How do I nurture a 15-year-old's interest in mathematics?

November 29, 2006 6:06 PM

How do I nurture a 15-year-old's interest in mathematics?

My girlfriend's 15-yr-old daughter shows some interest in math. She is getting A's in algebra (and all other classes) and she loves doing sudoku. How can I help cultivate her mathematical interest? Her other interest is music (she's a fantastic pianist). I'm thinking in terms of a Christmas gift; price is not really a concern. Books? DVDs? Other? Something fun, not intimidating.

Some books I'm aware of: Flatland, Conway's The Book of Numbers, Singh's The Code Book, and the Erdos biography.

posted by neuron to education (34 comments total)

Maybe a DVD of the first or second season of Numb3rs. I love that show - it's a really smart program that shows the real world applicability of various concepts in mathematics. I swear for an hour after the show each week I want to become a mathematician.
posted by jourman2 at 6:16 PM on November 29, 2006

Martin Gardner's recreational math books have nurtured many a young mathematical mind. They're fun, but a bit advanced. A 15-year-old might find them too trying unless she is already fairly into math.

The Chicken From Minsk, on the other hand, is very accessible and fun, while still offering plenty of opportunity to discover exciting new things. Definitely appropriate for a 15-year-old.

Archimedes Revenge by Paul Hoffman is another book that I liked as a teenager. It has good stories about mathematicians, not just mathematics.

Hofstadter's GEB and Metamagical Themas were critical in getting me interested in higher math, but like Gardner they are fairly heavy.
posted by mbrubeck at 6:26 PM on November 29, 2006

This one time at math camp...
posted by Pollomacho at 6:48 PM on November 29, 2006

A Beginner's Guide To Constructing The Universe:
The Mathematical Archetypes Of Nature, Art and Science
posted by hortense at 6:51 PM on November 29, 2006

Strong seconding for Martin Gardner's books. They weren't too advanced for me when I was 15, and they opened my eyes to a lot of great concepts.
posted by wanderingmind at 6:56 PM on November 29, 2006

When I was that age math came very easy (and so did music) and I became interested in the fact that music seemed to have patterns just like math - from there I discovered a few Scientific American articles discussing how Pythagoras used music to demonstrate mathematical principles, or how math was used to design a concert hall - blending those two interests kept my attention.

If you don't want to chase down those articles, I would look for a book relating the two topics. On amazon I just found a book called 'The Math Behind the Music' which seems interesting from the reviews.
posted by Wolfster at 7:01 PM on November 29, 2006

Fermat's Enigma is a fascinating and engaging sweep through the history of mathematics, centred on the quest to prove Fermat's Last Theorem. Good for a 15-year old's level of math knowledge, and it really shows the fascinating terrain of advanced math.

Innumeracy is also a great book for making someone glad they know some math and making them want to know more. Lots of fun examples of what math can do in day-to-day life. Remarkably polemical for a book about math, which makes it more fun.
posted by Dasein at 7:07 PM on November 29, 2006

I am a broken record... but I am in love with "The World of Mathematics", James R. Newman. 1988 Microsoft Press paperback version. 133 original papers with interstitial commentary by Newman. Written mid-century last, but just excellent. Find on eBay, Amazon, Powells, etc. Cost for good editions (that I don't buy for gifts!) about $20-25.

A multi-year read for most people, the articles are extremely accessible, cover a huge swath of the field, are foundational, philosophical, more math history and philosophy, all in easy bite-sized little chunks. Love it love it love it.
posted by FauxScot at 7:12 PM on November 29, 2006 [1 favorite]

Deadline is swift approaching for the CTY Talent search, probably one of the best academic experiences of my life.
posted by onalark at 7:12 PM on November 29, 2006

I'm not a mathematician or math historian but I loved "Zero: The Biography of a Dangerous Idea" by Charles Seife.
posted by Science! at 7:13 PM on November 29, 2006

Second Martin Gardner. A talented 15 yr old would be stretched, but rewardingly so.
posted by Neiltupper at 7:16 PM on November 29, 2006

Martin Gardner's books are great for people with a wide variety of math backgrounds. She'll definately get something out of them.

Despite it's title Men of Mathematics may be inspirational for her.

