Wednesday, April 30, 2008

Mathematics in Malaysia (2) - Overemphasis of Practice

Note: This post is adapted from my comment in ReCom, and I think it is an apt continuation of an earlier post.

Math Café IIIFrom my personal experience and brief scanning of math threads in ReCom, I observed that many teachers advocate "practice makes perfect" philosophy in the teaching of mathematics. And as someone who loves maths and wishes to see higher mathematical aptitude in Malaysia, the prevalence of such mentality in our schools disturbs me profoundly.

Maths is about understanding, logical reasoning, critical analysis and creativity. NOT rote memory and algorithmic drills. Among all our subjects in secondary and primary schools, maths is arguably the subject that requires the highest degree of comprehension. Ironically, among all subjects, it also tends to be the subject where the most number of teachers give their students a daily drill of "do more practise and you should do better in it", instead of "think and learn more about it to understand it better".

Now, I fully understand and empathize that not everyone is able to fully understand all mathematical concepts taught in school, as each and every one of us are born with unequal talents in different fields. You may be a fine artist but flunk your math tests on a regular basis; I may ace math tests but draw like crap. So in this regard, I understand that it's indeed necessary for teachers to make practice an essential component in mathematical education, as it is indeed the easier, if not the only way for many people to do well in maths exams.

mathHowever, I have a feeling that practice has been overemphasized in our schools, to the extent that it has now supplanted understanding which is the essence of mathematics. You often hear people giving advice like "do more, more and even more practice until you are sick of it, and that would be the highest level you could achieve in preparing for maths tests". But you don't often hear, "hey my friend, let's work together to understand what this formula actually mean, why it is true and how it actually works". From my personal experience, when faced with such approach of teaching, many people simply turn it down and say "hey skip the crap, just tell me how to do it from the first step to the last". It seems that understanding is now relegated to something that only Olympiad maths participants should be interested in, the rest of us should aim more at buying more practice books.

Practice is good for SPM exams, this fact nobody can deny. However, when understanding is being increasingly perceived as an unnecessary evil, and practice being supposed to be the most economical approach for good exam scores, I fear that we will do badly when it comes to "real world maths". When you go to university, you would realise that "step by step" and "practice" is no longer relevant - understanding is the key. With years of incessant practice and scarce attention to understanding, I fear that many people, even those who actually have the intellectual capacity in the first place, would have been blunted in their creativity and comprehensive faculty, and consequently face hindrance in their further studies.

I hope that this post doesn't come down as being elitist, but this is something I care deeply about so I would love to hear from others about this.


Anonymous said...

Nothing further to add and to agree -
practice is fine as long as understanding comes first..

- Ming

WP said...

Yup, understanding is the key!

And then just a little practice would be enough...

Alvin Ooi said...

practice and understanding are not mutually exclusive: practice helps one to understand better, esp in Maths.

emphasis on practice is okay if students are aware that understanding is the key while practice is a method to achieve it.

overemphasis that leads students disregard understanding and take short cuts ain't cool.

day-dreamer said...

Oh. My. God.

You've written exactly what I'm going through.

I can't even understand my Calculus... how to practice?

Eric Fu said...

First of all, kudos to Mr Yew who has produced yet another finely written article.

This is actually an ongoing debate in the field of education. Some mathematics educators believe that practice problems are of paramount importance. An example of a group of such educators are Malaysian mathematics teacher (in general). I can readily admit to you that the mathematics education I received during my high school years were tremendously practice-based. There were certain mathematical steps that I hardly understood back then when I forged through a problem.

What I have observed in the United States, however, is the exact opposite. Mathematics instructors here in general place great emphasis on the understanding of the material. This is definitely something laudable. Students are often assessed conceptually in a test. But the problem is, students in the US hardly get the drills. Instructors assign substantially less homework. At the end of the day, the result is that students, thinking that they understand the concepts, fail to solve problems of similar material with a twist within.

Personally, I believe that both understanding and practice are equally important. If possible, mathematics instructors should try their best to balance these components when outlining their syllabi. Germane theorem proofs should not be shunned and cumbersome drilling exercises should not be avoided all together. Exercise moderation to achieve what is the best equilibrial mathematics education.

Wun Min said...

Yay, which is why I can't do my math here. xD

changyang1230 said...

Thanks for your comments. :D

Alvin: Agreed! Practice and understanding are not mutually exclusive. A well-designed practice can go a long way in helping our understanding. However, quite often in Malaysian schools and tuition centres, practice is for the familiarity of formula plugging instead of understanding though. :(

Eric: Heh thanks for your insightful comment. It's interesting to see you say that US has gone just the opposite direction, and ended up having lots of people who can't do questions as well. Tricky indeed, there should be a good balance somewhere. More good teachers like you is a compulsory first step, I say. :D

qisti said...

oh you are so right, mr yew. i think understanding is very very important.

i am ashamed to say I am your typical malaysian that doesnt bother to understand the concept behind mathematical formulae.

May I blame the education system?


akmal said...

I did my phd at claremont graduate university (Los Angeles) in mathematics, and took highest level of mathematics courses.

What you mentioned here is absolutely correct. Training is the key. For serious mathematicians or serious mathematicians wanna-be, you need to perform a lot of reading and exercises, as well as discussions on fundamental issues. Yes you need to do tons of exercises, and yes you need to understand the logical reasons behind everything you do.

School can offer you so much, but the glory details can only be discovered by you.