Raising the Bar

[Daedalus]

You are never too young to learn math.

 

Introductory Calculus For Infants

 

What's next... "Quantum Mechanics for Toddlers"?

Edited December 14, 2011 by Daedalus

[CaptainPanic]

What's wrong with it? Some of calculus can be quite intuitive, and perhaps we all start with it much too late in our education. It's only an introduciton after all.

 

Kids can learn multiple languages at the age of 1 - 2. Any idea how complicated that is?

 

I am sure that the book does not start with nomenclature and an explanation of all the necessary symbols, and dig in on page 2 with an integration or two. Instead, it will take a more relaxed approach.

 

It's worth a try... if toddlers can start a bit earlier with math because the teaching method is improving, then the next generation may be a bit better at math in general.

[Daedalus]

I never said there was anything wrong with it lol. I didn't realize that my statements could be misconstrued as satire. I actually think it's a wonderful idea being a parent myself. Especially since I love math. That's why I asked what is next... "Quantum Mechanics for Toddlers"? I wish I had materials like this growing up. I wanted to share the link to the book with other parents so that they are aware of it.

Edited December 14, 2011 by Daedalus

[CaptainPanic]

Oh, lol. I use satire and sarcasm all the time myself. I guess I suspect the rest of the world to use it often too.

[Phi for All]

Oh, lol. I use satire and sarcasm all the time myself. I guess I suspect the rest of the world to use it often too.

Oh, riiiight. Sure you do.

[CaptainPanic]

Some random remarks, not really a response to anything (it's a bit of a rant), but hopefully on topic:

 

Maths may (or may not?) for a large part become intuitive for kids if they start early enough. I believe our brains would certainly be capable.

But it seems that at lower ages, most of us only learn elementary algebra. According to standard teaching methods, anything more complex seems to require an abstract way of thinking (using variables and the concept of the X and Y axis), which means kids must be a certain age - and even then it is complicated.

Why? Isn't maths meant to be used to model reality? Why can't we explain it in terms of every-day things, and go from there. I never understood why maths are made abstract to students.

 

Reality is something that kids will understand much sooner than abstract concepts. But it seems our educational systems think it needs to be made it abstract before we can advance from simple algebra - and that limits what we can teach kids at a young age. The abstract general laws can be a nice way to summarize something, but are not strictly necessary to make a student familiar with a certain concept. Students (especially young children) may grasp something a lot quicker when it is not initially described in terms of X and Y, but in terms of a lego toy doing something, or whatever is close to their experiences in life so far.

 

If you let kids play some game where something goes exponentially wrong (or right), they will soon enough get the whole concept of exponential growth, and might even intuitively understand its derivative for example.

Likewise, Trigonometric functions are not rocketscience. Most kids have sat on a swing at some point or another. A pendulum is something which people understand intuitively. But maths had to describe the basic rules first, meaning that I my first thoughts when I see such functions are about the actual sine function on a paper.

Or geometry. It all describes every day natural things, but we are explained in terms of X and Y, which we then must translate back to the real world. And it's sad to see that some students never make that step. To them, maths was never more than X and Y, until they drop out of school.

 

What is also fascinating, is that many people need language to work with math. They will, in their heads (silently), actually say the numbers and the operations, like they would if explaining to someone else. Try it: give yourself a couple of maths exercises, and listen to what you say to yourself. I bet you use words for numbers. Obviously, that's completely unnecessary to use the exact words. I find that the length of these words actually limits to how quick I can work... The words are utterly unnecessary while I am doing the operation. I probably only need the outcome, not the stuff in between input and outcome.

 

I can do without such words for very simple calculations, which are practically intuitive. That goes for more than just the multiplication tables and operations below 100. I just know the outcome without having to go through all the words. Make it too complicated, and I will talk to myself and go through the operations.

 

Similarly, young people who learn multiple languages will often truly speak those languages. When you learn a language at a later age, you learn it by translating it from your mother tongue. Very often, people speak one language, and will translate into another language (which we, in popular words also call "speaking a language"). However, they will have their thoughts still in their own language. You only speak another language when you start to formulate all your own thoughts in that other language too. It can be learned, but it takes a damn long time when you're older.

 

I really hope that we find a way to stimulate maths education at a younger age. It would be nice to know a few more concepts before going into the details of calculating the exact outcomes.

 

Oh, riiiight. Sure you do.

Please enlist for the course "thread hijacking 101" by clicking on Phi for All or CaptainPanic's name, and send one of us a message.

[Realitycheck]

The methods used for teaching kindergarten advanced maths is probably infinitely more optimized than most of what we have experienced. The level of understanding that the teacher has over it probably makes a huge difference in their ability to convey it, though I suppose the child's drive and willingness to learn it is a factor, as well. Some people have a way of chaining their children down in lala land forever, in comparison, it's really odd to witness.

[JohnB]

You only speak another language when you start to formulate all your own thoughts in that other language too. It can be learned, but it takes a damn long time when you're older.

 

So that's why I can't think in American.

 

But well said. You don't really know another language until you are thinking in it rather than translating it. (I've heard that thinking in Russian is great for those with paranoid thoughts.)