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Five-Year-Olds Can Learn Calculus (2014)

theatlantic.com

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

#31
Anyone commenting on this (whether saying 'yes' or 'no'), please first read the article. What it considers 'calculus', none of us here would consider calculus. Because very few 5 year olds are capable of understanding even something as basic as a line plot (or '2d graph' or however you want to call it). They simple do not have the neural matter to comprehend fairly advanced (from an evolutionary point of view) abstractions like the relationship between a value on an x and a y axis.

And of course someone is going to say 'but I did it' or 'my children do it' - sure. My 6 year old has a very rudimentary understanding of the relationship between area and volume, and speed and velocity (although I'm not even sure how much of it is real understanding or just parrotting; I'm not a very good teacher, I've learned by now, not so much in how I explain things, but more in reading feedback from students). But it's not applicable to the population at large. I've tried explaining to larger groups and at that age, understanding why 'half past 6' is called that, is already quite a feat. Let alone understanding that there's two 'half past 6's' in a day, and why that is.

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

#32

My favorite app for kids is Dragonbox Algebra. It starts by teaching simple algebra concepts with cute shapes. A couple hours later your 5 yr old is solving complicated equations by dragging and dropping. Just amazing. http://dragonbox.com/products/algebra-5

Seconded, and actually all the "We want to know" games had a lot of success with my kids. They loved the games, and they're really games first for them. I guess they'll only realize the math content in a few years ;)

Personally I'm most impressed with "Elements" [1], for geometry (from Euclid of course). I find the way they gamified geometry problems really impressive. It's very intuitive, and worked wonder even before the recommended age with both my kids. Even if you don't have kids yet, I would recommend to anyone interested in serious games to spend the ~5 bucks it costs and have a look at it.

[1] https://play.google.com/store/apps/details?id=com.wewanttokn...

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

#33

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…

They bypass conditioning because they are smarter and are good at it. Who do you think are the people who espouse anti-intellectual drivel like "math is scary" or "math is uncool"? Hint: not the smart people.

There's plenty of research on the "entity theory" bias, mostly applied to gender. I.e. if you tell girls that they're bad at math, on average, they will act as if they are.

Unfortunately, framing math as hard or scary only serves to reinforce stereotypes and bar people who do not have the keys to defuse that framing from advancing. It's not the rich male kids who are told math is hard and scary.

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

#34
This is my favorite book these days for exercising an aging mind : "A Moscow Math Circle: Week-by-Week Problem Sets" [1]

Is there something similar for kids i.e. a fun activity book that exercises your mind and helps you develop a love for mathematics ? (Not looking for generic puzzle books)

[1] https://www.amazon.com/Moscow-Math-Circle-Week-Week/dp/08218...

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

#35

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…

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...

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

#37
Personally, I think math should start at teaching kids useful stuff that 100% of them are going to use such as; taxes, credit products/home loans, budgeting, investments etc. I'm sure calculus is useful and great, but the reality is only a small percentage of kids are going to use it so it doesn't make any sense to force it on EVERYONE.

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

#38
post #26

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…

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…

Maybe they could present kids with timetable After showing them more variate and interesting concepts, so that at that point they have both the spark of interest and the maturity to understand multiplication is important and the attitude at learning that makes it not a torture.

I'm just making things up tho

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

#39
post #23
post #18

Earlier quoted context omitted.

The best way to learn math is to study physics. Or engineering, as in your case.

Maybe we can generalise - the best way to learn an abstract concept is to learn how applies to a discipline you find interesting.

Sounds about right, I'm always reminded of this gif that explains why and how to calculate the circumference of a circle : https://kaiserscience.files.wordpress.com/2015/09/when-radiu...

and suddenly a cryptic formula from maths class is made clear through the visual display of a wheel turning.

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

#40

I'm not even sure.. arithmetic really needs learned as much anymore... as a dev I rarely use my times table... if I need to calculate something I'll pull up a console and go into a repl and just ask php or ruby to calculate it for me... I know HOW the calculation works and why, but I don't need to know and remember times tables. I like the idea of thinking outside the box on how to teach math and science, as I feel m…

Start watching Countdown, the UK numbers and letters game. You will need your times tables for the math part. There is even a comedy version (same games with added silliness) to keep the interest of 'younger' audiences. Youtube search : 8 out of 10 cats does countdown. It's fun and funny.

Here is the 2017 final of the 'proper, serious' Countdown, also on YT https://www.youtube.com/watch?v=Q-VdiufVWrw

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