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As Conrad Wolfram said at the TED conference, in the future kids should focus more on new technology. Computers compute better than humans, so we should focus more on thinking and getting the knowledge how to use available software.

I teach programming to my young friend, he is 14. He is very talented, however he still has very much to learn. I wonder how I can teach them to use Mathematica to help with homework and maths materials...

I finished my IT studies. I have only used Mathematica a few times, but I am not an expert.

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    $\begingroup$ What level are we talking about? 14 is ... solving quadratic equations and drawing triangles? I think the problem with Mathematica here is that child-friendly applications aren't very much so on the back end. $\endgroup$
    – David
    Commented Jan 26, 2012 at 7:44
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    $\begingroup$ @David: something like that. However I don't know exactly program of current education system on this level. Nevertheless I have to say, that my friend is rather gifted and he is able to learn more difficult things a little earlier. I want to give him a kind of "leverage". $\endgroup$
    – noisy
    Commented Jan 26, 2012 at 8:13
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    $\begingroup$ I used this tutorial as a teenager, and enjoyed it: library.wolfram.com/infocenter/MathSource/1847 A big advantage is that is has homeworks/assignments (I find it easier to learn through them). Having started at not that much older, I strongly disagree that Mathematica is only suitable for those with advanced maths knowledge. Drawing a Koch curve is enjoyable at even an earlier age, and Mathematica makes is very easy. $\endgroup$
    – Szabolcs
    Commented Jan 26, 2012 at 9:31
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    $\begingroup$ Very apropos. $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Jan 26, 2012 at 9:45
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    $\begingroup$ @J.M. +1 I agree with the view point in the link, but I think there is also the other side which is not discussed there to the full extent. And it is better if we rely more on experts who don't work at WRI. $\endgroup$
    – Artes
    Commented Jan 26, 2012 at 13:13

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Mathematica is the best tutorial. It is a discovery tool - just start from something that he knows a bit already and you both take one little step at a time. Just try things.

  • 1st Thing - Try this Link => Hands-on Start to Mathematica

  • I personally would recommend engaging with him in a project of making an application and submitting it to the Wolfram Demonstrations Project.

http://demonstrations.wolfram.com/

Check out stuff for kids: Link => Especially this

It could be something simple, but because it is interactive - he may find it fun to play with. I suggest you guys design and make a game. When teens have precise goals it is easier to set them on track especially if it is fun. You can also look through demonstrations and try to figure out how they work. Taking thinks apart - kids like that ;-)

  • There are many videos here:

http://www.wolfram.com/broadcast/

  • But, again, Mathematica is the tutorial itself. It has some magic called "free form linguistic input". Basically you type in plane English and it gives you back the code or data. This is very cool for kids and teens. They can see how a concept is getting turned into code. You can find a few examples here:

Link => Virtual talk video

Link => Virtual talk notebook

This maybe a little bit adult level, but you can find some tricks how to teach him.

  • I generally recommend all talks here - videos & notebooks:

http://www.wolfram.com/events/virtual-conference/2011/presentations/

  • Mathematica Documentation is full of neat examples.

  • If he does not have Mathematica he can try using Wolfram|Alpha - it is free:

http://www.wolframalpha.com/

I very much like the idea of teaching programming to children. Below are a standard references for students:

M10: A Student's First Course in Mathematica

Wolfram Education Portal

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One unconventional but possibly very useful approach it to introduce him to Project Euler. While many of the newer questions are completely beyond me (mind you that is not saying much), many of the earlier ones are quite approachable. If your friend has the desire to learn and an interest in puzzles/challenges, this site will grow as he grows.

Most of the problems are best solved by a combination of mathematical logic and programming, and one can see what is possible with computer assistance.

Once a particular problem has been solved you will be able to view other's solutions which opens up whole new lines of thinking and provides exposure to foreign concepts.

The Wolfram Blog and Screencast Gallery are great for showing what Mathematica is capable of, and the Blog provides links to other useful areas.

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  • $\begingroup$ I agree about the project Euler, but have to also point out that many problems there require some exposure to number theory. $\endgroup$
    – Sasha
    Commented Dec 3, 2012 at 6:26
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    $\begingroup$ @Sasha Well, I improvised my way through 157 problems before getting stumped, and PE was my exposure to number theory. $\endgroup$
    – Mr.Wizard
    Commented Dec 3, 2012 at 6:38
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Affirming Vitaliy's suggestions I'll say something beyond his comprehensive answer and to a certain extent more specific.

