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Singapore Math

Friday, March 5, 2010

Math is "Nowhere"


To the average math teacher with twenty years of experience (not uncommon with one year teaching experience repeated twenty times), mathematics is probably nowhere other than the four walls of the classroom or within the few hundred pages of the textbook – MATH IS NOWHERE! Not so for the professional mathematician working in the ivory tower, who makes a living out of mathematics – MATH IS NOW HERE!

Like philosophy, mathematics requires hardly any equipment other than pen and paper. You practically need no expensive instruments and laboratories to gain entry or to contribute to the growth of mathematics – except your brain. Indeed, mathematics’s start-up costs are as low as they come.

Suffering from Information Anxiety

Even in an age of easy access to the Internet, math teachers are flooded with an overload of quasi-useless information – the challenge is to filter the relevant and the useful from the mass of plagiarized content input by ego-centric Wikipedians.

In price- and pages-controlled textbooks by the Ministry of Education, Singapore, both publishers and writers have to focus on either context or concept – one can’t have both given a fixed number of pages and the unit price per page that the publisher must abide by. Publishing houses aren’t charitable organizations, nor are writers, volunteers in the business of mathematics education.

Even if the MOE were to relax the rules on the extent and pricing of local textbooks (as is the case in Hong Kong) where publishers and writers would then have the freedom to dictate the price and control the content, there is no guarantee that the new textbooks would be contexts-based. Scapegoating the MOE for numerous restrictions provides an easy way for publishers not to innovate their products, blaming time and price for not producing decent titles.

On the other hand, few would exonerate the MOE, because if they themselves couldn’t produce a decent textbook even with a team of a dozen full-time teachers and consultants, how could these mathematics specialists expect the private sector to better them with a fraction of their resources?

Conceptual Math vs. Contextual Math

For too long, MOE-approved textbooks authors see the teaching of notions and notations more important than revealing the beauty and utility of mathematical concepts. Formulas and worked examples and practice questions are the staple of a local textbook, paying lip service to the recreational or humanizing aspect of the subject. 

Putting mathematics in a context, although desired, is still an option for many authors who find that linking concepts to contexts is hard and time-consuming – you can’t always rely on Wikipedia or on-line free resources to contextualize or humanize your teaching.

What Are They for, Teachers?

Not that there is a dearth of relevant applications to traditional or common topics taught in school mathematics, the problem seems to be a reluctance or indifference or apathy on the parts of Singapore writers and editors to make the most disliked subject in school more interesting.

For example, we'd expect our local textbooks to mention these, but they’re inexistent:

Quadratic equations are depicted on a MacDonald’s logo.
The remainder theorem is applied to electrical circuits.
Matrices are used to store or retrieve large chunks of data.

As math educators (teachers, writers, editors, tutors, …) we haven’t done a good job in promoting mathematics as a discipline that permeates our everyday living – from gizmos to the internet to security to GPS to barcodes. Whether it is on-line booking and sms- or mms-ing, mathematics is everywhere; yet, many of us seem to be unaware or indifferent to how the applications of mathematics affect or inflict our lives.

Many years ago, at an NCTM conference in St. Louis, Missouri, I bought a T-shirt with the words, “MATH IS NOWHERE” printed on it. It reminded me of a booklet I read many moons ago asking the reader to read, “GOD IS NOWHERE”.

Like God, mathematics often seems to have little bearing on the lives of most people – both God and mathematics seem invisible to them. Be in math or religion, our attitude towards it determines whether it is nowhere or now here!


© Yan Kow Cheong, March 4, 2010

Monday, March 1, 2010

Singapore at the IMO

Singapore at the IMO

In Singapore, the average ratio of female to male undergraduates at the university is three to one. Yet those who perform outstandingly are male. Few female undergraduates make it to the Honours class, and very few of them have a doctorate in the subject. In the last fifteen years, only one female Singaporean mathlete had represented Singapore at the International Mathematical Olympiad (IMO); indeed, not a universal anomaly looking at the number of over-represented male mathletes at regional and international math competitions. It almost seems that our local gifted and talented math female students lack the “math gene” to compete regionally and internationally!

Even in local publishing, only recently did we see some female writers experimenting with some school math textbooks. Traditionally, mostly male teachers or tutors have written Singapore textbooks, although increasingly and encouragingly we're seeing more female authors in the assessment (supplementary) math market. In many ways, they're still under-represented considering that up to the university level, females outperform males in most mathematics local examinations.

Singapore's Mediocre Ranking

Why do Mainland Chinese, Vietnamese and Iranian students outshine their Singaporean counterparts at the IMO? One would assume that better coaches, as compared to their counterparts in other developing countries, would provide better training to the six representatives of Singapore; yet, the prevailing situation reveals a different story.

