematical subjects, so I can really apply what I have learned, and understand it at a deeper level, and perhaps do more with it. I've given thought to going back for a BS and maybe an MS (not that I need it - I just want to do it).

Good luck to both of you; I hope it all works out great!

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

#334

Post by lsc »

inanutshellus wrote: post #85
throwawayjava wrote: post #69

Earlier quoted context omitted.

Tying students' progress through the curriculum to their age is silly. If you think about it for a single second, the whole thing is totally absurd. Vague pre-puberty/tween/teenager distinctions make sense, but within each grouping/building? totally unmotivated. Yearly age-to-competency distinctions continue by sheer force of tradition, and are harmful to all but the totally mythological "average" student.

But it works at-scale, which is where the focus is. Bang-for-the-taxpayer-buck. Further, socially-speaking, being with your actual peers is extremely valuable, obviously. But yes, the ideal would be a tailored-to-each-child education. Personally, having seen the power of a good Montessori education, I think it's frickin' genius and should be the template for all education (specifically the grouping of 3 yrs together…

>Further, socially-speaking, being with your actual peers is extremely valuable, obviously.

I would disagree... I think that there is huge value to being around a variety of people, and a strong negative value to only being around people in the same phase of life as yourself, especially when you are in the nasty phase. I think I made it through that part of my life because I had an after-school job where I fixed computers for a local office. I even enrolled in the vocational program at my highschool that let me out of school early to go to work (except every second Monday, when we learned how to spot shoplifters, short-change scams, and other hazards of the retail life.)

I think the number of people who felt good about their social lives, the things they did socially and the things, socially that were done to them in high school is... small. As far as I can tell, for most people, college is important because it is a kind of recovery from this, and prepares you for a workplace where conflict is muted, where yes, if you are good enough, you can still be an asshole, but where being an asshole has a pretty heavy cost that must be made up in other ways.

For me? Being expected to behave like an adult while being treated like an adult around a bunch of adults was amazing. It gave me a reason to keep going in high school, and when I came of age, I was all set to get a really nice job.

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

#335

Post by [deleted] »

alasdair_ wrote: post #247
watwut wrote: post #165

Earlier quoted context omitted.

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 never managed to memorize my times tables. I never managed to memorize other formulae either, which meant that in an exam without a cheatsheet I'd have to do things like draw a bunch of triangles, measure them (graph paper) then re-derive the Pythagorean formula that I vaguely remembered involving a square root. It sucked.

[deleted]

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

#336

Post by inanutshellus »

emilecantin wrote: post #205
inanutshellus wrote: post #85

Earlier quoted context omitted.

But it works at-scale, which is where the focus is. Bang-for-the-taxpayer-buck. Further, socially-speaking, being with your actual peers is extremely valuable, obviously. But yes, the ideal would be a tailored-to-each-child education. Personally, having seen the power of a good Montessori education, I think it's frickin' genius and should be the template for all education (specifically the grouping of 3 yrs together…

My kids are homeschooled, and I'm in charge of teaching Math, because my wife is one of those "I suck at math" people. Her parents focused exclusively on memorization when they helped her with homework, and then she got a few bad teachers, so her mental models are completely off. She's getting better, but that's not really my point. The math program I use with my kids is this one: http://www.defimath.ca/ecole-maison/…

That sounds wonderful. My kids are about the right age to do this, and I'm curious, are there any English-language versions of this text?

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

#337

Post by ice109 »

andrepd wrote: post #308
ice109 wrote: post #276

Earlier quoted context omitted.

you use intuition to come up with the argument. then you use a proof to convince others.

No, you use intuition to come up with an idea the use that idea to write a proof for yourself . Intuition is invaluable as a starting point, but it's often misleading.

you're very naive. i think you're probably still an undergrad or maybe have never done serious math.

https://terrytao.wordpress.com/career-advice/there%E2%80%99s...

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

#338

Post by gusmd »

ythn wrote: post #123
gusmd wrote: post #75

I studied Mechanical Engineering, and it was my experience that several professors are only interested in having the students learn how to solve problems (which in the end boil down to math and applying equations), instead of actually learning the interesting and important concepts behind them. My wife went to school for Architecture, where she learned "basic" structural mechanics, and some Calculus, but still cannot…

Reminds me of an anecdote in Richard Feynman's book in which the Brazilian education system revolved around memorizing definitions without understanding the underlying concepts: http://v.cx/2010/04/feynman-brazil-education

That was such an interesting read. I live in the US, but am actually Brazilian, born, raised, and educated there (BS and MS). I did have some GREAT professors in college who you could tell loved their subjects so much, and would give amazing, passionate lectures, full of real-life examples, etc. Those shaped my career. But some others were just like the ones in the article.

Funny enough, all the good ones were much younger professors (like, in their 30's, 40's), with very few exceptions. Since the original article is from the 80's, maybe Feynman's feedback had some effect? I did go to one of the best universities in the country, so maybe my experience is also different from other people's. I hope it isn't, and I hope it continues to get better over there.

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

#339

Post by gusmd »

VyseofArcadia wrote: post #328
gusmd wrote: post #75

I studied Mechanical Engineering, and it was my experience that several professors are only interested in having the students learn how to solve problems (which in the end boil down to math and applying equations), instead of actually learning the interesting and important concepts behind them. My wife went to school for Architecture, where she learned "basic" structural mechanics, and some Calculus, but still cannot…

> My wife went to school for Architecture, where she learned "basic" structural mechanics, and some Calculus, but still cannot explain to me in simple words what an integral or a derivative is. Not her fault at all: her Calculus professor had them calculate polynomial derivatives for 3 months, without ever making them understand the concept of "rate or change" I've taught Calculus close to a dozen times now. I talked…

> You hit a nerve. I've left academia for this and other reasons, but as you can tell I'm bitter about it.

Looks like I did! Sorry about that. I fully understand where you are coming from, as I've had the same experience when trying to help college colleagues with course work, tutoring for a few courses in college, or even giving private lessons to HS kids. Some people are 100% not interested in learning -- they want the bare minimum to pass the course and move on.

Not sure how we can change that, though.

I had one specific professor in college would would abuse those inquiry-based learning techniques that you have mentioned, and it was absolutely the best course I had during my 7 years in the university. Anecdotal, but students loved him. He ended up being my MSc supervisor :)

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

#340

Post by Balgair »

cr0sh wrote: post #332
kayoone wrote: post #284

Earlier quoted context omitted.

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 be…

Seems like both of you are doing what I plan to do once I finish my Udacity SDC Nanodegree course. I've known for a while (ever since AI Class and ML Class in 2011) that I need a refresher and more on math, because ML. This Udacity course just drove it home. I'm tired of hearing about "take the derivative" and "perform the integral" (or whatever), and not quite understanding it. Heck, just what I wrote probably indic…

Best of luck to you too! Try taking some community college (CC) courses too. Calc. is not fun or easy, and having a professor to help 'keep you honest' may be very useful in the long term. CCs are very useful for these things, cheap, good schedule for working people, and an attitude of 'here to learn, not to degree'.
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