Singapore Math

Social Media Math

2012-02-08T20:21:00.000-08:00

Here are some questions that might appear in future National Assessment of Educational Progress (NAEP), Third International Mathematics and Science Study (TIMSS), or Scholastic Aptitude Test (SAT) papers, to reflect the interests or changing habits of students, who are spending an unhealthy amount of time, Facebooking and Twittering friends, fiends, or foes, rather than doing their homework.

1. N stands for the number of hours Dennis spends on Facebook each day. Which of the following represents the number of hours Dennis spends on Facebook every week?

a. N + 7 b. N – 7 c. N × 7 d. N ÷ 7 [Grade 4]

2. If the number of Facebook members in a school is F and the number of Twitter members T, and there are 40 times as many Facebookers as Twitterers, write an algebraic equation that shows this relationship. [Grade 8]

3. For next year’s Singapore App Annual Show (SAAS), a child pays $x per ticket and an adult pays $y more than a child per ticket. If p children and q adults buy tickets, find the total revenue from the sale of tickets in terms of the variables. [Grade 8]

4. Sam has twice as many Twitter followers as Ruth. If Ruth has r followers and Sam s followers, and Sam helps Ruth to gain a dozen followers within a week, how many followers does each have in terms of r? [Grade 7]

5. In the following, write an expression in terms of the given variable that represents the indicated quantity.

(a) The cost of having an IT repairman spend t hours at your house if he charges $40 for coming to the house and $50 per hour for labor

(b) The time (in minutes) left to use the mobile phone with a battery life of 8 hours, after t minutes of SMS-es and k hours writing e-mails

(c) The resale price of a laptop after t years if its initial price is $P and the resale value of the laptop halves every year

(d) Arthur’s total earnings as an ICT tutor after three years if the first year he earned $x, the second year it was $8,000 higher, and the third year it was twice as much as the second year [Grade 8]

6. Last month, Jack, a hardcore ex-convict,

· illegally downloaded a pirated blue movies;

· secretly watched b YouTube adult-themed clips;

· sneeringly “defriended” c Facebook members;

· insincerely clicked “Like” d times;

· angrily unfollowed e followers on Twitter;

· anonymously left f mean comments on blog posts; and

· vengefully spammed g e-mails to his ex-math teachers.

How many on-line transgressions did he commit in the last month? [Grade 7]

7. Tom recently set up a Facebook account for his dog. Freakie has now more friends than his owner: x canine friends and y feline friends. Tom has z friends. Which of the following is true?

a. x + y < z b. x – y > z c. x + y > z d. z > x + y [Grade 7]

8. @cobrakill tweeted the following to @MathPlus and @Zero_Math:

Scared off 3 bullies; had x mice & y ostrich eggs for breakfast. Gobbled up a piglet & a wild cat for lunch. And terrified a trio of oldies!

How many fell prey to the king cobra? [Grade 7]

Selected Answers

1. c

2. F = 40T

3. px + q(x + y) = (p + q)x + qy dollars

4. s = 2r; Sam has (2r – 12) followers, and Ruth has (r + 12) followers.

5. (a) 40 + 50t dollars (b) 480 – t – 60k (c) P/2^t (d) 4x + 24,000 dollars
6. a + b + c + d + e + f + g
7. c

25 Christmaths Toughies from Singapore

2011-12-16T20:20:00.000-08:00

Here are 25 non-routine fertile questions for friends and relatives to solve during this festive season:

1. The Recurring 25

Convert 0.252525... to a fraction.

2. The Sides of a Polygon

If the sum of the interior angles of a polygon is 2525°, what is the maximum number of sides the polygon can have?

3. December 25, 2025

On what day of the week does Christmas Day fall in the year 2025?

4. Number of Diagonals in a 25-gon

What is the number of diagonals in a 25-sided convex polygon?

5. How Many Ways?

In how ways can you arrange the letters of the word CHRISTMASTIME?

6. Merry Xmas & Happy New Year

If the value of MERRY CHRISTMAS is 189, the value of A HAPPY NEW YEAR is _____.

7. Santa's Routes

Determine the total number of distinct shortest routes from point A to point B in the following diagram grid map.


A


B

8. A Sum of 25 Powers

Find the sum of S = 2 + 2¹ + 2² + 2³ +⋯+ 2²⁵.

9. Writing 25

What is another way of getting the number 25 using the numbers 2 and 5 only once, other than equating it to 5²?

10. Time Needed

Determine how long it will take to return all the gifts mentioned in the song “The twelve days of Christmas” if the gifts are returned at the rate of one gift per day.

11. Join the Xmases Family

A mother who was born on December 25, married to a husband also born on December 25, gives birth to their first baby on December 25. What are the odds of the mother doing that?

12. Four Fours to Make 25

Using four fours, the four basic operations and, if necessary, √4 and/or 4!, form the number 25. [Note: 4! = 1 × 2 × 3 × 4]

13. The Largest 25-digit Integer

What is the largest 25-digit number that can be divided by 2 and 5 without any remainder?

14. Number of Zeros in 1 × 2 × 3 ×⋯× 24 × 25

How many zeros are there at the end of the product 1 × 2 × 3 ×⋯× 24 × 25?

15. The Chocolate Bar

Given a 25-piece square chocolate bar, how many snaps are required to break the bar into its individual pieces?

16. A Creative Thinking Question

It is late on Christmas Eve and little Noel is waiting the Christmas tree to be finished. At exactly what time will this happen?

17. Christmas and Halloween

Prove that Oct. 31 = Dec. 25.

18. Divisibility by 25

Show that, if n is a positive integer, 16n + 10n – 1 is divisible by 25.

19. A Pair of Christmas Alphametics

In each case, replace each letter with a digit, different letters being different digits.