An informal investigation shows that the Singapore Mathematical Society (SMS), the body in charge of coaching high school IMO mathletes, doesn't seem to engage the best local or foreign-born trainers to coach the IMO Singapore team. Everybody seems too busy to put the time and effort to offer their expertise to prepare the best possible IMO local team to compete with the best teams round the world. Apparently, it's not due to a lack of brainpower or finance that is the cause of Singapore's mediocre performance at the IMO every year, but because of the reluctance on the part of some professors to play their social responsibility to the nation.

Singapore – a Deprived Math-Gene Nation!

Skeptics believe that even with the best resources, our small team of talented young mathematicians may not have what it takes to win some gold medals, because the often drill-and-kill educational system and the limited choice to compete in other olympiads doesn't provide them with the conducive milieu to wanting to excel in mathematics competitions.

Local math educators reveal that local talented and gifted students would rather compete in a physics or chemistry olympiad than taking part in a mathematics competition, simply because it's easier to win a medal in these subjects than being an IMO medalist. Paradoxically, there is too much choice for our talented youngsters to compete. The time and effort needed to prepare for an IMO seems to be a key factor in attracting the best brains to represent Singapore at the IMO.

One hypothesis is that developing countries like China, Vietnam and Iran can ill-afford modern laboratories to do research; so their gifted youngsters have little choice but to focus on subjects or disciplines that don't need much equipment and resources. Singapore young scientists and mathematicians, on their part, have much opportunity to interact or work with faculty staff of tertiary institutions - one interesting point here is that faculty members from the physical and social sciences seem more willing to mentor their students than their counterparts from the mathematics department. 

Relaxing IMO Criteria

Perhaps if the IMO relaxes its citizenship criteria, Singapore may do better, because it's no secret that many of the better math students in Singapore come from neighboring countries, such as Malaysia and Indonesia, but they're not eligible to represent their host country at any math competitions. Although raised and schooled in Singapore, their nationalities hinder them from doing Singapore proud, especially when the pool of local gifted math students is infinitesimal. Many of these foreign bright students are dealt a double blow: on one hand, they can't represent their country of birth for political and racial reasons; on the other hand, as non-Singapore citizens, their brilliance prevents them from representing their host country.

Singapore's First IMO Invitation

Singapore was first invited at the IMO by host Australia in the late eighties. Since then, we have only produced few gold medalists. Singapore mathletes continue to disappoint or underperform at Olympiads, despite its relatively high standard of mathematics education, as compared to many developed and developing countries.

After all, it's hardly a coincidence that Singapore was ranked first three consecutive times at the TIMSS (Trends in International Mathematics and Science Study) - it lost its top position to Taiwan at the last TIMSS. Excellent performance at the TIMSS but average at the IMO! Nonetheless, Singapore mathletes have so far performed relatively well in other regional math competitions such as the Australian Mathematics Competition (AMC) and the Pacific Asia, where they'd collected a handful of gold medals, as compared to their other Asian counterparts.

So, what must be done to help Singapore make a significant impact at the IMO? Better coaches or better coaching methods to prepare our local mathletes? What are some of the missing ingredients, which would propel Singapore to the Top Ten in the IMO ranking?

© Yan Kow Cheong, March 1, 2010

Sunday, February 28, 2010

Mathophobia is curable!

Mathophobia is curable!

Although millions of people suffer from mathophobia (fear of mathematics in all its forms and degrees), however, it was not too long ago that more attention had been given to this disease, fueled partly by the influx of self-help math books to tap on the huge market of mathophobics and mathematically challenged citizens.

I believe that in a-not-too-distant future books on mathophobia and its related symptoms will be shelved under the Health Section in the library. There may also be titles written on numerical phobias or conditions, such as triskaidekaphobia (irrational fear of the number 13) and acalulia (inability to do basic arithmetic).

Once mathophobia is recognized as a psychological illness that affects workers' performance, perhaps doctors will henceforth issue a medical certificate that may look as follows:

To Whom It May Concern

This is to certify that Aziz Salamat is suffering from Mathophobia (Graphobia).

She has been granted medical leave for 2 days, starting from Monday 2 April 2015 to Tuesday 3 April 2015.

Dr. Adrain Gan

The best cure for mathophobia is prevention; the best antidote is math confidence. Every child can learn math successfully, and every teacher can teach math successfully. In fact, no one is “math-dumb”. Learning math is both logical and emotional. So, treating any math anxiety must include both affective and cognitive elements, as mathematics is both logical and psychological.

What is needed is not a one-for-all syllabus, but rather a curriculum that is challenging, yet at the same time catering for children's different cognitive developments.

Mathophobia: A disease transmitted by parents and teachers to children.

© Yan Kow Cheong, February 28, 2010