My colleague Ralph Raimi is witty, acerbic and wise about many things, but particularly about mathematics education. A little time spent browsing around his web page will reap ample rewards in the form of both entertainment and edification. Today I’d like to share a little passage he sent me by email:
I have never tried to count the times I have read a newspaper article explaining that students are bored with math that has no visible practical application, and follows with an example of a teacher, or club, that rectifies the situation in some novel and engaging way.
In the present case a class has built a sculpture that resembles a graph of a modulated wave motion. Of all the practical, real-world
applications of mathematics! It is as practical as a snowman.Why doesn’t anyone ask for real-world applications of table tennis? What a bore any game must be, that has no real-world application! Why do kids stand for it? Ping-pong again? Ugh.
But I can think of something: Let’s all make a model of a ping-pong ball in the school yard, seventy feet high, blocking all the entrances and thus preventing all us students from entering the (ugh) school. Then we can take our fishing poles and torn straw hats out from under our beds and, with the hats on our heads and fishing poles over our shoulders, all traipse together down the dusty road to Norman Rockwell’s house.
I think the analogy between math education and tennis is not a good one. For one thing, math is compulsory and tennis is a hobby. Hobbies do not have to have a real world application, their only requirement is that to give pleasure.
This reminds me of initiatives to get kids interested in taking sciences by making the subject “exciting”, usually prompted by an apparent shortage of chemists / math teachers / physicists. Somebody tours round schools with a “flash bang” show, and everyone gets inspired. For some reason, there is not a travelling accountants show, to inspire kids in accountancy. Yet somehow, we have enough accountants. They do get paid rather more than scientists, wonder if that could have something to do with it?
I personally don’t understand how anyone can not find science exciting, just as it is. What could be more exciting than getting to understand things? For some, math seems to press these buttons.
Having said that, I think the teaching profession should continue to try to get and keep kids, and adults, engaged. The problem is that education tries to do 2 jobs: train future mayh / science professionals, and teach utility to the rest. Everyone in todays world should understand some basic arithmetic, just to get by. Nearly everyone will benefit from some more, to enable some undersanding of statistics, risks etc. Many will probably not get much benefit from calculus, geometry etc. I think most would gain more from a basic logic course.
How about ending compulsory math after primary level, and “devolving” the rest into other subjects? Math would still be available as an option. This would require math teachers to liaise closely with subject teachers, and turn much of their teaching into a “service” for other subjects. I can’t see it being popular with math teachers.
I agree with Harold’s sentiment. I think mathematicians have a projection bias when they bemoan that “Kids don’t appreciate math like I do, if only we could connect with them the right way!” By no means is this limited to mathematics – I personally wonder why more people don’t read Steven Landsburg – but I then go on to concede that most people wouldn’t ever gain an appreciation for his work regardless of what font it was printed in.
One recoils in horror alongside Profs. Landsburg and Raimi at most examples of educators (usually not genuine mathematicians) trying to make mathematics “accessible” or “fun” or “exciting.” If any of them–group projects! paper-mache models! applications to pop music or sports!–had been the common mode of teaching mathematics when I was a child, rather than the traditional–here is a list of axioms, let’s show you some proofs of the most important corollaries, now you go prove or disprove this list of theorems–I might never have learned mathematics, rather than spending a few decades in pursuit of honing my skill in it.
So I’m prepared to argue that discarding the traditional approach to teaching mathematics would likely greatly reduce the already small percentage of students who ever become genuinely adept at mathematics.
But what about the rest? Not all of them are congenitally stupid. Do they just lack the math gene (or, more likely, that constellation of genetic and environmental factors that permits learning of real mathematics)? Perhaps and, if so, we should just stop torturing them with more than elementary mathematics. But perhaps there is a way to provide genuine understanding of something more to a larger group of students? While I would not bet on it, the uncertainty is enough to prevent me from condemning all of these experiments (as long as they are alternatives, rather than substitutes, for the proven way to teach mathematics to those who can learn it).
Well as Tahsin pointed out. Maths is usually required and table tennis isn’t. I’m pretty sure that making table tennis compulsory would have made pretty much every kid that isn’t already doing table tennis annoyed (some prefer maths, some prefer swimming etc etc).
If maths wasn’t required up until a certain point we might have fewer engineers for example which would probably be a problem (Yes, I’m assuming we don’t have too many engineers at the moment). If we had fewer people involved in table tennis, well then we’d have fewer people involved in table tennis.
Yes the sculpture project is a pretty useless application of mathematics especially as applications of mathematics go but the real question is weather or not it stimulates interest (that was the intent). I’d guess it doesn’t but then again I’d also guess that everyone was interested in mathematics if I didn’t have evidence to the contrary. In any case I feel like giving the teach at least a little credit for trying.
Here’s the thing. Math is interesting to DO. Wedderburn’s theorem or the Lebesgue Dominated Convergence are interesting to prove but as statements of fact they are pretty dull. That will always limit the demand for mathematical education. The interesting statements of fact — such as the 4 colour theorem, Whitney’s embedding theorem, indepence of the axiom of choice – are too hard to prove so in a popular account it just comes across as a dictum from on high.
Want to make Math palatable? Add a sister course or a lab class to the math curriculum starting around the 9th grade.
Base it on the scheme programming language and use the textbook How to Design Programs.
Here’s the preface.
http://www.htdp.org/2003-09-26/Book/curriculum-Z-H-2.html
It’s like the SICP book but for a younger less experienced audience.
It also beats the heck out of the AP Computer Science course in terms of fun and concepts taught.
@Andrew de Andrade
Scheme is an excellent teaching language and SICP probably is the finest computer science textbook ever written. But, based on personal experience, I fear that they will excite almost exactly the same set of students who already love classical math instruction. You might as well offer them Haskell instruction.
So by all means, do it. But don’t expect this to move many students even from the intelligent-but-unexcited-by-math category to the excited-by-real-mathematics category.
First of all I am immediately suspect of a teacher who thinks kids are clamoring into school (or anywhere else) to play ping pong. Is this guy straight out of the Nixon administration?
The Nixon reference actually makes a good segway. Look at the heroes and role models we put forward back then. Educated men like Kissinger. Back then our leaders were on the cutting edge, even if that edge was ping pong, it was also putting men on the moon.
Today we have politicians lamenting that we have a constitutional scholar in the white house, and gutting the education system in Texas with such gems as “The intellectuals have had their turn now it’s our time to set the agenda”.
I think the real question regarding this letter’s complaint (that kids are being enticed into math with crazy schemes) is if they work or not?
Aeternatis has the right of it, so long as these programs supplement a standard curriculum and not replace it it is just casting a larger net. And if it makes a few elderly teachers feel even more out of touch with the world, to the point that they would complain about new forms of engaging children in education without addressing the new methods efficacy, then I’m willing to make that sacrifice.
Seriously, this guy sounds like the quote from a 1915 teacher’s convention. Some teacher was upset that the schools would be installing pencil sharpeners because the kids might forget how to whittle a point on their pencils.
The way to make math fun like ping-pong is fun is to make it competitive. I enjoyed learning my multiplication tables because my mother, teaching them to a large group of children (me, my siblings, and a number of neighborhood kids), made it competitive; we raced to solve problems, we won prizes, etc.
Kids don’t like ping-pong because it’s inherently beautiful, they like it because it’s a competitive game. If you make math competitive, kids will enjoy it more. Except the ones who are bad at it, like the ones who are bad at ping-pong, won’t want to play. Like I don’t want to play ping-pong. And therein, probably, lies the problem…