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Five-Year-Olds Can Learn Calculus (2014)

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Re: Five-Year-Olds Can Learn Calculus (2014)

#101

Post by eberkund »

nogbit wrote: post #89
hyperpallium wrote: post #35

Earlier quoted context omitted.

One thing that's difficult about math is all the "mathematical maturity " required, much of which is notation and... abuse of notation. Math seems like an Arts subject, where you must learn all the cultural background, as in English Literature. I'm not sure it's necessary, given it's not logical nor self-contained, but is arbitary and historical. Then again, I'm not absolutely convinced it's not necessary...

It is necessary but could be improved. If all we had was roman numerals we would still be in the dark ages.

Is it really necessary? I have so many memories of sitting in math classes and the teacher simply starts writing letters on the board and I am thinking to myself: what the hell does that symbol or letter represent? Before we even get around to the concept that the equation represents.

Re: Five-Year-Olds Can Learn Calculus (2014)

#102

Post by ajuc »

roceasta wrote: post #45
chii wrote: post #26

Earlier quoted context omitted.

There are some aspects of doing math that isn't fun, because it is grinding. Learning the time tables for example - you just have to do lots of exercises to get used to multiplying. No way around that. Just like in sports, where you must also do a lot of basic practise to get good. Making the practise like a game can be done to done degree, but ultimately, a kid is going to see through that after a while, since it ge…

>Learning the time tables for example - you just have to do lots of exercises to get used to multiplying. No way around that. Learning how to perform mental arithmetic with the aid of pencil and paper was a way to escape from the grind of farm work. One could get a respectable job as a clerk. However with the advent of electronic cash registers and smartphones a way around this later form of grind has also been found…

Can't understand modern world without understanding statistic, can't do that without algebra and basic calculus, can't do that without being at least adequate at mental multiplication (for calculating parameters in equations and understanding how they change without interrupting your train of thought every 3 seconds).

So yeah, I think you still need to grind these multiplication tables, even if you have perfect version of Wolphram Alpha on your smartphone. It won't tell you what question to ask.

Re: Five-Year-Olds Can Learn Calculus (2014)

#103

Post by iovrthoughtthis »

occultist_throw wrote: post #67
iovrthoughtthis wrote: post #60

Earlier quoted context omitted.

Hard and scary carry differently meanings in those contexts though, surely? Video games are safe e.g you can always try again, you can do incrementally well. Video games are scary in an exhilarating way, you blood will pump and your pupils will dilate but at the end you can put it down, turn the lights on and watch funny cat videos to recover. Math (at school) is hard because you get one shot. Finite lives. After eno…

And you succinctly put why I despise "School". I love learning new areas and new techniques. And when Im teaching myself, I can fail and I go back a step or 2. Not the end of the world. If I do similar in a class, then I set myself further back with a slowly growing chance of doing badly (D or F). And in College, then its another 1-4 credit hours to pay for the privilege. They not only fail me, but demand more money.…

I must have attempted to implement a lisp many times before I got it "right", or a "simple" perceptron etc.

Without the pressure I'm not scared of revisiting hard things, I'm driven to actually.

Edit: to indicate that a "simple" perceptron isn't actually that simple.

Re: Five-Year-Olds Can Learn Calculus (2014)

#104

Post by baldfat »

We teach mathematics backwards and in the wrong order and we push students through things they have not mastered.

"A Mathematician’s Lament" by Paul Lockhart

https://www.maa.org/external_archive/devlin/LockhartsLament....

BOOK published in 2009 https://www.amazon.com/Mathematicians-Lament-School-Fascinat...

Re: Five-Year-Olds Can Learn Calculus (2014)

#105

Post by GuB-42 »

This article misses the point of early math education.

We don't teach elementary school kids to be future math researchers, or even engineers. We teach them things that everyone should know : reading, writing, basic science, a common cultural basis, and counting.

Arithmetic is important in everyday life : calculating change, knowing what a 10% discount means (percentages are more tricky than most people think), converting currency, measuring surfaces, etc... Calculus, not so much.

In France, they experimented with "maths modernes", which was an attempt to help kids with more advanced concept at an early age : starting with set theory and bases, delaying basic arithmetic. It failed miserably, it produced kids that were unable to do everyday life operations. We are now back to a more down-to-earth approach, with an emphasis on approximations and mental calculations.

Re: Five-Year-Olds Can Learn Calculus (2014)

#106

Post by roceasta »

ajuc wrote: post #102
roceasta wrote: post #45

Earlier quoted context omitted.