(a) SANTA - CLAUS = XMAS

(b) A + MERRY + XMAS = TURKEY

20. A Sum of Squares

Find the value of 1² – 2² + 3² – 4² +⋯+ 25².

21. Number of Rectangles

A board has 25 squares. How many individual rectangles are there in all?

22. A Christmas Party

At a Christmas party, each child brought a present. Presents were put in a large basket. All presents were different but identically wrapped. Going home, each child randomly selected a present from the basket. What is the expected number of children who carry home their own presents?

23. How Many Lines?

Using only horizontal and vertical lines, what is the most number of straight lines you can draw between the dots in a 5 × 5 grid without lifting your pencil?

24. A Table of 25 Boys and 25 Girls

A total of 25 boys and 25 girls sit around a table. Show that it is always possible to find a person both of whose neighbors are girls.

25. All n's End in Zeros

For what values of n does 1 × 2 × 3 ×⋯× (n – 1) × n end in 25 zeros?

A Merry CHRISTmaths to all!

Selected answers
1. 25/99 2. 16 sides. 3. Monday. 4. 275 diagonals. 5. 778,377,600 ways.
6. 158. 7. 252 routes. 8. 2^26 - 2 9. 5 ÷ .2 = 25 10. 364 days.
11. 364/1 12. 4! + (√4 + √4)/4 13. 999…99990 14. 6. 15. 624 snaps.
16. Midnight. 18. 600. 19. (b) 2 + 97,445 + 6,928 20. 325.
21. 225 rectangles. 22. 1. 23. 34 lines. 25. 105, 106, 107, 108, 109

For full solutions, consult the title in the Reference.

Reference
Yan, K. C. (2011). CHRISTmaths: A Creative Problem Solving Math Book. Singapore: MathPlus Publishing.

© Yan Kow Cheong, Dec. 16, 2011.

Now available as an iPad app
http://tinyurl.com/7pn8pau

25 Things You Wished Were Untrue about Christmas

2011-12-14T21:09:00.000-08:00

25. Toys are made affordable for millions of parents thanks to the appalling working conditions endured by under-aged children in Santa’s sweatshops, in China.

Fractal Christmas Trees
© Dreamstime.com

24. Proud CEO: “My time in looking for a five-dollar present for my company Christmas party is worth more than US$2,525—I’d rather issue a check 100 times the amount for the gift.”

23. An e-card costs much less than 25 cents—maybe a mere 2.5 cents plus or minus a few bits and bytes.

22. There are fewer joyful people on Christmas Day than on any other day of the year. Do you know why?

21. Men dishonor Christ more in the 12 days of Christmas than in all the 12 months of the year—by their boozing and carousing.

20. Even staunch Christians may not be aware that Christmas is a pagan feast, originally meant to worship the Sun god, instead of the Son of God.

19. There may be more non-believers celebrating Xmas than believers every year.

18. Singles, poor people, and entrepreneurs could not wait for Christmas to come and go—not a happy time to be alone or be lonely.

17. Many believers and non-believers celebrate Christmas without a genuine understanding of the meaning of the public holiday—probably the most celebrated and the least understood festival of the year.

16. Retailers rely on Xmas significantly on the festive sales to remain financially afloat.

15. People merry so much on Xmas Eve that they don’t have time to open up their Xmas gifts—Boxing Day often becomes a sleeping day!

14. Even believers forget that Christmas needn’t be merry to be meaningful—it is the Christ of Christmas that needs to be celebrated, not Christmas itself.

13. Believers and non-believers are more and more expensively anxious or stressed to buy something to please others—as a sign of showing off their wealth, or exhibiting misplaced generosity.

12. New Christians do not want to be excluded from Christmas as they await for their employers’ Christmas bonus—that universally revered figure.

11. Employees are willing to work under unreasonable bosses because of the Christmas bonus—many at the same place, for the same boss, for more than 25 years.

The Search

by FREED Jesus is LORD♥

10. Believers from other faiths often feel morally obliged to celebrate Christmas with their Christian colleagues and neighbors, all in the name of religious harmony.

9. Religious fanatics intolerant of Christianity wished Christmas were celebrated every quarter of a century instead of every year.

8. Some people would buy off a Christmas gift for their children on eBay for several thousand times the original price.

7. People max out their credit cards to finance the gift storm, as compared to their grandparents who saved money for Christmas.

6. Some allegedly US-friendly Arab nations tend to treat Christians worse than those living under dictatorial Muslim rule.

5. A month after Christmas, the holiday is only halfway paid off—credit card debt resulting from a borrowed merry Christmas. And a third of the money borrowed for Christmas spending is still not paid off two months after the holiday.

A Christmas gift for numbers lovers
http://tinyurl.com/7pn8pau

4. This Christmas over a billion people in the world are surviving on less than 70 pence a day.

3. Politically correct retailers have banished Jesus and Christmas from the mall to accommodate to the secular demands of agnostics and non-theists.

2. Christmas is celebrated today more like a sales frenzy than as the most important birth in history—the commercial mentality has robbed the message of giving.

1. The closer people get to Christmas, the pressure to give these (useless) unnecessary gifts goes up and they feel depressed and unworthy if they can’t give.

Merry X-W/g to all!

11 Random Musings on 11/11/11

2011-11-10T22:07:00.000-08:00

On this "auspicious date" for the superstitious, and "marriageable date" for those tying the knot, here are eleven random numerical thoughts for this year's most memorable date.

1. When Numerology Meets Biology
A possible aftermath for this year's hot date is to expect a slight increase in the birthrate this coming August—maybe some 11 percent points up for greying nations like Singapore and Japan, where the fertility rate is currently below its replacement level.

