December 16, 2002
One Hundred Interesting Math Calculations
My kids--both The-Nine-Year-Old and The-Twelve-Year-Old--get the payoff from reading immediately. But they don't immediately get the payoff from math. I'm going to have to convince them that the payoff from math is there and is interesting, or else I'll have failed as a parent, and their future opportunities will be much smaller than they might have been.
So now I'm getting ready to begin this task. I'll start for real over Christmas vacation...
My User-Editable Interesting Math Calculations Page.
Posted by DeLong at December 16, 2002 02:50 PM
The reason reading makes sense to them and the reason math doesn't is that reading stories is FUN, but doing math problems is NOT. Gotta find a way to make math FUN.
Kids love to compete. Get competitions going with math, multiplication tables, division tables etc as the basis. Use the 'puter as well.
Figure out what the boys like and then work'em over hard with that as the incentive. Money, in small denominations, would be a fine reward.
I myself was absolute hell on multiplication tables in 3's and 7's in second grade 'cause of football. the scores were always in multiples and combinations of 3 and 7, with an occasional safety thrown in for fun.
Let me "go out on one leg" and say that if sociologists are right, the mere fact that you would spend time on maths with them, will get them more involved.
The rule of thumb would be: what you care about in front of them, they care about in your back... (which in turn is supposed to explain a large part of why educated people have educated children, musicians breed musicians, university professors... etc.)
It's perhaps a cultural thing, but I don't think we need to turn everything into a hyper-exciting game, maths are maths and they should be enjoyed for what they are. Their "hardness" is, in a way, part of the fun. They're natural brain-teasers.
Work through some of the examples from Pleasures of Counting with them. It's absolutely on target for what you're writing about.
Finding the source of cholera in Victorian London, deciding whether ships should sail singly or in convoys to avoid subs, breaking Enigma, determining the optimum size of a blood vessel. And much, much more, all told as stories, which should suit your literary-minded children.
Don't let them read this webpage until you've corrected "they're" to "their" above and relax. You can pick up maths at any age if you need to.
My brother the math professor often prefaces classes by stating, "This should be simple. It's the only class you're ever gonna take in which all of the rules are explained in detail before the work begins, there are no exceptions or irregular forms or idioms to memorize, and the rules always work the way I will teach them to you."
Dunno if this helps, but it seemed to help his students, he reports.
Consider lifting a least two calculations from "Innumeracy" by John Allen Paulos: how bad is the news that you have tested positively for a desease if the desease is rare and the testing procedure is subject to error; and how likely is it that with each of your breaths, you inhale at least one molecule of air that came out of Cesar's breathing "Et tu, Brutus"?
The HIV testing is done very badly.
Even though there are two separate tests (ELISA and Western Blot) run before reporting a "positive" result, there's serial correlation in the errors (false ELISA's and false Western Blots are highly correlated) . . . . . so the odds of a person with a positive test result actually having HIV can range anywhere from only 10% at the low end and are rarely higher than 80% or so, depending on the assumptions.
good data here:
I think the most fun I ever had with math, and I'm not a big math person was with an elective HS Math class I had. The class was Surveying Math... effectively applied Trig. Being able to use the math for something makes it much more interesting.
Our final project was trying to measure the distance between two poles on the other side of the river from our side. :)
Oh, and here's another entry for 'interesting math calculations'.
How many vampires in Sunndale?
The American Museum of Natural History has a wonderful Einstein exhibit that should give you all sorts of ideas about how visualize what Einstein was about and how to relate what is visualized to mathematics. The images should be accessible to both your children, though the older will "see" considerably more.
The exhibit is wonderful, but the web site is quite nice as well. Also, a follow could be "One, Two, Three, Infinity."
Just finished discussing a Rhodes Scholarship application for next year with a terrific student. Not really a math bone about this student, but math is handles when necessary.
My other half is at the top of a branch of medicine. Yet, again, not a math bone about.
There are all sorts of wonderful things to know, some of which directly involve math and some of which do not. Imagine being a good father if the children decide to be non-mathematical painters or novelists or my dear my dear non-mathematical lawyers.
Poor Dear Brad worrying about whether superb children may be a trifle more literary than numerical....
Here's another vote for applied trigonometry--I did not why my teachers were forcing me to learn such pointless stuff until I saw a TV special on the mapping of India--the survey towers built every hundred miles with glorified protractors on top; the measurements telegraphed back to Delhil; the simple calculations to give you the height of the Himalayas...
This is going to sound cynical and dark, but don't try to make math fun. It isn't. Even people whose lives revolve around various forms of math don't do it for fun. Better an ugly truth than an obvious lie. Math shouldn't be any more difficult than necessary, but never pretend something is fun. Children know when you're BS'ing them.