A great mathematician S.Banach used to say (maybe as a joke) that children shouldn't be taught mathematics early because that would be a too sharp tool for them. There is an obvious analogy and this is why children shoudn't be taught Mathematica too early. I'm affraid the events such as C.Wolfram's talk at the TED conference make some kind of delusion and I feel similarly when reading (pointed out by J.M.) an interesting discussion Will it rot my students' brains if they use Mathematica?

Though in general I agree with the statements therein and find Mathematica a great computer system, however one should carefully consider WRI employees' arguments concerning such a delicate issue as teaching.

To point out helpful resources if one's aim is to be capable doing more than just press the button, it is a good way to read a clear and concise compendium by Richard J. Gaylord:

Mathematica Programming Fundamentals: Lecture Notes

Many programs at the demonstrations project are certainly useful, however in principle it is much better for understanding if they come together with Gaylord's excellent introduction to Mathematica programming. More throughoutly is just to read the whole book by Paul R. Wellin, Richard J. Gaylord, Samuel N. Kamin (a bit more advanced for the very beginners):

An Introduction to Programming with Mathematica, Third Edition

If one needs a video tutorial I suggest to start with something fast and easy, this one by Adam Berry from the Virtual Conference 2011 is good enough :

Introduction to Functional Programming
(note that one has to register to watch it)

I find useful also this video tutorials accompanying Mathematica Cookbook by S.Mangano, which presents a wide range of interesting examples of programming from beginners' level to more advanced issues.

At last but not least I suggest that young people have to study also mathematics, since it is (in my opinion) dangerous if one accustoms to use functionality for solving equations without understanding what it really does.

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Vitaliy's suggestion is indeed very good.

What I want to add is that the Documentation is a good place to start. Say he's interested in drawing some graphs to illustrate something, then the Guide page for Graphs is a great place to start and the reference pages have tons of examples to build from.

Once one has solved a problem or two with Mathematica it's easy to go on with Gaylords lecture notes (referenced by Artes above) or similar. The hard part is getting started, the rest is easy :)

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  • $\begingroup$ Hi Johan! Good suggestion (+1) - I think we all started that way one day. Great that you joined the site! $\endgroup$
    – Leonid Shifrin
    Commented Jan 26, 2012 at 17:09
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I started learning Mathematica a couple of months ago, and all these suggestions are good. I'd also say that, although it's possible to surround yourself with books and tutorials, it's even more important to have some focus or goal to give shape to your learning efforts. You can find yourself bouncing from one interesting corner to the next (particularly with Mathematica's far-reaching functionality) ... I'd suggest you choose some project that you can hang your various Mathematica explorations on.

Perhaps, as Vitaliy suggested, a game or a Demonstration. Other possibilities include starting a blog - showing a cool thing in each blog post - or even start writing your own tutorial... (In fact that's what I'm doing: I've got up to Chapter 4 of my "Basic image processing with Mathematica" book. It's partly a record of my progress, partly the kind of thing I wanted to have before I started.)

Or you could work on the Wikibooks book on Mathematica, adding simple examples and notes about your discoveries.

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I know this is an old thread now, but this might prove useful to someone. I have been teaching Mathematica to high school students for almost a year now. I have had to make my own resources, as I couldn't find any that were fit to purpose. I am happy to share them, and here is the Dropbox link:

Mathematica Exercises

All mistakes are my own! I am also happy to hear from anyone who has any comments, suggestions or questions about using Mathematica in school education.

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This page could be quite interesting in your case

http://education.wolfram.com/algebra/

The animations here explain some common Mathematica functions in a quite funny way.

http://reference.wolfram.com/legacy/flash/

There's a huge list of other resources here where you could pick what you think suits you.

Where can I find examples of good Mathematica programming practice?

Also, something that I think is always very important is to control what you're doing by controlling the dimensions of the lists you generate using Dimensions or Length.

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There's such a good video explaining how mathematica functions work using cool animation, i insist on watching this, it will seriously help you https://www.youtube.com/watch?v=_0Y42ExmBoY

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Steven Wolfram's 2016 book An Elementary Introduction to the Wolfram Language includes high school students among the target audience.

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    $\begingroup$ This is an excellent recommendation. I started using Mathematica at 0.9beta and read the first edition of Wolfram's Mathematica manual from cover to cover—it was the best possible introduction and overview of the entire language. EIWL is the closest book I've seen to capturing this same sense of excitement I had back at Version 1.0 and I think that it is ideal for all potential users. $\endgroup$
    – TheDoctor
    Commented May 2, 2016 at 9:31
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I have written, with John Kennedy, an introduction to Mathematica programming that takes "a hands on" approach by tackling real interesting problems from the outset. The notebooks can be found on my website here. We feel it is suitable for self study or in the classroom.

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