13 Ways to Spot a Math Nerd

Thirteen Ways to Spot a Math Nerd 


1. They are aroused at the sight and sound of numbers. 


2. They wait for the bus and say, "I bet three buses will come all at one go."

3. They have irregular-sized pizza delivered to the mathematics or computer science department. 


4. Their idea of rebellion is to go to the whiteboard and compute everything in binary, or do calculations in Roman numerals. 


5. They sleepwalk uttering obscenities at Greek symbols, or murmuring in Latin.


6. They send e-mails to each other even though their desks are less than two meters away.


7. They refer to their friends, fiends or foes by their e-mail coordinates.


8. They explain to their five-year-old neighbors the difference between number and numeral, minus and negative, or zero and nothing.


9. They see a woman's boobs and think of a smooth polynomial curve, with its pair of minimum points.


10. They insist that "1 + 1 = 2" is not true until they use the axioms (undefined terms) to prove it.


11. They say, "I'll see you there at 7PM plus or minus 10 minutes."


12. They use insults like "You’re two standard deviations from the norm, you symbol-minded dummy!"


13. They prefer doing math to dating, dining or having sex.
© Yan Kow Cheong, March 17, 2010 

Immoral Algebra

Immoral ALGEBRA

Here is an online algebra question, forwarded to me almost every year, which has been circulating the globe many times:

Maya is 21 years older than her son Raju.

In 6 years from now Maya will be 5 times as old as Raju.

Question: Where's Maya's husband?

My reply to the sender was: My limited algebraic knowledge leads me to infer that the "normal-child-to-be" was some one year away to see the world (Answer: x = –1). Challenge: Try solving this problem using the Singapore model method.

(

So I can only conclude that the "conservative couple" was in some "missionary position" then.

My sender's forwarded answer was: 

Current age of Raju is -0.75 ie -9 months ie he is 

being conceived therefore husband is on top of wife

And my reply following the e-mailer's answer was:

 

I bet is that if we've a few of these CRE8TIVE word problems in our traditionally sterile MOE-approved textbooks, more students would be excited to reading algebra until they're old enough to have kids of their own. Students would be begging teachers and tutors for more algebra and more word problems – two bêtes-noires of school mathematics. Who knows? This may turn out to be an inexpensive cure to addressing our declining birthrate! When most students' favorite four-letter word would then be MATH MATH MATH ... and MORE MORE MORE!

Stripping Off Your Maths

The above online algebra word problem reminds me of a math workshop organized by the Singapore Science Centre in late eighties, when the speaker-and-author, Mr Ang Tok Woon, shared with fellow teachers that a good metaphor could help weak or uninterested students recall mathematical concepts or formulas rather effectively.

He used the idea of ‘stripping off’ some unknowns when teaching the topic on "Subject of Formula" to a group of academically challenged [ITE or SAF mature] students. For instance, given E = mc², ‘making c the subject of formula’ means expressing c in terms of E and m. And he was surprised that years later when some of his ex-students met him, they reminded him that they had forgotten everything else he taught them except for that part on stripping off.

Sexing Up the “Sixth Factor”

Only a lack of imagination and creativity would deprive hundreds of thousands of pubescent teenagers from experiencing the joys (and pains) of algebra.

As we explore how best to incorporate the sixth factor — the ‘context knowledge’ — as suggested by Assoc. Prof. Wong Khoon Yoong from the National Institute of Education, Singapore, to extend the present two-decades-old Singapore Mathematics Curriculum Framework comprising of the five factors (Skills, Attitudes, Concepts, Processes and Metacognition), diagrammatically placed along the sides of a pentagon, I think posing ‘real-world problems’ with a recreational or cultural flavor would go a long way to arousing the algebraic interests of our students who might otherwise give algebra a miss, once it becomes an optional topic. 

Indeed, we need a fertile dosage of algebra to debunk the myth that the common language of mathematics is difficult and boring. Algebra, or any topic in mathematics, for that matter, is amoral and neutral. Mathematics can only be boring as long as we’ve boring teachers and writers (and editors, math consultants and math specialists) — or all five — churning out unexciting textbooks. However, matters would have been a notch above boring if we had had fewer boring reviewers and curriculum specialists.

Some Nudity May Promote Numeracy 

Another episode proves that infusing some perceived elements of decent nudity – art for mathematics’ sake – to enhance numeracy (quantitative literacy, as it is commonly known in the US) may not be a far-fetched idea. Years ago I was attending a two-day teachers’ course entitled Andragogical Principles, an in-service program for those teaching working adults or mature students, when the lecturer confided to us that by letting his students write about their [wild?] fantasies, they actually improved their language proficiencies. In fact, I wouldn’t be surprised that some of them are now working as freelance writers or editors for some adult publications!

Indeed, numeracy spiced with some exciting part of human biology may act as a catalyst (‘mathematical aphrodisiac’) to attracting even mathematically dull students to sign up for some extra-mathematical activities to enhance their quantitative literacy. As mathematics educators, we critically need creative methods to promote our mathematical trade; otherwise, we’ll end up losing potential candidates with a mind for the abstract to major in other disciplines that often promise more tangible rewards.

MATH$ I$ MONEY

Like guerrilla marketers, we need to go all out to promote and sell the idea that MATHEMATIC$ I$ MONEY! Some born with the ‘mathematical gene’ definitely stand a high probability of becoming millionaires, by cracking some unsolved mathematical nuts – for example, a few million-dollar prizes are on offer by the Clay Mathematics Institute to whoever can find the solution to some fiendishly difficult mathematical puzzles. For the majority of us, we can at least hope to secure some decent jobs thanks to the logical, analytical and deductive skills acquired through years of toying around with notions and notations.

