So... I spent the first 10 years of my life in India going through its education system and am currently a mathematics major at Caltech. From my experience, the Indian education system is heavily geared towards attaining high average output. The education system in the US is much more laissez-fair in this regard. It allows students to adjust to their needs and capabilities. Neither system is perfect. In the Indian system, the exceptionally smart students get shafted because they are bogged down by the rigid and usually rote curriculum. For the average person, arithmetic is sufficient but for an advanced major, giving them problems is crushing (I speak from personal experience). The complete lack of intellectual stimulus is very counterproductive. On the other hand, in the US system, a large portion of the students slack off and fail to use their opportunities. Going through the US education system has put me years ahead of where I would have been if I was still in India but along the way, I have seen many students miss out and just sit on the sidelines. [1]
This startup can be immensely helpful but please, don't see this as a begin and end all for mathematics education. If a student is capably of grasping the axiomatic principles of mathematics, such a learning path is infinitely preferable to the do-lots-of-problems method. [2]
[1] This is pretty much the exact same gripe that I have with programs like Kumon which give students lots and lots of problems without giving a solid mathematical foundation for why these problems behave as they do. For more information, Lockhart's Lament (http://www.maa.org/devlin/devlin_03_08.html) is an excellent essay written by a mathematician on this topic.
[2] This is not to say that an axiomatic mathematics education is for everybody. For one thing, a student may not be interested or capable of such an education (just like how I am completely incapable of remembering anything). However, for students interested in mathematics, it is the way to go.
For the average person, arithmetic is sufficient but for an advanced major,
giving them problems is crushing (I speak from personal experience).
This is a very insightful observation. I loved mathematics till high school (in India), and solving problems was real fun (with a good understanding of what it was all about). Then i started my engineering (again in India), and was completely put off by the insanity of solving only problems without much thinking and appreciating the beauty and underlying principles.
I was also startled a bit by the following statement in the article:
Math homework in India consists of math problems that students work through, as opposed to the United States,
where homework is heavy on reading about math topics in a textbook.
To me, it's almost impossible to think of basic math without problem solving. May be it's only me, but the real 'fun' is not complete without it, and i daresay it is not the greatest strategy of attracting inquisitive kids to it.
For some reason, American kids seem to be willing to put in the work with athletics,
but not put it in with the one subject that’s going to matter more to their lives than any other activity.
Honestly, even i would prefer my kid to put more work in athletics if (s)he can handle the money and understand the way around converting measurement units. :-). I can't think of anything else i use it for these days.
I think an example of the failures of rote learning is a simple math problem.
An army is marching down a road at Xmph and stretches out 1 mile in length. An officer at the rear of the army notices a problem. How long does it take him to get to the front of the line traveling at Ymph and how many minutes does it take him to do the round trip?
Now, if you hand this to a bunch of collage students who have not seen it before a surprisingly small fraction is going to be able to do it quickly and they are not generally the ones who think of math a series of steps from problem to solution.
I totally disagree with this! It isn't a fault of the curriculum, it's the fault of your teachers. I had my entire HS/college education in India. And if I may say so, I would put myself in the "exceptional" category as well: I was in the international math olympiad, and rarely scored less than 100% in school tests.
Anyway, I found the math classes thoroughly enjoyable. The teachers pretty much let me do whatever I wanted as long as I didn't disrupt the class. I'd usually be a few chapters ahead, or helping out the kid next to me, or something like that. Very often, the curriculum was challenging even for me. We had Fermat's infinite descent in the eighth grade! I distinctly remember ruler and compass construction problems in my ninth grade that I'd have great trouble solving even now.
The good thing was, the super-hard parts that I've mentioned were all optional and were never on the exams. It worked out perfectly -- students who were both smarter than average and self-motivated would spend most of our time on those parts. My teachers were happy to answer my questions about that stuff after class, even though it was irrelevant as far as our grades were concerned.
One teacher in particular was amazing. She rewarded outside-the-box thinking, and if there was more than one way to solve a problem, she let us present them all. She acknowledged when she was wrong. Damn, writing this has made me all nostalgic and want to find her and thank her :-)
One time, I was working through a textbook that was two or three grade levels ahead. I had a question that she couldn't answer right away. She went home, did her research, and helped me out the next day. How awesome is that?
We had one horrendously bad teacher. They fired her after two months.
Some other great memories.. we all learned to program in the fifth grade. That was tons of fun. A computer cost more than a building back then in India :-) Vector calculus in the ninth grade. And so on.
Of course, everything except math and science was a disaster, but there's no way there was anything wrong with the math curriculum. I'm quite aware that 90% of my friends at other schools had completely unmotivated teachers, but again, not a fault of the curriculum.
I agree with the point that the teachers make a huge difference, especially in the formative years. (Not only in math, but all subjects).
I distinctly remember a few who made subjects like Sanskrit, Organic Chemistry, History (that itself is interesting in any case) appeal much more, and never let the curriculum dictate or slow down the learning process of fast moving kids.
You're right, being good at arithmetic isn't a substitute for training in axiomatic mathematics (for someone who is interested in math). Programs like this are about making sure everyone can make change without a calculator & and do back-of-the-envelope estimations, rather than training Putnam winners or even breeding more math majors.
I would recommend an India like system if your daughter is deficient in mathematics. Also, mathematics is unique in that it deals with absolutes. It starts with some axioms and places everything else on top with irrefutable proofs along the way. Its not for everybody (even though I would like to think that most people can enjoy the beauty of the subject). I also have several friends who are brilliant but run away from mathematics like it was the plague. There's nothing really wrong with this unless it affects their success in their own field/life/career etc..
Maybe you daughter just isn't very fond of arithmetic (what most high schools teach). An introductory book on some axiomatic branch of mathematics may be useful in that case.
I agree. Though even with the axiomatic approach I have to do a lot of problems to really understand. Of course the problems are mostly of the type "Prove that lemma" or "Find out whether that proposition is true and prove your answer".
This startup can be immensely helpful but please, don't see this as a begin and end all for mathematics education. If a student is capably of grasping the axiomatic principles of mathematics, such a learning path is infinitely preferable to the do-lots-of-problems method. [2]
[1] This is pretty much the exact same gripe that I have with programs like Kumon which give students lots and lots of problems without giving a solid mathematical foundation for why these problems behave as they do. For more information, Lockhart's Lament (http://www.maa.org/devlin/devlin_03_08.html) is an excellent essay written by a mathematician on this topic.
[2] This is not to say that an axiomatic mathematics education is for everybody. For one thing, a student may not be interested or capable of such an education (just like how I am completely incapable of remembering anything). However, for students interested in mathematics, it is the way to go.