How should mathematics be taught to non-mathematicians? (2012) • Hacker News Board

Re: How should mathematics be taught to non-mathematicians? (2012)

#21

Post by keithpeter » Sat, Oct 08, 2016, 11:30 AM UTC

Myrmornis wrote: post #6

Great article. Did anything come of the Gove-era math education policy changes he's referring to?

In my opinion: Gove's main change in Maths was in the exam syllabus that is taken at age 16. The new syllabus will be examined for the first time this summer, most schools started teaching the material in 2015. It will take another 3 years or so to see the effect of that on the GCSE classes (basically age 14 to 16) and then another five years for earlier years to shift what they do.

Change takes a bit of time when it is 700,000 children in each year group moving through 10 years of compulsory education. Politicians know this but the news cycle requires changes on top of changes...

Re: How should mathematics be taught to non-mathematicians? (2012)

#22

Post by semi-extrinsic » Sat, Oct 08, 2016, 12:00 PM UTC

ankurdhama wrote: post #2

Mathematics is just the extreme end of the two most fundamental concepts Abstraction and Generalisation. Start the intro to these concepts including showing how these concepts are useful and used by everyone in their day to day life in using natural language.

My wife has studied mathematics pedagogy, and one concept that really struck me from what she learned is compression. Put simply, you can't learn a new thing until you've compressed the old thing it builds on. If you have not compressed "addition" to the point that it requires little effort, you won't be able to learn "multiplication". Same holds for e.g. "derivatives" and "Taylor series", or "group theory" and "rings and fields".

(I think this was from Piaget, or maybe Brissiaud.)

Re: How should mathematics be taught to non-mathematicians? (2012)

#23

Post by fiatjaf » Sat, Oct 08, 2016, 12:24 PM UTC

ankurdhama wrote: post #2

Mathematics is just the extreme end of the two most fundamental concepts Abstraction and Generalisation. Start the intro to these concepts including showing how these concepts are useful and used by everyone in their day to day life in using natural language.

That is the best way to not learn mathematics.

Re: How should mathematics be taught to non-mathematicians? (2012)

#24

Post by axiomabsolute » Sat, Oct 08, 2016, 12:28 PM UTC

laurieg wrote: post #5

Animats wrote: post #3

Gower suggests story problems. Many, many story problems.[1] [1] https://pbs.twimg.com/media/BTwHsS5CAAAzBBu.jpg

The problem with story problems is, as the article states, that they are never really presented in the open ended way they claim to be. You almost always teach a class a fixed operation, multiplication for example, and then give them a bunch of word problems where multiplication is thinly disguised. A much better exercise is to give an absurdly open ended exercise. "I'm at the supermarket, which checkout should I go…

So much this. Through a series of unexpected events, I ended up studying math in undergrad with no clue why or what I was going to do with it. My senior year I took a class called "Applied Modelling". The first project was a simple, one sentence question: "What would happen if the Greenland ice cap melted?".

It reminded me a lot of Randal Munroe's "What If" blog on the XKCD site [1]. Easy to understand, open ended questions that encourage readers to learn a little about topics _outside_ of math to answer the question. The class gave me an appreciation for math that was lost during all those years of study before that, and it's basically my career now.

[1]: http://what-if.xkcd.com/

Re: How should mathematics be taught to non-mathematicians? (2012)

#25

Post by ivansavz » Sat, Oct 08, 2016, 12:43 PM UTC

Wow, that's a nice collection of problems. They are exactly the opposite of the dry and artificial "word problems" students are used to.

The discussion at the bottom of the blog post is also very interesting. The socratic approach is very good to "break the ice" and introduce the application, but I wonder how scalable this approach is. Does the teacher need to be very knowledgeable/entertaining to pull this off?

BTW, I'm working on a new project, which is essentially "math lessons by email" that will walk readers through the math material from the NO BULLSHIT guide to MATH & PHYSICS. Anyone interested in learning or reviewing basic math (expression, equations, functions, algebra, geometry) should signup: https://confirmsubscription.com/h/t/4C2D9C45B88734F3 (it's free)

Re: How should mathematics be taught to non-mathematicians? (2012)

#26

Post by pbhjpbhj » Sat, Oct 08, 2016, 12:46 PM UTC

ankurdhama wrote: post #2

Mathematics is just the extreme end of the two most fundamental concepts Abstraction and Generalisation. Start the intro to these concepts including showing how these concepts are useful and used by everyone in their day to day life in using natural language.