Ugh to Numb3rs, which has as much to do with math as CSI has to do with forensics.
posted by phrontist at 7:18 PM on November 29, 2006

I thought that Sudoku wasn't really math related.
posted by Memo at 7:20 PM on November 29, 2006

Seconding 'Fermat's Enigma' (in NZ it's titled 'Fermat's Last Theorum'). Really interesting stuff.
posted by Paragon at 7:22 PM on November 29, 2006

I'll second Innumeracy as well as both of Simon Singh's books that are recommended above (Fermat's Enigma and The Code Book).

I'd also suggest getting logic puzzle books, which aren't exactly math, but are great at exercising the same area of the brain.

A book that I loved when I was young is Raymond Smullyan's What is the Name of this Book?. Great logic puzzles that start out easy, but get harder and harder.
posted by freshgroundpepper at 7:37 PM on November 29, 2006

Sudoku isn't math in the obvious sense; you could replace the digits with any nine unique tokens, and it would work just the same. But it's a logic puzzle, and that turns out to run back into math by way of set theory and/or boolean algebra.

Second the vote for GEB. To this day, no matter why I find a given topic fascinating, once I begin exploring it I find it's got connections to GEB. I can't even say how much it's influenced me.

And second the Beginner's Guide to Constructing the Universe, which I discovered and loved at just that age. (Thanks, hortense! I didn't know there was a website.) The math was the initial draw, but in the end it was also a huge boon to my cultural and symbolic literacy; it makes frequent excursions into periods of time and currents of thought where the 'two cultures' (science and humanities) are not such strangers to each other.

I also got a lot of jollies, at that age, out of a textbook: Fundamentals of Musical Acoustics. Anyone who gets interested in the technical side of music is going to keep rubbing shoulders with signal analysis (at a minimum, with spectrograms and the Fourier transform). How to turn that into a Christmas present, I'm not sure, but it's something to keep your eyes peeled for.
posted by eritain at 7:41 PM on November 29, 2006

Sudoku isn't about math-math; you could use letters or symbols or anything instead of numbers. What it is about is logic -- not exactly complicated or challenging logic, but still. Would she be interested in logic-related stuff? Monty Hall-esque problems, general probability, programming...?
posted by booksandlibretti at 7:45 PM on November 29, 2006

My math teacher wife's answer, make it relevant to the student's interest...anything can be connected to math.
posted by HuronBob at 8:07 PM on November 29, 2006

I really liked Pickover's The Mathematics of Oz. Many of the (fun) problems are nearly impossible, but the solutions are best part. A lot of math people also like cellular automata; she might be able to have a lot of fun with a simple simulator.
posted by aye at 8:15 PM on November 29, 2006

Mathematics: It's Methods, Content, and Meaning

is the Soviet equivalent of the Newman work. I've always found the Newman work more congenial but ultimately less inspiring than the Alexandrov-Komolgorov-Laurentiev work with its typically-Soviet mix of sweeping rhetoric and attention to problems of industry, but each girl is different.

Men of Mathematics is also excellent in that it humanizes the mathematical profession; Jan Gullberg's From The Birth of Numbers likewise does much to contextualize mathematics (and can serve as a look-ahead at most of the math she'll see pre-university). In fact, if I were buying a gift for someone that age that'd be my first pick, especially if she has any interest in history.
posted by little miss manners at 8:18 PM on November 29, 2006

I'm going to get laughed at for this, but find someone who can teach him Calculus. Calculus was the first branch of mathematics that seemed to me to have any relevance to the real world. It shows, in a few simple rules, how everything relates to each other. Cases in point:

When you apply your car brakes, just as the car stops, you feel a sudden jerk forwards. Why?

Why, when driving, do the trees in the distance appear to be moving slower than those close to the roadside?

Why is the area of a circle Pi * r^2?

