Teaching Kids to Love Math

Where would we go to find a real-world example of mathematics being taught in the correct order to elementary-age pupils? There are many different schools (and many different settings for learning outside school) in many different countries. What is a good place to look for examples of demonstrably successful practice?

AFTER EDIT: Thanks for the reply. The thing I would want to look at in such intervention studies is how the teaching effectiveness is measured.

AFTER FURTHER EDIT: Oh, I see the video "Teaching Math Without Words, A Visual Approach to learning Math from MIND Research Institute" is one I have watched before, and have discussed among other mathematics teachers. Similarly, the publication Mathematics Teaching in the Middle School is a publication I subscribe to as a member of NCTM. I should start out in my reaction to both of these links you've kindly shared by pointing out that my own bent in thinking about mathematics is to think visually, and indeed that is why I like Sawyer's book Vision in Elementary Mathematics (which leads off my longer reply in this thread) so well.

But although I like visual approaches to teaching mathematics very well, and use them in the mathematics classes I teach, I also like studies of educational interventions to check results. So far, I can't find a publication by independent researchers (after searching Google Scholar and the new Microsoft Academic Search) that verifies the educational effectiveness claims made in the video for the proprietary intervention described there. The company's own website

http://www.mindresearch.net/cont/research/re_publications.ph...

provides only a very sparse set of links to published research on the issue.

Plainly, a more visual approach along the lines of the typical school textbooks used in Taiwan, Singapore, and Japan would be a better presentation of mathematics content than is found in typical United States textbooks. That should be possible to deliver without any computers at all, as it was delivered to pupils in Taiwan in my wife's generation, when Taiwan was still a poor, Third World country.

The popular books by mathematician Ian Stewart

http://www.amazon.com/s/ref=ntt_athr_dp_sr_1?_encoding=UTF8&...

are very interesting and mathematically accurate. Some readers also like the books by Keith Devlin,

http://www.amazon.com/Keith-Devlin/e/B000APRPC6/ref=ntt_athr...

one of which I am reading right now.

I like almost every book by John Stillwell

http://www.amazon.com/John-Stillwell/e/B001IQWNS2/ref=ntt_at...

and especially recommend the latest edition of Mathematics and Its History

http://www.amazon.com/Mathematics-Its-History-Undergraduate-...

as a book you should try to obtain from a library to see what a book with challenging, interesting, but accessible problems looks like.

Many people like the videos that feature Edward Burger

http://www.thegreatcourses.com/tgc/professors/professor_deta...

or Arthur Benjamin lecturing about math in the Great Courses (Teaching Company) video lecture series, which you may be able to find at a library.

AFTER EDIT: Here is a link for Calculus Made Easy, a book recommended by another participant here.

http://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/d...

A good introduction to math would turn a person's innate interest in thinking and logic into an interest in math. After all, at its base, math is really just a way to approach logic in an organized and systematic fashion. I think at least a basic understanding of some more abstract math--especially formal logic--is as valuable to a well-rounded person as an appreciation of literature or knowledge of basic history. Sure, the basic person on the street doesn't need to be an expert on algebraic topology, but they don't need to be experts on romantic literature or 17th century Belgian history either. This doesn't mean that they shouldn't be well versed in some--and probably a fair bit--of literature and history, and, in the same way, they should be well versed in at least basic mathematics.

Now, one of the problems with math education is that what they teach is not really basic math. Rather, they teach subjects that are readily applicable at a fairly superficial level. I think a good grounding in formal logic and set theory, for example, is far more valuable in general than a thorough understanding of differential calculus. And yet it's the latter that is considered basic and widely taught, probably because it is immediately useful to engineers and physicists.

Oh, this is so wrong. Did you like Avatar? Then you like math. Avatar is one long, beautiful mathematical expression, from beginning to end.

> This is like trying to become smarter by listening to classical music.

Granted the problem with the basic idea, this has it all over trying to become smarter by listening to Country & Western music.

> Is it ironic that those suggesting these ideas can't separate correlation from causation?

Math is neither a cause nor an effect -- it is both.

I could argue this point in detail, but instead I will get Bertrand Russell argue it for me: "Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry."

Richard Feynman said, "To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature."

I can't think of a place that equals America for complete and willful misunderstanding of mathematics.