Interesting discussion from insightful people. Conrad Wolfram's 4 steps sounds good but it does have the flavor of: We're putting you through boot camp and then you can go out to the industrial front lines and start identifying problems. High school students don't have to solve any such practical problems, they're not yet equipped for it, and most of them will never use mathematics later. Besides, most of them are bored to death with the material thrown at them.

So how can Mathematica be used to open some new avenues? First, CDF documents (especially if package code and style sheets can be included) are an absolutely tremendous tool for providing new material to students. With the free player, practically anyone can read them. I don't see any reason why CDF documents (and Mathematica documents for more serious students) won't eventually replaced the present textbook format. What kind of look and content should such documents have?

They shouldn't look like a Manipulate statement! Especially one with five or six sliders with everything moving around with very little explanation.

They should look more like a tutorial, or better yet an essay, or even a story about mathematics. And mathematicians, and topics in the history of mathematics. The more advanced documents might be similar to the style of John Stillwell in several of his educational books (Numbers and Geometry or Mathematics and Its History). The documents might show at least one or two easy proofs (The irrationality of the square root of 2, visual proofs of the Pythagorean theorem?) And maybe a case where mathematics disproves some intuitive idea.They could tell stories about mathematics and art (flutes and lyres, or perspective.) They might talk about Galileo and mathematics as the language of nature, or Wigner on the unreasonable effectiveness of mathematics. Or the belief that some people have or had that everything that exists is really just mathematics! They might concede that mathematics is difficult and that it took millennia to solve some problems and there are plenty of unsolved problems. Maybe they could be assured that they aren't expected to do a lot of practical mathematics or mental calculation. They might make it interesting and stop threatening them with standardized tests on the routine mechanics of it. Do you want to find out if someone can do some mathematics? Just talk to them, you'll find out fast enough.

The material in the documents should be leisurely, with development by multiple diagrams, calculations and dynamics so they might see how a simple line of mathematical development goes. Our technical prowess should go toward making the exposition simple, clear and elegant - perhaps not so easy.

Thanks David and George for your thoughtful replies. My son is 20 years old so my control is less than when he was a young lad in elementary school. Looking back on those years I believe I missed the opportunity to push more learning and less sports.

I'm really wondering if something like I suggest could help salvage math study for other students? Could students learn to do the problems using technology as opposed to learning to manually do calculations? It seems we need a major course correction to avoided the huge fallout we see now in math study. The "I'm not smart"enough factor would be taken out of the equation if all students had the same technological assistance. More like learning levels in a video game than working through 1000's of problems on their own. This is merely one suggestion to change the system and I'm curious what folks think about it. My buddy Roger Schank, a math major himself, has many ideas I seem unable to disagree with.

Paul

You are certainly to be commended, Paul, for your interest in this subject, your analysis, and your efforts on behalf of your son.

But if you expect your children to get an education in the American public school system, especially in regards to mathematics - forget it. The only ones who get educated are those who take it upon themselves.

I'm not an educator and not really qualified to answer the question: "What kind of mathematics education should a general student receive." As far as "how to input the correct formula format into the magic box and come up with an answer." there are plenty of Apps to do that and will be even more in the future and one doesn't have to understand any mathematics to use them.

But let's say instead that you and your son want to learn about mathematics because of its beauty, because of its long history in our culture, because of its bedrock position in the infrastructure of our civilization - and just for the fun of it.

Then one approach that might be useful to you is to look into the National Association of Math Circles, which has a hands-on, extra-curricular approach to teaching mathematics.

http://www.mathcircles.org/

Another approach might be to explore mathematics with Mathematica, since this is a Mathematica forum. Will this really work? I think it might if the person is curious and has a sincere interest. It is much easier to talk about Mathematica as an educational tool than to actually do it. The thing is to get Mathematica and just try it. Use it to explore SIMPLE things. There are simple things that are nevertheless quite profound. Mathematics is not just calculating numbers, but seeing patterns, creating and manipulating structures, proving or at least convincing yourself of things, creating informative representations of things, seeing how one thing changes with another thing. Another trick is not to just calculate but to also write about what you're doing - which you can do with Mathematica notebooks. Don't produce just a number but a short essay or tutorial on what you're learning. Then you or your son would have something substantial to show for your efforts. You might even publish a book from it!

I should also mention that you can get plenty of help through the various Mathematica forums.

So, that's my two-cents.