Calculus has the answers (and little to no arithmetic to boot) !
posted by Popular Ethics at 9:07 PM on November 29, 2006

Let me be the first to point out to Popular Ethics that the he is a she in this case. That said I agree with the suggestion is she has a sustained interest in the topic and you can find someone to teach her; most of the years after algebra and before calculus are largely wasted on those with mathematical aptitude.
posted by little miss manners at 9:10 PM on November 29, 2006

As for ways to pique her interest, why not a series of real-world challenges with cash prizes? For example plan to build a ball ramp and see if she can predict the ball's landing distance within a few inches. Make it big (like gymnasium big) for extra motivation. Personal contests would plug right into the "tell me I'm special" drive most 15 year olds ache over.
posted by Popular Ethics at 9:14 PM on November 29, 2006

Martin Gardner is the winner here, as far as books go -- some of Isaac Asimov's old books of essays are great, too (fewer puzzles, more lively writing, cover the sciences as well as math.) GEB is fantastic for the right kind of person -- if she likes music, too, I'd definitely recommend it.

MathCamp is a fantastic program -- very high-powered group of students, though, so she should try the qualifying quiz and see if she's ready. If not, lots of people swear by CTY.

In defense of Numb3rs, which I used to consult for: I think that given the constraints they're subject to (i.e. the conventions of a fifty-minute cop show) they do a very good job of getting some mathematics in each episode and making it as honest as possible.
posted by escabeche at 9:46 PM on November 29, 2006

I'm a math graduate student. My first real introduction to the world of higher mathematics was Fermat's Enigma. It has some real math in it that is understandable to a 15-year-old, and it has allusions to much more complicated mathematics as well. Also, it relates lots of interesting anecdotes about mathematicians who worked on the problem over the last 350 years or so. I read it in a day and loved it when I was 17.

Also, I'd like to exercise veto power over Numb3rs. For fuck's sake, it has a 3 in the word. Numb3rs might be good for getting somebody interested in math in the first place, but it sounds like your friend's daughter already has that. You should give her something that has mathematical content, not just style. Please, don't give her Numb3rs.
posted by number9dream at 10:01 PM on November 29, 2006

Martin Gardner, yes. Also Clifford Pickover.

Imagining Numbers, Especially the Square Root of -13, by Barry Mazur is very fun, an accessible introduction to the part of math called number theory.

Here are some suggestions for FUN:
A subscription to Games magazine, which has a great range of puzzles (logic and math and word and visual) in a range of difficulties every month. There's bound to be something every month that she'll enjoy, and the magazine makes it easy to work up to harder puzzles.

If she has someone to play with, a board game that is not chance-based would be great. Here are the first three that came to mind:
- Quarto is a quick, logic-intensive 2-player game. Super-easy rules, but always a mental challenge; plays in 1-15 minutes.
- Through the Desert is a more-complex game where you are placing camels in caravans to try to score the maximum points; the board set-up changes every time you play so it's always a new experience. Through the Desert is for 2-5 players and plays in about 30 minutes; very fun, cute pieces, easy to get started.
- On the more difficult side, Puerto Rico is a great, strategic game for 3-5 players that plays in about an hour and a half once you understand the rules. The rules are a bit tricky the first time through, but once you play, they become clearer.
- (If you think she might like a game, but these don't appeal, I'm happy to recommend others -- especially if she has some specific interest like ancient Egypt, there are games that have themes that might fit.)

Finally, show her the mathematician riding this square-wheeled bike smoothly on a specially-designed surface. So cool! Every mathematician gets one*!

*Ok, that's a lie. But we have to dream big when we're teenagers.
posted by LobsterMitten at 11:24 PM on November 29, 2006

Another vote for Godel, Escher, Bach.

I'd also recommend Surreal Numbers, a fable about two ordinary folks (non-mathematicians) stranded on a desert island who discover stone tablets with the beginnings of a new number system (Conway Numbers) and derive the rest.

And this pamphlet by Britney Gallivan who became the first person to fold paper in half twelve times while in high school.
posted by zanni at 3:17 AM on November 30, 2006

She might like to learn some computer programming that would let her develop mathematically. For example yesterday I saw Levitated - a site with a large number of examples of Flash programs that are fascinating and are provided with open source.
posted by rongorongo at 3:30 AM on November 30, 2006

Godel, Escher, Bach in small doses. It's a very challenging read for a high school kid.

I liked the Smullyan Books around that age, but they revolve pretty strictly around logic.

Stephen Wolfram put together and interesting book about modeling natural phenomena that looked pretty good.
posted by plinth at 5:13 AM on November 30, 2006

I'm the author of one of the books mentioned in the thread.

