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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

#271

Post by tnecniv »

sjg007 wrote: post #225
BeenThere888 wrote: post #60

Earlier quoted context omitted.

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.

The thing that made it click for me was getting a "first principles" book for something relatively simple like Linear Algebra (or some basic CS-flavored discrete math book). These books prove everything, and reading the proofs the author wrote made me recognize what you needed to do to prove something.

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

#272

Post by analog31 »

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.

At my college, there were "calculus based" and "non calculus based" physics classes. It seemed like the calculus based class was a lot easier for just the reason that you state.

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

#273

Post by sjg007 »

tnecniv wrote: post #271
sjg007 wrote: post #225

Earlier quoted context omitted.

I never got proofs. I wish I did.

The thing that made it click for me was getting a "first principles" book for something relatively simple like Linear Algebra (or some basic CS-flavored discrete math book). These books prove everything, and reading the proofs the author wrote made me recognize what you needed to do to prove something.

Would you recommend one?

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

#274

Post by jacobolus »

jacobolus wrote: post #242
steanne wrote: post #229

Earlier quoted context omitted.

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."

Not to mention, the quadratic formula per se is needlessly complicated. If you break it into two or three steps it makes a lot more sense: Step 1: move pieces around and divide by the leading coefficient to put equation into the form x ² + b = 2 ax (or if you like, x ² – 2 ax + b = 0; or feel free to swap the sign of b if you prefer). The equation for the parabola is then x ² + b = 2 ax + y . Step 2 (optional): rearr…

Or even better in some contexts is the form x² + b² = 2ax, in which case we have a = ½(x₁ + x₂) [the arithmetic mean of the roots] and b = √x₁x₂ [the geometric mean of the roots], and the discriminant is a² – b², which has a nice symmetry.

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

#275

Post by toomanybeersies »

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…

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.

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

#276

Post by ice109 »

andrepd wrote: post #269
alistproducer2 wrote: post #266

I can't agree more. Math is about intuition of what the symbols are doing. In the case of functions, intuition about how the symbols are transforming the input. I've always thought I was "bad at math." It wasn't until my late 20's when I took it upon myself to get better at calculus and I used "Calculus Success in 20 Minute a Day[0]" did I finally realize why I was "bad" at it; I never understood what I was doing. Th…

But math isn't about intuition, much to the contrary, it's about rigorous reasoning. In math "intuition" and "common sense" are worth nothing. Only objective proof matters. It's a valuable lesson too, learning not to take anything on a hunch and only take as true what what you carefully and logically prove.

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

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

#277

Post by alistproducer2 »

andrepd wrote: post #269
alistproducer2 wrote: post #266

I can't agree more. Math is about intuition of what the symbols are doing. In the case of functions, intuition about how the symbols are transforming the input. I've always thought I was "bad at math." It wasn't until my late 20's when I took it upon myself to get better at calculus and I used "Calculus Success in 20 Minute a Day[0]" did I finally realize why I was "bad" at it; I never understood what I was doing. Th…

But math isn't about intuition, much to the contrary, it's about rigorous reasoning. In math "intuition" and "common sense" are worth nothing. Only objective proof matters. It's a valuable lesson too, learning not to take anything on a hunch and only take as true what what you carefully and logically prove.

For me, before you get a level where you can understand proofs or even how to read them, you need to understand why lemmas, axioms, and other components are true. My take is more about how to learn to understand the calculatory side of math, which I think is a prerequisite for taking on the reasoning and logical side of it.

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

#278

Post by iclouddrive »

aphextron wrote: post #211
greenmana wrote: post #171

Earlier quoted context omitted.

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?

https://en.m.wikipedia.org/wiki/Concrete_Mathematics

https://www.csie.ntu.edu.tw/~r97002/temp/Concrete%20Mathemat...

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

#279

Post by kamaal »

toomanybeersies wrote: post #275
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…

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?

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

#280

Post by webmaven »

agumonkey wrote: post #234
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 often think that kid psychology is probably extremely well suited to kinetic problems. Things that involve their own natural desires, all kids want to move, jump, interact with the world. Connect their eagered mind with a way to denote the world and let them abuse math to communicate and reason their own desires.

A kinetic/kinesthetic approach probably would have worked well for quite a few classmates of mine, but definitely not for me. In fact, the only approach that would have appealed to me even less would be musical.
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