If the oldest profession on earth continues to thrive because of the money factor, there is no reason why it cannot share a common denominator with the most disliked subject in school. With some financial carrots, more people would be motivated to speak the language of science and technology. Like sex, mathematics is money — and it can be enjoyable, too!

MATHESAURUS, Anyone?

For a few years now, I've secretly been writing mathematical words and terms, to be categorized under a so-called MATHESAURUS. I wanted to christen the title A Politically Correct Mathematics Glossary or A Quick-and-Dirty Mathesaurus Dictionary.
 
Offhand, here's a sample of my irreverent definitions:

• Abacus A primitive calculator that questionably originates from China. The Japanese version, called the Soroban, claims to be able to perform square and cube roots, as well as differentiation and integration. Unlike the calculator, its batteries last a lifetime. 

• Actuary One who misuses or abuses statistics to justify the high premiums charged by one's insurance company.

• AMC Abbreviation for “Australian Mathematical Competitions.” The world’s popular competition, AMC caters for those mathletes who do not qualify for the IMO, but hope to be medalists, nonetheless. See IMO.

• Boolean Algebra The Arithmetic of “Or” and “And.”

• Coordinates A way of describing a location on a grid. For instance, the author's e-mail coordinates are: kcyan.mathplus@gmail.com Some common daily use of coordinates are: (a) A cab driver looking for (5, 8), 5th Avenue and 8th Street; (b) Finding a seat in a theatre, say L25 (Row L, Number 25), and the like.

• Mathophobia Anonymous A gathering of people who pride themselves of their mathematical ineptitude. The members meet clandestinely to avoid being overcharged and conned by unscrupulous agents. 

• Quadratic Equation A misnomer for naming an equation of degree 2; should be renamed “biratic equation.”

• Trial-and-Error Method A hit-and-miss approach. The mathematical equivalent for looking for a word in the dictionary.

• World Wide Web (WWW) Comprises virtual cities of bits; the world of 1s and 0s. A city of bits. A communications medium that encourages gossip, freedom of speech, and gambling; sale of pink pills, yellow literature, blue movies, and so on.

• NCTM’s Standards An ideal list of guidelines and recommendations for mathematical excellence in K-12 by the National Council of Teachers of Mathematics, to be implemented in a non-ideal classroom.

• One-to-one correspondence The most primitive and also the most sophisticated method of counting. Used by farmers to count sheep, and by mathematicians to study different sizes of infinities and to come up with some visual (look-see) proofs.

Would you, readers, be keen to co-author with me the above irreverent guide to relevant mathematical terms? Any takers (friends, fiends or foes) who would be excited by such a general math-lite title? Please direct them to me. 

I couldn't be more serious about this funny title. I think it's going to be exciting to co-write and publish such a MATHESAURUS.

Irreverently yours
K C Yan 

© Yan Kow Cheong, March 11, 2010

The Thinking Like a Mathematician Series

The Thinking Like a Mathematician Series

In an age when apparently human beings use only ten percent of their brain, the public hasn't been spared of the Think Like a Genius syndrome. We've titles like Think like Da Vinci, Think like Einstein, and the like. Interestingly, but not surprisingly, we've yet to see a Thinking Like a Mathematician Series.

Probably we won't see such self-help series for some time, if the rate of innumeracy among writers and journalists doesn't dip in future. It's unlikely that untenured professional mathematicians (whose rice bowls depend on the number of published journal papers) would be lured into writing this type of pop math titles. However, non-fiction writers with post-graduate qualifications in science and mathematics are potential candidates to popularize such math-lite titles to the lay public.

Those who are fluent with abstract ideas would undoubtedly want to read about their mathematical idols of yesteryear – the habits of those highly successful mathematical minds. Monkeying the language of positive thinking, our chances of becoming a mathematician or mathematics educator would presumably be higher if we started acting or thinking like one. It is the intention and going through the motions of being or thinking like a mathematician that counts. 

Self-help books and circuit speakers tell us that if we want to think like a mathematician, and actually go through the motions of being one, we will become at least an adequate [probably, third-class] mathematician. We may not become another Archimedes, Gauss or Newton, but we'll be much more of a pseudo-mathematician than someone who doesn't practice the yoga of applied positive thinking. 


Meanwhile, let's look forward to some of these feel-good math titles, which may give the mathematical brethren some psychological boost to their often-unappreciated vocations.

Chicken Soup for the Mathematician Series
Chicken Soup for the Pure Mathematician
Chicken Soup for the Applied Mathematician
Chicken Soup for the Math Professor

Chicken Soup for the Math Assistant Professor

Chicken Soup for the Math Associate Professor

Chicken Soup for the Math Adjunct Professor
...

Chicken Soup for the Algebraist
Chicken Soup for the Geometer
Chicken Soup for the Group Theorist

Chicken Soup for the Number Theorist

Chicken Soup for the Probabilist

Chicken Soup for the Statistician

Chicken Soup for the Topologist 
...


© Yan Kow Cheong, March 8, 2010

Math is "Nowhere"

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!

NOWHERE IS MATH? MATH IS NOW HERE!

© Yan Kow Cheong, March 4, 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

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:

CERTIFICATE

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

MBBA, FRSE, HISM, DDFT

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