2. The Heck of a Date

Let's celebrate, or meditate on, a dozen 1's at 11 seconds past 11:11 on November 11, 2011: 11:11:11 11/11/11

3. Murder by Numbers
Health risks for both mothers and babies, resulting from induced births or Caesarean operations, as parents-to-be long for an auspicious birthdate—a union of superstition and innumeracy!

4. A Mental Stimulation
A mental calculation for lovers on a hot date: Find the value of 111111 × 111111.

Predict the patternful answer for 11111111111 × 11111111111.

5. Timely Birth, Untimely Death
What is the probability that one born on 11/11/11 will have one's last heartbeat on 12/12/12?

6. Born on 11.11.11 Died on 11.11.11
What are the chances that someone born on 11/11/11 (2011) will also die on 11/11/11 (2111)—when he or she is a centenarian?

7. The 11:11 Phenomenon
Are you a superstitious, or faithful, believer in the numerology of the 11:11 synchronicity?

Do you wake up every night at the same time, sometimes 11:11 p.m., sometimes 1:11 a.m., 2:22 a.m., 3:33 a.m.?

Your minor medical expenses from a minor accident: $11,111.
Your hospital room number: 1111
Date of accident: November 11

Your mileage read 111111!

8. Special Birth-dates
What percent of children (or twins or triplets) in the world would be celebrating their 11th birthday on 11/11/11?

9. A Mathematical Quickie
The product of the ages of Mr. and Mrs. Yan, and their daughters, is 111,111. If Mr. Yan is two years older than his wife, find the sum of the ages of their children.

10. Expressing Oneself in Ones
Using 1's only and the four operations (+, —, ×, ÷), what are some ways of expressing 111111?

For example, 111111 = 11 × 111 × (111 - 11 - 11 + 1 + 1)

11. A Pseudo-Mathematical Toughie
Mrs. Ones bought a certain number of pens for $1111.11. She sold each pen at $1.21. If one pen costs more than $1.00, how much did she earn in total?

Selected Answers

9. 18 11. $200.20

© Yan Kow Cheong, November 11, 2011.

20 Things You Probably Didn't Know about Singapore Math

2011-11-02T23:43:00.000-07:00

The media love to paint a positive or negative picture of life's successes and failures, and Singapore's success in mathematics education is no different. Here are some unwritten, often undesirable, factors contributing to Singapore's mathematical success.

20. About sixty percent of students know how to differentiate and integrate un-pathological functions by grades 9 and 10—they read two-year "Additional Mathematics" plus four-year "Elementary Mathematics."

19. About ninety percent of students would have had a math tutor by the time they reach grade 6—private tuition is a multi-million-dollar business in Singapore because school teachers know tutors and anxious parents would eventually fill in the gap.

18. Some sixty percent of students complete their secondary education in four years, which includes reading calculus, trigonometry, and proofs in plane geometry.

A title that promotes
the model method
SingaporeMath.com

A Singapore wallet-friendly
grade 4 title of
a six-book series

17. On average, most students would practice three to four assessment [supplementary] math titles every year, up to grade six, mostly purchased by parents and recommended by tutors, because local textbooks ill-prepare them for school tests and exams.

16. An estimated 60% of students in every cohort dislike math, because it’s taught in a boringly sterile manner in schools, and often by boring math teachers who are simply teaching math to the test.

15. Statistical anecdotal evidence suggests that as high as 80% grades 1-6 teachers prefer to teach other subjects to math—the painful truth is that grades 5-6 math (with their share of challenging word problems) are harder to teach than grades 7-8 math.

14. Most K-6 math teachers are non-college graduates; interestingly, they’re also known to be better math teachers than their peers armed with a university degree.

A Formula for Singapore's Math Success = 20% Textbook + 30% Teacher + 30% Tuition + 20% Parental Involvement

13. The better math teachers and tutors aren’t teaching in the top schools, but rather in neighborhood ones, with far less-ideal facilities and resources.

A dear pseudo-monograph
about the
Singapore model method

12. Since the 2000s, the standard of math education in Singapore has dropped significantly, due to the recruitment of non-math majors—many have a degree in Accountancy, Engineering, or Computer Science. This means that many wouldn’t have been exposed to a rigorous treatment of college math (abstract algebra, topology, or complex analysis).

11. The majority of math teachers moonlight, often compromising their day-time jobs—the better ones teach in tuition or enrichment centers, or give private tuition, often charging obscenely.

10. Up to 70% of Singapore students are probably one grade higher than their peers in the United States—for instance, a primary 2 student in a good neighborhood school in Singapore would have covered at least 60% of what a grade 3 student in the US had read, based on the textbooks’ contents from both countries.

9. Other than those few expensive-cheat math titles written by some lecturers or tuition centers' owners, most Singapore-published math textbooks and assessments are value-for-money titles vis-à-vis the expensive, thick, colorful—inch-deep, mile-wide—textbooks published in the US.

8. The power and beauty of the Singapore model (or bar) method is mostly appreciated by those outside Singapore, as compared to an unappreciative lot of local math teachers. Since the late eighties, they've been inundated with an unhealthy number of assessment (supplementary) books, aimed at promoting the visual heuristic—today, most local math teachers treat the model method as a hype or a bore.

7. Most elementary math teachers and graduates-parents have difficulty drawing a model when faced with a grade 5 0r 6 challenging word problem, preferring to use algebra instead to solve them—without peeking at the model-or bar-method solutions, most parents are unable to help their grades 5-6 children with their school homework.

6. Most math teachers feel uncomfortable or ill-prepared to coach their own students for math contests and competitions, leaving the task to trainers from private companies, or to coaches from mainland China.

A decade-old
Singapore bestseller
http://tinyurl.com/3cctqcg
http://tinyurl.com/3uy5hou

5. Local mathletes are trained to answer questions that would defeat most secondary teachers, who are primarily drill-and-kill specialists employed to produce exam-smart students to outperform their peers from other Commonwealth countries.

