Kill Math Project: Solve meaningful problems of quantity

[ƒ(x)]

"kill math"

Kill Math is my umbrella project for techniques that enable people to model and solve meaningful problems of quantity using concrete representations and intuition-guided exploration. In the long term, I hope to develop a widely-usable, insight-generating alternative to symbolic math.

This made me sad: https://worrydream.com/KillMath/

I'm all for pretty graphs, but I have limits.

 

[Hepth]

"This "Math" consists of assigning meaning to a set of symbols, blindly shuffling around these symbols according to arcane rules, and then interpreting a meaning from the shuffled result. The process is not unlike casting lots."

As a theoretical physicist, I agree with this paragraph :)

 

[Geezer]

"This "Math" consists of assigning meaning to a set of symbols, blindly shuffling around these symbols according to arcane rules, and then interpreting a meaning from the shuffled result. The process is not unlike casting lots."

As a theoretical physicist, I agree with this paragraph :)

^^Me, too.

The "Kill Math" people sound lazy to me.

 

[chiro]

Whats the problem? Is there something I'm missing?

In any kind of learning, analogies are used all the time to explain things and math is no exception. If someone can't pick up the algebraic definition and automatically connect it to a visual analogy (or representation that isn't an analogy per se, but something that is in fact equal), then new ways of making learning accessible to more people is good.

All math is created out of building something new on top of what already exists. Motivations are different, and are sometimes based on discoveries from areas like physics, biology, and other natural sciences, but none-the-less the point I am making is that they are man-made. Some man or woman (or maybe multiple people) created it, and based on this there is a motivation for it, and any good teacher of any subject should be able to take their knowledge and tailor it to the perspective of their student.

If they can't, then they do not know it as well as they had thought.

 

[ƒ(x)]

Doing away with the equations in favor of guess and check methods is just stupid.

 

[Hurkyl]

Ah, the irony. His complaint boils down to "I never developed an intuition for the mathematical concepts I was using"... but he's advocating that people should be taught to use "intuition-guided exploration".

It's hard to use intuition to solve problems if you never develop the needed intuition.

 

[thegreenlaser]

Someday there will be an introductory essay on this page, and it will move you to tears. That essay is not yet written

Sounds legit.

I have trouble believing that someone who starts with a high-school education can learn enough math completely based on intuition that they can solve differential equations. I mean, sure, someone may understand how a certain system modeled by a differential equation behaves when you show them the graphs in a pretty way, but could they actually use that 'intuition' to solve a meaningful problem from scratch? I think this is useful to help students understand what they're doing but I don't think it could ever replace abstract math.

 

[chronon]

If you read more of what he has written, you'll see he actually knows quite a bit of mathematics. What he is advocating is less manipulation of symbols, more use of simulations to get an intuition for mathematics - something I would very much agree with.

 

[Hurkyl]

If you read more of what he has written, you'll see he actually knows quite a bit of mathematics. What he is advocating is less manipulation of symbols, more use of simulations to get an intuition for mathematics - something I would very much agree with.

A problem with the essay is that an introductory section is supposed to set the frame in which the rest of the essay is cast, which is rather antagonistic to symbols.


Also, he talks a fair bit about innumeracy, but I'm pretty sure the majority of his focus is on things far too sophisticated to address that issue. IMO, the #1 most prevalent problem people have is that they are bad at creating mathematical problems.

(And I think this is closely tied to the fact that people are usually quite bad at giving directions, following directions, and paying attention to details)

 

[AlephZero]

I have trouble believing that someone who starts with a high-school education can learn enough math completely based on intuition that they can solve differential equations.

I think there is a bigger issue here, which is that the average person who starts with a high-school education doesn't have any need or motivation to even intuit what a differential equation is, let alone how to solve one. If you can afford a $5 calculator, you don't even have any motivation to remember that 9 7s are 63.

But, at age 11-12 you can't easily discover which subset of children will want to study science seriously later, and unless you start teaching them math soon enough, their later science education will take longer. The current solution - throw math at everybody, and hope it sticks to some people, and let the others suffer the consequences of being branded as "failures" - doesn't seem optimum, but what's the real alternative?

 

[AlephZero]

What he is advocating is less manipulation of symbols, more use of simulations to get an intuition for mathematics - something I would very much agree with.

I'm not sure. I was working through the "computer revolution" in the 60s and 70s, and there was a lot of debate in the company I worked for about the relative advantages of mech engineers having to spend time doing hand calculations - and to get useful answers in a usefully short amount of time, think hard about what was important and what was not - compared with the ability to quickly create computer models get much more information on "what if" scenarios, and look at a much wider set of alternatives.

Having seen the quality of the end products produced both ways, I really can't convince myself one approach is "better" than the other. I suspect the people who are good engineers using one set of tools would also be good engineers using the other. But the people who whose specialism is producing convincing looking nonsense backed up by computer generated animations might have a harder time producing convincing but nonsensical hand calcs...

 

[ƒ(x)]

The current solution - throw math at everybody, and hope it sticks to some people, and let the others suffer the consequences of being branded as "failures" - doesn't seem optimum, but what's the real alternative?

I'm all for branding the plebeians as failures : P

 

[chronon]

I'm not sure. I was working through the "computer revolution" in the 60s and 70s, and there was a lot of debate in the company I worked for about the relative advantages of mech engineers having to spend time doing hand calculations - and to get useful answers in a usefully short amount of time, think hard about what was important and what was not - compared with the ability to quickly create computer models get much more information on "what if" scenarios, and look at a much wider set of alternatives.

Having seen the quality of the end products produced both ways, I really can't convince myself one approach is "better" than the other. I suspect the people who are good engineers using one set of tools would also be good engineers using the other.

I would expect people to be able to use both methods, but it's a question of which is encountered first. It's clearly much easier to play with a simulation , and so develop an intuition for what is going on, than to start by learning how to do the mathematics.

But the people who whose specialism is producing convincing looking nonsense backed up by computer generated animations might have a harder time producing convincing but nonsensical hand calcs...

I'm not convinced about this, I would say it is more the other way round. If you see someone's new idea, and it's backed up by mathematical calculations are you really going to check the mathematics in detail? But if you see a simulation then you know that if it looks at all reasonable then it must have something going for it, and you can then test out varying parameters to see whether it accords with your intuition - and if not you can dig deeper to see whether the simulation or your intuition is wrong.