Practical advice: I think that some of the books mentioned are great -- you know about Abbott's Flatland and Hoffman's The Man Who Loved Only Numbers; I think Paulos' Innumeracy, some of Pickover's work, and (*cough*) mine might appeal without being too intimidating. But don't limit yourself to math literature.

You might want to try to spend some effort trying to get her interested in physics -- as a 10th grader she'll have to decide soon whether to continue her science education or drop it. If you pique her interest in the physical sciences, you would be doing a great deal for her mathematical development in the long term. Feynman's Surely You're Joking Mr. Feynman and Gamow's Mr. Tompkins series come to mind immediately.

Less practical advice: one of the big problems with high-school math is that almost nothing that's taught has any real relationship to mathematics -- the beautiful stuff that mathematicians do. Algebra, trig, precalculus, etc., are all tools that mathematicians need to acquire before they get into the fun stuff, which begins with calculus and continues through college and grad school. The only elements in the high-school sequence that capture the spirit of what mathematicians do are proofs in geometry and symbolic logic. (And I've heard complaints that the former is getting less and less time while the latter is disappearing altogether.)

I'd caution against rushing through to calculus, though. If she's taught outside of class, she'll be terribly bored when she takes calculus in school for credit. If she accelerates through the sequence in school, unless the high school is exceptionally good and offers solid post-calculus courses, she'll spin her wheels during her senior year with nothing to do -- and I've seen this kill people's interest.

Instead, if you want to bolster her math knowledge, I'd supplement what she's learned with some of the things that have disappeared from the standard curriculum: walk her deeper through Euclid's elements than she's done in class; have her puzzle over straightedge-and-compass constructions; teach her logic proofs and have her think about logical and rhetorical fallacies.

But above all, try to steer her to teachers who see the beauty of mathematics. With a mundane teacher, even the most profound and lovely mathematics can seem dry and boring. Conversely, I know lots of physicists and mathematicians who can point to a high-school teacher whose love of the subject got them started on their career paths.

Good luck.
posted by cgs06 at 5:42 AM on November 30, 2006

Couple more books:
Tom Körner - The Pleasures of Counting - this guy was by far the most entertaining lecturer when I was doing maths at Cambridge, and this book has lots of interesting anecdotes. There's a fair bit of maths, but mostly using fairly basic techniques cleverly, rather than heavy-duty theory. I'm sure there'd be something in there for a smart 15 year old - there's stuff on everything from cholera epidemics to Enigma machines.

Rudy Rucker - Infinity and The Mind. Rucker has a great knack for describing some of the more mind-breaking parts of maths, and I think this is one of his best. You could also try The Fourth Dimension and how to get there which I remember enjoying.
posted by crocomancer at 6:01 AM on November 30, 2006

Another for GED, but buy two copies if you haven't read it and read it with her. There's nothing a smart 15 year old can't understand in it, but some of the ideas are pretty big. She might like to have someone to bounce questions off of.
posted by miniape at 6:38 AM on November 30, 2006

Try the last two volumes (VI & VII) of The Contest Problem Book, each a collection of the previous six years of contests sponsored by the Mathematical Association of America and given in high schools throughout the country.

Solving the problems almost always involves a step of understanding beyond routine application of formulae, and many actually disclose something of the beauty of mathematics. None of them are mathematical drudgery. If she gets good enough...who knows; winners used to get full rides at Harvard.

Being able to solve these problems is very satisfying. Lots of them involve very useful sophisticated elegant tricks she'll resort to for the rest of her life, and are often beyond the ken of the average high school math teacher. If you go this way, please make sure she understands that these problems are very challenging at their hardest, and that almost no one in high school will be able to do them all without assistance.

I have big, big reservations about GEB. It's full of metaphors, connections, teaching stories and dazzlingly hyperbolic appreciations, but the actual mathematics is not there. It's like a beautifully constructed stable full of straw and fresh droppings, but pony-free.
posted by jamjam at 1:45 PM on December 1, 2006

Buy her a book on origami. I just found out you can derive the golden ratio from a square piece of paper.

Maybe Finger Math (chisanbop)?
posted by ostranenie at 8:35 PM on December 2, 2006