4. Singapore-published textbooks and assessments are mostly written or ghostwritten by foreign-born authors, most of whom have never taught in primary or secondary schools, or by lecturers supervising trainee-teachers.

3. Most Singapore-published math titles are "edited" by non-Singapore citizens, who only have a smattering understanding of the local educational system.

2. An unhealthy number of school textbooks are rewritten or ghostwritten by editors for their PhD authors—many titles-conscious general editors or consultants are notoriously known to contribute quasi-zero input and to collect an undeserved royalty or lump sum payment.

1. Singapore is a haven for assessment math titles, but a hell-on-earth for mathophobics who are forced and terrorized by parents and tutors to go through hundreds of non-routine or challenging word problems, so that they'd remain ahead of the competition. The only consolation is Singapore's top ranking in TIMSS; more medals at contests and competitions, and more university places at top universities.

Indeed, Singapore firsts in math education comes with a high price and with much pain and suffering for students, teachers, tutors, parents, writers, editors, and publishers. Not to say, tens of thousands of students who feel shortchanged and alienated by the culture of mathematics challenge, resulting in poor self-esteem and a dislike for the subject!

Mathematical Haikus for Kiasus

2011-07-12T00:35:00.000-07:00

Some 17 odd hours ago, I posted "Mathematical Haikus for Goondus* and Suakus" on Facebook. I hypothesized that composing or formulating these 17-syllabled verses may help one to balance the left mathematical part with the often-atrophied right part of the brain. Here's another lot of these 5-7-5-like crude non-seasonal poems.

Make Every Nanosecond Count

Three scores and ten

Roughly a billion heartbeats

Use your time wisely

How Many Misteaks Are There?

On the train platform

Train arriving in ''one mins''

That's non-SI time!

Issued by Japan in 1984

Rightly Theirs

That kids can recall

Pythagorean Theorem

That proves their "math rights"

The Craze Is Back

http://www.rubiks.com

Dare to sign up for

Rubik's Cube Competition?

That's raw math talent!

A Modern-day Rubik Cube

Sudoku, again?

Think of something more worthy

To tickle your brain

http://en.wikipedia.org/wiki/Fifteen_puzzle

Sam Loyd’s Alleged Invention

The 15-Puzzle

That cheap toy of yesteryear

Order it on eBay

A Math Competition for All

AMC* is best

The most popular contest

In the world today

*Australian Mathematics Competition

Where Cool Math Things Happen

MAA is cool!

The association to be

For math geeks and nerds

The World's Most Disliked Subject

Why you dislike math?

MATH is a four-letter word

A turn-off for kids

A Key to Unlocking the Universe’s Secrets

Math is a language

With notations and notions

To model the world

Some Like It With an “S”

Is it MATH or MATHS?

It all depends where you live!

Your location counts.

The Most Quoted Verse

What's John 3:16?

God's numerical message

Of His Love for you

NUMBERS 1:1-36:13

The Book of Numbers
Is not really a math book
But God's Almanac!

Social Media MATH

To blog or to tweet?
It's hard to make up my mind
I choose to do both

TWITTER Math

Micromath 4 U

In 140 words

To share your sweet tweets

FACEBOOK Math

Five-minute math posts

On pop culture and gossip

For friends, fiends, and foes

The ~~Chewing Gum~~ Land

A math sanctuary

The ''fine city'' Singapore

Offers jail and cane

Triple Firsts in TIMSS

SINgapore’s success?

A haven of ''cheat/cheap'' books

To meet kiasus’ needs

Superstitiously Yours

Friday the 13th

An urban myth to promote

Irrational fear

Apocalypse now

Faith in the Mayas

Dec 21, 2012

Where will you be then?

Singapore’s Papyrus

The model method

A mere fad or a cool tool?

To soothe the mind's eye

Faith or Fear in 1’s and 2’s

The Y2K scare

Next it's 12/21/12

Marketing faux fear?

Another Creative Math Title

Cre8tively yours

Who Took My Calculator?

Coming your way soon!

It's time to compose a few mathematical haikus to tickle the right part of your grey matter. And remember to share them with the rest of the mathematical brethren.

A 17-letter

m-a-t-h-e-m-a-t-i-c-a-l H-A-I-K-U

Longs to be composed

* Suakus and Goondus are the Asian equivalents of Dummies, Idiots, Blockheads, and Morons.

# Kiasus are those who are afraid to lose out, displaying signs of self-centeredness and selfishness.

© Yan Kow Cheong, July 10, 2011

Censored Math Questions from Singapore

2011-06-05T22:45:00.000-07:00

In late nineties, during the dot-com fever, while providing CD-ROM contents for a local multimedia company, I came up with a mild collection of contextual word problems, following the call by the National Council of Teachers of Mathematics (NCTM) then to pose some real-life problems to make the subject relevant and meaningful. Unfortunately but not surprisingly, the board of [conservative] editors vetting the questions rejected them.

Here’s a sample of that collection, which were deemed “contextually relevant” but “pedagogically insensitive” or “culturally loaded,” whatever those terms meant.

