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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

#241

Post by noonespecial »

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…

All I ever learned in high school math was isolated "number tricks" that had to be memorized and then performed on que.

Parrots have deeper understanding than was required of us.

I didn't even get a cracker.

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

#242

Post by jacobolus »

steanne wrote: post #229
taco_emoji wrote: post #86

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. 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."

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 x² + b = 2ax (or if you like, x² – 2ax + b = 0; or feel free to swap the sign of b if you prefer). The equation for the parabola is then x² + b = 2ax + y.

Step 2 (optional): rearrange that equation to get (x – a)² = a² – b

Step 3: x = a ± √(a² – b)

In this form, the “discriminant” is just a² – b, the x coordinate of the vertex is a and the y coordinate is b – a², Viète’s formulas tell us that the two roots satisfy ½(x₁ + x₂) = a and x₁x₂ = b. If the coefficients are real but the roots are complex, then we know each root has amplitude √b and phase arccos(a/√b). Etc.

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

#243

Post by gxs »

Late to the party but wanted to share my experience.

I was an Applied Math major at Berkely. Why?

When I was in 7th grade, I had an old school Russian math teacher. She was tough, not one for niceties, but extremely fair.

One day, being the typical smart ass that I was, I said, why the hell do I need to do this, I have 0 interest in Geometry.

Her answer completely changed my outlook and eventually was the reason why I took extensive math in HS and majored in math in college.

Instead of dismissing me, instead of just telling me to shut up and sit down, she explained things to me very calmly.

She said doing math beyond improving your math skills improves your reasoning ability. It's a workout for your brain and helps develop your logical thinking. Studying it now at a young age will help it become part of your intuition so that in the future you can reason about complex topics that require more than a moment's thoughts.

She really reached me on that day, took me a while to realize it. Wish I could have said thank you.

Wherever you are Ms. Zavesova, thank you.

Other beneits: doing hard math really builds up your tolerance for building hard problems. Reasoning through long problems, trying and failing, really requires a certain kind of stamina. My major definitely gave me this. I am a product manager now and while I don't code, I have an extremely easy time working with engineers to get stuff done.

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

#244

Post by alasdair_ »

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.

Coming up with actual uses would have been enormously helpful to me when I was younger. All I was literally ever told was "you need this to pass the exam"

The one thing I really wished I'd have learned more of, younger, is stats. Knowing how basic probability works would have been fantastic - it took a lot of poker theory to really understand it in my bones.

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

#245

Post by alasdair_ »

autokad wrote: post #160
taco_emoji wrote: post #86

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. 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…

that sounds utterly dreadful. computer science is often taught like this; to its folly. imagine a kid learning to speak 'stop just memorizing words, you need to understand how language was derived before you learn how to speak it'. its completely counter intuitive to how creatures learn. learn easy things, especially those that relate to problems we deal with, and then get deeper into the subject if necessary.

This would be true if calculating the volume of various shapes was something that kids did for 16 hours a day, every day.

Formulae without context are meaningless to most.

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

#246

Post by [deleted] »

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

[deleted]

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

#247

Post by alasdair_ »

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 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.

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

#248

Post by [deleted] »

bitwize wrote: post #98
taco_emoji wrote: post #86

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. 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…

> 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…

[deleted]

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

#249

Post by alasdair_ »

jamesrcole wrote: post #46
sixo wrote: post #31

Earlier quoted context omitted.

Not sure it's exactly the early years. But I think there's zero point to moving past a topic until you have mastery & can think WITH it (not just, about it, or hack through it on paper). And since the early years are often where that fails, they need to be rethought.

I remember listening to an episode of The Science Show podcast where the guest was arguing (based on their experience) that chemistry and physics concepts should be taught to young children as it's actually easier to teach it to them. With the stated reason being that if they're taught it at a later age, as they are now, they've already built a view of the world where those concepts are somewhat unintuitive. If they…

One of the most fun things I ever did with my five year old son (now six) is build a cloud chamber with dry ice and a fish tank and talk about it. Strongly recommend.

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

#250

Post by gizmo686 »

d3ckard wrote: post #189
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…

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…

>That's why almost every professional athlete starts as a child.

Professional athletes are highly competitive. People don't hire basketball players to throw balls into hoops; they hire them to beat other basketball players. Unless you are one of the best humans at basketball, you are worthless as a basketball player.

In almost any profession, you do not need to be the best to have value.

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