Could you expand on your second sentence, perhaps with an example or two and how you'd imagine they're be taught in class?

Re: How should mathematics be taught to non-mathematicians? (2012)

#27

Post by pbhjpbhj » Sat, Oct 08, 2016, 1:00 PM UTC

keithpeter wrote: post #21

Myrmornis wrote: post #6

Great article. Did anything come of the Gove-era math education policy changes he's referring to?

In my opinion: Gove's main change in Maths was in the exam syllabus that is taken at age 16. The new syllabus will be examined for the first time this summer, most schools started teaching the material in 2015. It will take another 3 years or so to see the effect of that on the GCSE classes (basically age 14 to 16) and then another five years for earlier years to shift what they do. Change takes a bit of time when it…

Which all means changes have to be made at a slower rate than the parliamentary cycle; which politicians won't heed.

But then Gove hadn't a clue and seemingly doesn't care either. Each parliament IMO should get chance to make one change - presented to parliament with optional amendment suggested by third parties (unions, parent groups, students). Let them go the Lords to win the right to make a further proposal to parliament.

That should at least slow them down enough to allow teachers to weave something useful out of the crap that they can enhance over a couple of years before the next half-wit comes along and arses it all up.

Re: How should mathematics be taught to non-mathematicians? (2012)

#28

Post by wolfgke » Sat, Oct 08, 2016, 1:19 PM UTC

M_Grey wrote: post #13

frozenport wrote: post #11

Earlier quoted context omitted.

Much of advertising is emotional appeal.

Plenty of advertising, car sales, consumer financial products, lotteries, etc... rely on people not having an innate understanding of math, and especially probabilities. Hell, if people understood those issues, they might even have something to say about Gerrymandering and the electoral college!

> Hell, if people understood those issues, they might even have something to say about Gerrymandering and the electoral college!

It's not obvious whether this is good or bad (too many cooks spoil the broth).

Re: How should mathematics be taught to non-mathematicians? (2012)

#29

Post by TheOtherHobbes » Sat, Oct 08, 2016, 1:33 PM UTC

ivansavz wrote: post #25

Wow, that's a nice collection of problems. They are exactly the opposite of the dry and artificial "word problems" students are used to. The discussion at the bottom of the blog post is also very interesting. The socratic approach is very good to "break the ice" and introduce the application, but I wonder how scalable this approach is. Does the teacher need to be very knowledgeable/entertaining to pull this off? BTW,…

They are, but I think non-math people will look at just about all of them and think "I have no idea where to start."

Worse, I think they don't teach generalisable skills.

That's probably the core problem with all school-level math and science teaching. You learn a vocabulary of basic symbols and some rules for manipulating them, but you don't learn math skills - in the sense of understanding the real world well enough to make the leap from symbols and abstractions to useful life skills.

The point of math teaching shouldn't be to know how to solve problems like these, but to learn how/when you can use math to answer your own questions for yourself.

There's also a deeper level where you can teach the process of abstraction as an end in itself. I suspect that may be too far for most people - although I haven't completely convinced myself that's true yet.

Re: How should mathematics be taught to non-mathematicians? (2012)

#30

Post by striking » Sat, Oct 08, 2016, 1:46 PM UTC

wisty wrote: post #7

> Objection 5. You’d never find enough teachers who were capable of teaching a course like this. To do it well, you need to have a very sophisticated understanding of probability, statistics, game theory, physics, multivariable calculus, algorithms, etc. Objection 6: If it's hard to find teachers to teach it, maybe it's a little challenging for students (even though a good math expert might find it interesting). Just…

> what bunch of high school students wouldn't want an IT class that taught compiler design

The majority of high school students can hardly wrap their brains around the AP curriculum (probably for lack of time or effort, rather than ability). There are some that are honestly, actually interested in computer science and are thus capable of stuff like that... but they are low in number.

What might be able to work is a fully-fledged web design course, using modern standards instead of boring stuff from ten years ago. With HTML, CSS, and finally JS (probably React, then Node). Maybe even SQL. With knowledge like that, you have more than enough of a base upon which to stand. You could likely even get a job.

> Even Python is more fun than spreadsheets, right?

Spreadsheets are easy computation for a wide audience, with a little learning curve. What can Python do, out of the box? What could you convince a high school kid to program with it that isn't a derivative of "10 PRINT HELLO WORLD; 20 GOTO 10;" ?