Questions

1. Joe managed to bribe the customs officer by bringing in boxes of chewing gum to be distributed among his gang members. The merchandise was allowed after Joe agreed to pay $20 per box for half the number of boxes smuggled, $10 for every three of the remaining boxes, and an additional sum of $50. If Joe was charged $330, how many chewing gum boxes did Joe smuggle? (24)

2. A property agent hinted to his client that he could help him pay less on stamp duties for his flat, if he agreed to undervalue his property. The unscrupulous seller found that he could gain $67,500, if he were to declare to the Housing Board that he was selling at 2/3 of the actual price of his apartment, and was giving the agent 1/10 of the difference. How much did the buyer actually pay for the apartment? ($225,000)

3. Mike Ray got six strokes of the cane for his juvenile crimes. Fearing that a heavy penalty might lead to a boycott of the country’s goods, the judge decided to sentence the American teenager leniently. The light sentence was formulated based on the number of offences committed: two strokes for every five offences for the first half of the total number of offences, and one stroke for every five offences for the other half of his transgressions. How many offences did Mike commit? (30)

4. A principal had his jail sentence halved after he admitted to molesting two of his female teachers and some of his school girls. Because of his outstanding contribution in the field of education, the lady judge mercifully sentenced the principal to five years for every three victims. How many girls did the principal take advantage of, if his sentence was reduced to 10 years? (10)

5. A foreign tourist was found guilty of multiple crimes perpetrated against foreign maids working in Singapore. He was charged for outraging the modesty of two women, and the penalty carries a maximum jail sentence of 5 years. His pick-pocketing activities landed him with another 3 years behind the bar. He served one quarter of his remaining jail sentence for exhibitionism, and served his last six years for beating two policemen. How long did he stay in jail? (16)

Some reasons given for rejecting the above questions were:

Question 1 allegedly promotes bribery and corruption.

Question 2 encourages corruption and dishonesty.

Question 3 nurses permissive juvenile delinquency and xenophobia.

Question 4 supposedly promotes rape, outrage modesty, and the like.

Question 5 encourages crime and murders of the second, third, and fourth degrees!

Of course, these tongue-in-cheek questions were written lightheartedly to add some spice to the pool of hundreds of artificially posed questions needed for the CD-ROMs. But they're censored right away without any suggestions to rewriting them.

Indeed, one recurring complaint among scores of local math educators and parents that our locally published math titles are replete with sterile, politically correct questions (which bore many students to tears), is an understatement, to say the least.

We, teachers and writers, look to the days when we'd truly and fearlessly be able to set real-world questions that our students and their teachers could relate to—by posing contextual problems that offer a rich conceptual understanding of mathematical topics.

If you think that your child or student may not be quite ready or mature enough for the above fertile, politically incorrect questions, may I invite you to some aha! math questions instead? You may download them from http://tinyurl.com/3cctqcg and http://tinyurl.com/3uy5hou

© Yan Kow Cheong, June 5, 2011

The Lighter Side of Singapore Math (Part 3)

2011-05-01T06:48:00.000-07:00

Is the Singapore model method a plus or minus?

Skeptics or critics: "The model method is pre-algebra in disguise."
Proof: Use of a bar instead of a variable x.

Agnostics: "I've faith in Back to basics!"
Proof: I never use x, y, z nor any models in everyday life.

Believers: "The model method is visual algebra in elementary math."
Proof: Singapore's top rankings in TIMSS.

The Aftermath of TIMSS

One by-product of Singapore's top TIMSS ranking: Low fertility rate of 1.16 of its population—way below the replacement level of 2.1 At the current rate, Singapore might cease to exist!

Outsource your math to Singapore, not to Bengalore.
Bengalore the tedious and monotonous, Singapore the creative and innovative.

The red dot in South East Asia [Singapore] had leaked into the sea of math education, forcing [American] states to reassess both curriculums and pedagogies.

Half-baked Papers from School of Education researchers:

"How to wean the elementary student from models to algebra"

"Beyond the Singapore Model Method"

"Should SINGAPORE MATH be ©opyrighted?"

"Could Korea Math be the next mathematical fad?"

Six Top Oft-quoted Factors for Singapore's Success in TIMSS

1. Excellent textbooks

2. Good teachers

3. High pay for teachers

4. Society's high regard of teachers

5. Good career path for math teachers

6. Teachers mostly math majors or minors

Six Key Factors of Singapore's Success in TIMSS

1. Nation-wide private tuitions (individual or group) to make up for poor teaching in schools.

2. Parental involvement—many parents taking leave to coach their kids closer to exam time.

3. Practice of drill-and-kill assessment [supplementary] questions assigned by kiasu parents, tutors, and teachers.

4. Self-help groups such as CDAC, MENDAKI, SINDA to help the weaker—and economically challenged—students.

5. Remedial math lessons disguised as "enrichment math" programs.

6. Community clubs (CC's) tuitions for average or below-average income earners.

In the Pipeline...

New citizens- and permanent-residents-to-be may soon have to know how to solve one or two word problems, using the model method, as they sit for the literacy-numeracy test for those who don't have a formal education. Indeed, a stressful time for new immigrants!

Line Method vs. Bar Method

The line method is to the bar method what the soroban is to the Chinese abacus. http://tinyurl.com/4rxdky3

A Dozen Tweets from @MathPlus

The Light Bulb: How many Singapore math educators does it take to change a light bulb? It depends on the type of model they draw.

A numerologist is a "make-believe" number theorist trying to fool the innumerates that numbers have powers to rule their lives.

How many US politicians does it take to adopt Singapore #math? Three: To prove Singapore's existence, location & its relation to election.

Singapore #math authors may be the least credited in the world, as their first names are often mistakenly referenced for their surnames.

Beyond Singapore math textbooks & workbooks, here are some enrichment & creative math titles to tickle the brain: http://tinyurl.com/3lfuzsf

Anything cat-size or smaller tastes like chicken. Creatures roughly dog-size taste like pork; anything larger tastes like beef.

Benjamin Vitale: "Russian Math is hard work, Singapore Math is smart work." Famous Russian mat'cians aplenty proves they're doing sth right!

Her double masters didn't help her math⎯she lost $100,300 in casino. http://bit.ly/hWnVms She's faith in the "Lore of Averages"!

Singapore math on its own cannot magically turn a bad teacher into a good one, but it can make a good one better.