>Learning the time tables for example - you just have to do lots of exercises to get used to multiplying. No way around that. Learning how to perform mental arithmetic with the aid of pencil and paper was a way to escape from the grind of farm work. One could get a respectable job as a clerk. However with the advent of electronic cash registers and smartphones a way around this later form of grind has also been found…

Can't understand modern world without understanding statistic, can't do that without algebra and basic calculus, can't do that without being at least adequate at mental multiplication (for calculating parameters in equations and understanding how they change without interrupting your train of thought every 3 seconds). So yeah, I think you still need to grind these multiplication tables, even if you have perfect versi…

Have you noticed that most adults don't know what nine times seven is? If you ask them on the street they'll mostly either get it wrong or tell you quite rudely to go away. This is despite (and because of) a decade of grind at school. Or have you noticed that people are unable to hold a conversation in a foreign language despite years of 'study' in a classroom? Whereas an enthusiastic individual can pick up basic conversation for themselves in a matter of months.

This is because coercion in education is: (1) painful, (2) prophetic, (3) it doesn't work!

What happens in real life is that if somebody needs to know something because they are keen to do something else then they will learn it efficiently, 'just in time' and precisely to the extent needed. Assuming their creativity is relatively intact...

https://www.youtube.com/watch?v=iG9CE55wbtY

Re: Five-Year-Olds Can Learn Calculus (2014)

#107

Post by lingua »

eberkund wrote: post #101
nogbit wrote: post #89

Earlier quoted context omitted.

It is necessary but could be improved. If all we had was roman numerals we would still be in the dark ages.

Is it really necessary? I have so many memories of sitting in math classes and the teacher simply starts writing letters on the board and I am thinking to myself: what the hell does that symbol or letter represent? Before we even get around to the concept that the equation represents.

What you are describing is not unique to math. It is required in any discipline. In fact, it is required in any social interaction. People are constant;y building common vocabularies. The words and phrases you use at work are different than the ones you use at the neighborhood block party. Even among different friends you have different vocabularies. "Elbow" means something different to plumbers, fishers, basketball coaches, and musicians. "Panama" means something different to a very small subset of your friends. Humans are constantly building common vocabulary, and everyone maintains several different vocabularies simultaneously.

To complain about the effort to build a common vocabulary is to complain about the effort of participating in any society.

Re: Five-Year-Olds Can Learn Calculus (2014)

#108

Post by lingua »

This reminds me of a topic that comes up a lot at my house: late homework.

What should teachers do about late homework? Should you get a zero if you don't turn it in? Should you get 50% off for anything late? Should there be a limit on how late it can be?

If a student turns in 10 missing assignment in the last week of the semester, then gets a 96% on the semester exam, what grade do they deserve?

What is the point of a grade anyway? There are so many different meanings built into a grade. A grade can teach discipline and responsibility. It can teach respect. It can teach cheating. It can teach to do just enough to scrape by. It can teach that the important thing is to be higher than others. It can represent competency in a subject. It can represent value to the income of the football team.

Education is about so many things that it's hard to have a useful blanket discussion.

The correct approach depends upon the intention. If you are trying to improve people's understanding, you take one approach. If you are trying to vet competency for potential employers, you take a different approach. If you are trying to build a minimum base on which society can be anchored, you take yet another approach.

Re: Five-Year-Olds Can Learn Calculus (2014)

#109

Post by headcanon »

jonnybgood wrote: post #2

I have no doubt they can. There's so much negative cultural conditioning towards mathematics by eliciting negative emotions that it's ridiculous (i.e. math is scary, math is hard, math is for smart people, etc.). I believe kids who excel at math is not due to them being smarter but due to the bypassing of the cultural conditioning. The bypassing can be due to the parents, teachers, some mentor, or their particular fa…

Its the same for programming. Most of programming isn't rocket science (unless it is :P) and anyone with the ability to apply basic logic can figure out what most programs do. However the language, the text itself, gets in the way, and people throw up their hands immediately once they see something unfamiliar.

The difference between literacy and illiteracy in this case, IMO, is almost an emotional one - its the ability to say to yourself, "ok, I may not know what this keyword means, but I know what is in front of me is not magic, that it can be understood, and I can understand it with some research and patience"

It helps a lot for ones future if someone is able to be taught this skill early on.

Re: Five-Year-Olds Can Learn Calculus (2014)

#110

Post by mclehman »

RobertoG wrote: post #97
mannykannot wrote: post #86

Earlier quoted context omitted.

Up to a point, but does it not all grow out of the concept of limits?

I would say that the fundamental idea to understand is the concept of changing ratios. Limits seems to me to be more a tool in order to calculate the ratios than a fundamental concept.

I agree with that. You can hand limits as a tool to someone already comfortable with the concepts and present them as a way to quantify their intuitive understanding.
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