I had some luck with male students - my students were usually in their early teens - with an appeal to personal power. Math is power. It's power over your own life and over other people. It lets you understand why things happen and tells you what to do about it. It's magic - in the dark, sensual, almost evil sense. That's why grown-ups do math - not for fun but for insight and for the power insight gives them.
That approach sometimes worked with boys, sometimes not. It almost always worked for my language students but sometimes it didn't work with math. Language is power seems to be a more obvious equation than math is power.
With girls, I never had to make such blunt points. All I ever needed to show was that math lead to insight. Girls in their early teens always seemed to get the relationship between insight and power without help.
Either way, the best way to get to children is to enter into a conspiracy with them, usually against their parents, teachers or grown-ups in general. Letting them in on what seems like one of the secrets of adulthood is a remarkable motivator.
Several days ago, I heard Margaret Chou mention that a young Chinese girl had written a letter about her to a San Francisco paper. The girl claimed to be ashamed of possibly the only Asian-American female comic. "Should have been a violinist, laughed Ms. Chou." I am glad she is a comic.
I love math and enjoy the suggestions given, but I imagine the kids will do fine simply because you expose them so well to different fields even if they are swept ever so far from math lands.
'This is going to sound cynical and dark, but don't try to make math fun. It isn't.'
As a math major, I can say this is kraaaaaaazy talk. It's no less fun than, say, obsessing about football.
Here's a list of mathematical techniques that I found to be deep magic as a kid. I call these deep magic because they are high-leverage tricks: once you know them you can learn much more from the data than someone who does not. Most of these should be accessible to a kid who knows algebra, if you do some handholding.
- Solving systems of linear equations
I loved solving these. Taking some interdependent equations and solving them
- Linear regression.
Taking data and *creating* an equation for it makes a kid feel really powerful, because you've just shown him how to generalize from the data.
- Interest rates and net-present value computations
This is the basis of *all* strategic thinking.
- Boolean logic
This has two nice benefits. First, it is good preparation for dealing with computers. Second, you can easily motivate it with brain teasers.
- Newton's method
Even if your kids aren't doing calculus yet, they will get a big kick out of being able to compute the decimal expansion of square roots and cube roots.
When I was a teenager, I had fun constructing magic squares and doing calculations in number systems with a base other than 10.
I agree with Anarchus that fun is a motivator, but I think parents need to evaluation their own kid's situation to decide whether competition is a good source of fun in learning. The younger one may be at a disadvantage, while the older one may be in for a shock when, after wholloping Jr for a few months and getting used to winning, he discovers human frailty at the hands of somebody his own intellectual size.
Perhaps what we need is a long list of terrible errors that could have been avoided with math. Then, we (the kids) get to be right vs somebody else's wrong, without making it an outright competition. It also not-so-subtly shows the virtue of using math to test ideas before spending your lunchmoney on them. Kids love screw-ups.
Nobody has mentioned rulers and protractors. Kids the age of yours may already be doing geometry. If not, they certainly will have to. It is a step toward trig, it involves ratios, ... lots of virtuous stuff. At the same time, it has a more physical "feel" to it than working only with equations. I also like the simultaneous equations notion above. It is so satisfying to whittle down a pile of unknowns into certainty. Like reading to wee ones to teach them the joy of books, finding something that has a satisfying feel of accomplishment (contructing a nest of pentagons, finding out what X is equal to) is likely to lead to a willingness to try the next mathematical thing.
I await the results of your experiment. I have two of my own - girls 4 and 5. In this culture, I hear girls and math can be a troubled mixture.
Math isn't fun, even for those who practice it? Perhaps for some, but many people find it enjoyable, without having power trips. Here's a test: would you think it cool if you could prove that there IS NO LARGEST prime number, and that you could even prove this to your friends and colleagues?
Here's how it goes: first, you have to remember that all numbers have a single possible factorization into prime numbers, like 6 = 3*2, 12 = 3*2*2 and 17 = 17. Now suppose there is a largest prime number, call it Pm. Take the product of all the prime numbers up to Pm, and then add 1. That is:
N = 2*3*5*7*11*13*....*Pm + 1
According to our assumption N cannot be prime, because Pm is the largest prime and N > Pm. But if you divide N by any of the primes, you get a remainder of 1, so it cannot be factored into primes. We've got a contradiction, and the only resolution is that there isn't a largest prime number.
You might not find that fun, but you cannot convince me that I don't enjoy that.
I didn't really get the payoff from math until advanced college math classes. Up till then is just "you gotta do it till you're through it so you better get to it."
Sorry, will try to close that link.