A Postmodern Equation: Life - Love = Autumn + Spring + Winter

Since 1991, Lee Kuan Yew gave some $13 million to #charity⎯earnings from his memoirs, speaking engagements, and being on advisory boards.

With perfect equality at zero, Singapore's Gini score (a measure of income inequality) is World's No. 2 at 0.42, behind Hong Kong's 0.43.

Zero Tweets from @Zero_Math

Join the ZERO-MATH Fan Club, by following K. C. Yan as @Zero_Math and share your zero tweets with the Zero-Math brethren! Here's a sample of them:

A #Math Quickie: The temperature is forecast to be twice as cold as today. If today is zero degrees, what will tomorrow's temperature be?

Zero is inarguably a Hindu invention, but textbooks still attribute its origin to both Hindus and Muslims. Political or racial correctness?

How to Lie with Zero: 0% Bank Loan, 0% Interest, Zero Down-payment, ... #zero #interest #marketing

A Dangerously Zero Thought: "It's the thoughtlessness that counts!"#zero

Are You a Number?

2011-03-04T20:49:00.000-08:00

There is no dearth of books offering advice on what you might call your baby (and even your dog or cat), many of them focusing on the meanings of names. How many of you actually know the meaning of your own names?

Recently, I posted these “Apple people” on Twitter (@MathPlus):

I. Pad Born 11 November 1944; died Toa Alta, Puerto Rico, 30 August 2009.

I. Phone Born Romania, c.1881 (Bronx, New York, 1920 US census).

I. Pod Baptized Whatfield, Suffolk, 20 May 1638.

I. Tunes Married Durham, 1874.

Of course, we can’t discount the possibility that some names might have been recorded thanks to a mistake on the part of a registrar who misheard, or have been transcribed from a half-legible census return. For instance, a number of mainland Chinese fleeing the Communists for a better life had their names “mutilated” by the natives of the countries they landed in.

My Bogus Surname

The Chinese character for my surname translates into “Chew” or “Kew” [depending on the dialect], but an Indian chap of yesteryear mis-registered my father’s surname as “Yan” instead. The aftermath of such an error had only led to anger and frustration; and imagine how much wasted money and time that represent in having to explain why the Chinese and Romanized characters don’t match. Changing your name by deed poll simply can't undo a faux pas of that nature!

In Praise of Numbers

Many of us had read about or met people with names like John Smith, Jr. and Tom Bacon II, where some numeral or abbreviation is being appended to a name, but have we ever come across folks whose names are a number itself? Here are a baker’s dozen of such “numerical characters.”

Zero

Zero Queen, born Cleverland, North Carolina, USA, 10 September 1888; died Elbert, West Virginia, 9 April 1954

One

William No. 1 Harris, married Islington, London, 1896

Two

William No. 2 Harris, married Maria A. Trent, Islington, London, 1913

Harry Two Smith, married Derby, Derbyshire, 1900

Three

Three Worthy, born 1 June 1907; died Linden, Alabama, USA, April 1981

Four

Four Souls, born 16 April 1907; died Box Elder, Montana, USA, July 1984

Five

Five Bumball, born Pennsylvania, c.1840 (Jackson, Missouri, 1920 US census)

Six

Six Hix, born South Carolina, c.1898 (Waterloo, South Carolina, 1910 US census)

Seven

Number Seven Fell, born Alton, Hampshire, 1879

Eight

Eight McClurg, born Iowa, c.1879 (White Breast, Iowa, 1880 US census)

Nine

Nine Sparks, born 18 July 1939; died Jackson, Montana, USA, 25 August 1995

Ten

Ten Hipkiss, born Birmingham, Warwickshire, c.1898 (Birmingham, 1911 Census)

Eleven

Eleven Moore, born 11 July 1900; died Coalgate, Oklahoma, USA, January 1982

Twelve

Twelve Ripley, born Illinois, 1887 (Ora, Illinois, 1900 US census)

Thirteen

Thirteen Sneed, born Tennessee, c.1882 (Tipton, Tennessee, 1920 US census)

As expected, there are also names for Fourteen, Fifteen, Sixteen, Seventeen, Eighteen, Nineteen, and Twenty. And names like Thirty, Forty, Fifty, Fifty Six, Fifty Nine, Sixty, Seventy, Eighty, and Ninety. Should you decide to organize a Math Trail, aimed at visiting cemeteries to locate these “numbers,” get a copy of Russell Ash’s latest humorous book, Frou-Frou, Frisby & Brick for your references.

Fractional Names, Anyone?

Even christening “fractional names” on babies hasn’t been spared:

Tenth (⅟₁₀)

Tenth Lily West, baptized Bedminster, Somerset, 22 June 1880

Eighth (⅛)

Eighth Hendricks, born Texas, c.1909 (Robertson, Texas, 1910 US census)

Fifth (⅕)

Fifth Jesse, born 14 November 1909; died Sacramento, California, USA, 16 March 1999

Quarter (¼)

Quarter Harris, baptized St Andrew Holborn, London, 1 May 1823

Half (½)

Half Robinson, born Banbury, Oxfordshire, 1859

In Love with Power-ful Names

If you want to lay flowers on the tombstones of multi-digit numbers, here are some Powers of Ten:

Hundred (10²)

Hundred Evans, died Greene, Alabama, USA, 1 January 1949

Thousand (10³)

Thousand Poindexter, born Louisiana, c.1888 (Gibson, Louisiana, 1920 US census)

Million (10⁶)

Million Airth, born Ontario, Canada, 4 June 1869

Billion (10⁹)

Billion Pride, born c.1898 (Brooklyn, New York, 1930 US census)

Trillion (10¹²)

Trillion Cummings, born Mississippi, c.1907 (Kirkville, Mississippi, 1910 US census)

Zillion

Zillion Long, born 16 March 1899; died Petersburg, Virginia, USA, October 1977

Infinity (∞)

Infinity Hubbard, born Georgia, c.1839 (Tippah, Mississippi, 1850 US census)

The Whys of Numbering a Name

As author Russell Ash remarked, could those numbers-names be due to some after-effect of an epidural? Maybe those bizarre naming decisions are merely the result of the tensions and euphoria of childbirth. Or, could those names commemorate a roulette win, or serve as a reminder of the sequence of one’s offspring from a previous unregistered polygamous marriage? My hypotheses are as wild as yours!

