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Five-Year-Olds Can Learn Calculus (2014)

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

#121

Post by ajuc »

roceasta wrote: post #106
ajuc wrote: post #102

Earlier quoted context omitted.

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 con…

Not really (but then I never asked random people to multiply for me :) ).

But I can kinda understand why, you almost never have to multiply 9*7 by hand. If you're doing algebra or any symbolic calculations you rarely use digits other than 0-4.

In real world Benford's law + usual rounding greatly reduces the need to multiply by 7 or 9 (or 8 for that matter).

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

#122

Post by unboxed_type »

pamqzl wrote: post #54
userbinator wrote: post #48

Earlier quoted context omitted.

There's also nothing stopping toys from being calculus-related either, although at the moment I can't think of any examples of such.

Imagine a toy truck that, as you drive it back and forth, plots the first and second derivatives of its position with respect to time on a little screen on the side. Hmm, that's not the worst idea...

Nice idea for a toy! But learning an internal machinery of that process isn't that fun if you are not inclined for that kind of activity.

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

#123

Post by unboxed_type »

monsieurbanana wrote: post #47
unboxed_type wrote: post #43

Please let Five-Year-Olds play their toys instead of learning calculus, so they can grow up healthy people.

Completely baseless comment. You can both learn calculus and play with toys. And if calculus is presented as a fun group activity, like suggested in the article, I don't see why it would hinder the kids growth. It's the other way, really.

It looks like we have a misconception of the verb "to learn". Conveying some very general intuition of the subject from adult to a kid is not learning, actually. Learning assumes conscious effort to comprehend relatively complex things, constantly overcoming pain of uncertainty, most mathematicians will agree with me here. This is not what is usually expected from a kid. Don't do that.

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

#124

Post by throwawayjava »

mannykannot wrote: post #113
mclehman wrote: post #110

Earlier quoted context omitted.

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.

But without limits, you cannot actually do much with the concepts. Whether you call limits a concept or a tool, they are essential to the practice of calculus, and, historically, to its emergence (and not trivially so, either.)

Yeah but you can do well on the AP calculus exam without understanding limits, if you can calculate derivatives and solve some word problems related to derivatives.

Hence, the gap between "5 year old calculus" and "high school calculus" is smaller than the gap between "high school calculus" and "actual calculus"

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

#125

Post by iovrthoughtthis »

kazinator wrote: post #111
iovrthoughtthis wrote: post #103

Earlier quoted context omitted.

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.

> I must have attempted to implement a lisp many times before I got it "right" How did you know it wasn't right? Did you run into a problem trying to implement requirements which you knew all along and accepted? (As in, you started coding without planning for some of these requirements ahead of time, then got stuck?) Or did you learn about and adopt new requirements which weren't easy to retrofit into the existing wo…

Good question. I guess by "right" here I mean an implementation that I was happy with. Not nessesarily standards compliant or complete.

In my early attempts it was things like parsing which tripped me up. I'd implement something that broke the bracketed lists up into a list of tokens and then get stuck nesting those lists into an ast. Abandon an implementation for a while and then try again at the problem, often with a fresh implementation.

Then is was evaluating expressions, when to evaluate the arguments and exploring different approaches (fexprs).

I'd do these iterations across months and with different languages. First python then JavaScript, Ruby, C.

My favourite was the JavaScript implementation. Lisp code is literate and I bootstrapped most of the built in functions by exposing the environment as a cons tree (and working with cons trees internally in the interpreter).

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

#126

Post by [deleted] »

throwawayjava wrote: post #124
mannykannot wrote: post #113

Earlier quoted context omitted.

But without limits, you cannot actually do much with the concepts. Whether you call limits a concept or a tool, they are essential to the practice of calculus, and, historically, to its emergence (and not trivially so, either.)

Yeah but you can do well on the AP calculus exam without understanding limits, if you can calculate derivatives and solve some word problems related to derivatives. Hence, the gap between "5 year old calculus" and "high school calculus" is smaller than the gap between "high school calculus" and "actual calculus"

[deleted]

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

#127

Post by zaptheimpaler »

Ntrails wrote: post #120
zaptheimpaler wrote: post #112

Earlier quoted context omitted.

Well a lot of people who dislike math do so because they think its all about rote calculation. Not just times tables, even algebra can be seen as a completely syntactic procedure - memorizing a bunch of rules. Another example - if you are taught 10 different "templates" of problems and solutions in calculus class and memorize which equations to apply where, you can solve a lot of problems without ever building any in…

> If every thing is taught as a cookie-cutter process to follow its not surprising that people associate math with blindly following processes. A hammer and a chisel are tools. You can use them to shave a bit of wood off the door, or you can use them to carve a beautiful sculpture. You can do neither without knowing how to use them. I agree that too much of maths teaching is "here are 100 quadratics, go solve them" -…

Seems like we agree. I am only saying current math is too focused on the mechanical processes, so much that many people never even see the other (more important) conceptual side. Times tables don't need to be taught in class - there is nothing to teach. They just need to be memorized by students.

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

#128

Post by roceasta »

thomastjeffery wrote: post #115
roceasta wrote: post #21

Earlier quoted context omitted.

The fact that school math is thought to be 'scary' and 'hard' is not the issue. Plenty of video games are known to be scary and hard. For instance, they contain monsters and are difficult to complete. They even have objective grades (scores). What makes the difference is that video games aren't compulsory. So they represent true play . Which is what makes them educational, unlike a school curriculum, however much it…

> math is thought to be 'scary' and 'hard' > Plenty of video games are known to be scary and hard Those statements seem related because of the ambiguous definition of "scary". In relation to math, "scary" causes anxiety, whereas in relation to video games, "scary" causes excitement. As soon as you grasp the different meanings, you can clearly see that even though both statements are about the same word they are still…

Yes, it's complicated. Yet I don't think I committed an equivocation. As I said, what makes the difference is compulsion/coercion, which causes us to interpret scariness in one context as bad (e.g. falling off a ladder), and scariness in another as being good and part of the fun (e.g. skydiving).
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