Promoting Name-calling via Name-giving

I recalled a couple in my previous fellowship group had christened their newborn after some biblical personality, which was difficult to pronounce, not to say, remember. Much as the parents might think they’re being clever and original (or even spirit-conscious), I wonder whether they had considered the correlation between bullying and the name they had bestowed upon their baby, when he began formal schooling. Talking about name-calling, how bad can it get for those who are a “number”?

Profiting from Numbers-Names

The last thing we want is to be treated as a mere digit or statistic in society or at work, much less being negatively associated with some number. Meanwhile, I’m seriously thinking of registering some trademarks (One Two™, Two Three™, Googolth™, Googolplexth™, Aleph One™, etc.) in anticipation of odd couples wising to numbering their babies. Like domain names, mathepreneurs could creatively turn these trademarked numbers-names into decent profit.

Reference
Ash, R. (2010). Frou-Frou, Frisby & Brick: The book of unfortunate baby names. London: Headline Publishing Group.

© Yan Kow Cheong, March 4, 2011.

Mathematical Clerihews

2011-02-06T06:19:00.000-08:00

A clerihew is an irreverent, rhyming quatrain based on a fanciful biographical theme, which begins with the name of its subject. A cousin to the limerick, the clerihew is a form of short comic verse which was popular in England in the 1920s.

The name "clerihew" came from the middle name of the English journalist named Edmund Clerihew Bentley (1875-1956) who developed the novel verse form.

On the mathematician-architect, Sir Christopher Wren (1632-1723), Bentley wrote:

Sir Christopher Wren
Said, "I am going to dine with some men.
If anybody calls
Say I'm designing St. Paul's."

Let’s focus our attention slyly on some famous mathematicians and math educators of yesteryear.

Paul Erdös
Wasn’t crazy about MS-DOS
For his brain worked like a cutter
Sharper than any MS-DOS computer

George Boole
was nobody's fool:
but never forget⎯
his mathematical legacy is the empty set.
⎯ Robin Harte
Fibonacci da Pisa
Who exported Hindu numerals as far as Czechoslovakia
Is remembered today for a pair of highly fertile rabbits
Which kept on reproducing in the most irrational habit.

Archimedes of Syracuse,
To get into the news,
Called out "Eureka"
And became the first streaker.
⎯J. C. W. de La Bere

Clerihews on a Singapore Mathematician-Amateur

What about composing a few clerihews for the new millennium? Here are two on Singapore's Prime Minister, Lee Hsien Loong, who would have undoubtedly become a first-class mathematician had he not followed his father's political footsteps.

Prime Minister Lee
Reluctantly had to flee
His beloved mathematical brethren
To take charge of some political harem

Brigadier General Lee
Could not foresee
His mathematical love
Succumb to a political move

K C Yan
Didn't think he can
Churn out some clerihews
Until he knelt on some pews

Who's your "mathematical idol" (dead or living)? Why not formulate some clerihews about him or her? And share them with the rest of us.

Eves, H. (2003). Mathematical circles Vol III: Mathematical circles adieu and return to mathematical circles. The Mathematical Association of America.

© Yan Kow Cheong, February 6, 2011

Why Malaysia is absent at the IMO

2011-01-04T09:30:00.000-08:00

Those of us in South East Asia would have conspicuously noticed that neighboring Malaysia is absent at all International Mathematical Olympiad (IMO) meets. Not that they are afraid to under-perform, but simply because Malaysian matheletes aren't allowed to take part in these international math competitions due to politics or race. Years ago, I recalled reading in a journal published by the Malaysian Mathematical Society (MMS) when they openly and courageously revealed that racial or/and political reasons were behind their not sending their best students to take part in any of these IMO’s every year.

Bumiputras Rule

It's an open secret that in Malaysia the majority Malay students lag behind educationally, as compared to their Chinese and Indian counterparts. And even the government acknowledges that Malay students are under-performing in both mathematics and science. That there has to be a corrective action policy — privileges given to the bumiputras (peoples of the land) — testifies to the educational and economic gaps between the majority Malays and the other races.

The Chinese control the economy of the country, and it isn't surprising that the majority Malays aren't comfortable with this economic imbalance. Feelings of envy and jealousy aren't uncommon among many local Malays who feel alienated or marginalized because of limited job and career opportunities as a result of their lower educational levels.

Malaysia isn't a Chinese but an Islamic nation

Imagine five Malaysian-born Chinese mathletes were to represent a country of predominantly Muslim citizens at the IMO. The world may just think that Malaysia is predominantly Chinese, and that may not augur well with the Malay community which has been lagging behind the other racial communities in education for decades, particularly in science and mathematics. Indeed, it reflects badly on the Malay leaders and politicians. The result is gifted or talented math students are barred from competing in international competitions because of race or politics.

Although many better-off Malaysian Chinese students do their studies in neighboring Singapore, they still wouldn't be able to represent their country of adoption at the IMO, as they're mostly permanent residents, especially for those who are on an ASEAN scholarship. Their citizenship simply prevents them from taking part in those international competitions.

A lose-lose outcome

No statistics are publicly available to prove it, but it's not uncommon to find many bright math students among Malaysian and Indonesian Chinese, who are studying in Singapore schools. Many had left their country of birth for a better education and some would easily be recruited in an Olympiad math team. On one hand, politics prevents them to represent their country of birth at the IMO; on the other hand, nationality bars them to represent their country of adoption. It's a lose-lose situation for these talented or gifted mathletes.

Singapore says NO to race-based politics

A similar scenario was averted in predominantly Chinese Singapore, where the national football team consists mainly of Malays. Singapore would be foolish to let race prevail although a team representing a racial mix would have been preferred, considering that the majority Chinese are doing well in other areas. But that hasn't deterred the Singapore government or the local sports council to field the best Malay footballers to represent the country. Meritocracy and ability cannot substitute race and politics, when it comes to representing the country in athletics and games, much less in mathematics and science competitions.

Malaysia at its first IMO?

We can only hope that in a-not-too-distant future Malaysian political leaders wouldn’t let race and politics to interfere with education. Every child should be given the opportunity to pursue his or her educational goals to the best of his or her abilities — and this includes being able to take part in an IMO if their God-given mathematical abilities endow them to do so.

When race or politics stands in the way of one’s mathematical advancement, the world has a responsibility to intervene (or even interfere) to stop political or religious race-based leaders from thwarting the educational progress of a child.

© Yan Kow Cheong, January 4, 2011

52 Ways to Become a Zero Hero

2010-11-18T22:30:00.000-08:00

Not too long ago, even the Catholic Church banned the use of zero, blaming it as some Godless number. Today, in some religious or philosophical quarters, zero is still associated with some abyss, hell, or nothingness. And in mathematical circles, it took a while for mathematicians and scientists to treat zero just like the other nine numerals – indeed, zero was the last one to gain its rightful citizenship in the number system.

Despite zero’s early struggle to be recognized before it was eventually immortalized, how could we, mathophiles and mathophobes, play our part in promoting the idea that zero is not nothing, but something?

Here are some yearlong activities you may promote and pursue to elevate Zero to a Hero. Who knows? You may turn out to be a zero celebrity!

52. Buy a lottery with the four digits 0000, thus increasing your chances of probably being the sole winner.

51. Solve some math problems with zero clothes (in the privacy of your home), and get to share your aha! moments with your mature students.

50. Be part of a “Zero Tolerance Week” – no complaining or swearing for 24/7.

49. Solve the zeros (or roots) of some quartics (polynomials of degree 4) at a fast-food outlet, or while you are lining up in a supermarket.

48. Write some graffiti about zero, which would likely be a talking-point among geeky pedestrians during lunchtime or at pubs.

47. Call a dozen people with a phone number containing five or more zeros, and unearth any possible correlation between choice of digits and superstition.

46. Work out how many seconds you have left to live in standard form, and make every second count, before your last heartbeat.

A DIY Shirt

45. Wear a T-shirt with the words, “Zero is my hero!” and jot down the facial expressions of onlookers.

44. Tweet or blog about a stereotype on zero: “The rich are dispensers of zeros!”

43. Depict the imagery of some imaginary zero god, drawing people to “zero worship” instead of “hero worship.”

42. Write a novelette entitled, “The Naked Zero” or “A Tale of Zeros.”

41. E-mail a proverb or aphorism about zero to 100 friends, such as “Nothing ventured nothing gained,” and summarize their common responses in a pie.

40. Review 10 books on or about zero, and compile them into an e-book, entitled The Savage Truth About Zero, to be downloaded free of charge.

39. Write an anti-virus program that afflicts PC users with dates ending with a zero.

38. Count down to everything, NASA-style – from praying to playing to paying.

37. Call anyone you meet in the street a zero – a Zero Ridicule Day.

36. Create an optical illusion or random-dot stereogram about the number zero.

35. Imagine a world sans zero and write about its potential benefits.

34. Be a zero-schizophrenic, by zeroing on anything with nil, nought, and naught.

33. Be an advocate of the Zero Defect Movement – zero accidents, zero casualties, and so on.

32. Sponsor obituaries of strangers with zero heartbeats, who left zero savings for the family.

31. Give or ghostwrite eulogies of people with zero heartbeats, who used to issue or give away checks with no fewer than five zeros.

30. Send a month of problems to the Mathematics Teacher with all answers zero.

29. Give away a million seconds of your time to charity every year (about 34 days of 8 hours) at zero costs.

28. Google “zero,” and compile a list of most-visited sites, which reveal some odd behaviors of the numerical troublemaker.

27. Borrow some books on “Nothing” or “Nothingness” and annotate them to lure readers to borrow one of them.

26. Write a features article on a football match that ended in a 0-0 bore-draw.

25. Imagine what would happen if there were a zero year: 1 BC, 0, 1 AD.

24. Meditate on nothingness, then compose some Zen-like inspiration messages.

23. Publish a book with all blank pages – a revised edition of The Nothing Book for the third decade of the new millennium, or create a cottage industry with zero-texts titles such as “What Men Know About Women,” What Men Know about Aliens,” and the like.

22. Popularize a series of Christmas lectures, christened Zero-Lite, to an often-innumerate or mathophobic public.

21. Compose jaws-dropping limericks and haikus about the number zero.

20. Write and mail checks of zero dollars to 100 friends, then expect the unexpected from them.

Shot taken from a train's ad

19 Organize a Zero Festival to humanize the beauty and power of zero.

18. Run a campaign to educate the public about corporations and retails outlets, which are out to lure the public into falling into the "zero syndrome” trap: zero interests, zero down payment, zero fats, ....

17. Plan a Math Carnival with Zero as the theme for the month.

16. Explain to an eight-year-old why a point has zero dimensions.

15. Persuade decision makers in your faculty to add a few zeros to the budget for “zero” research, such as on the Zero Option, to commemorate or recognize the contribution of zero to humankind.

14. Recount the aftermath (pain, casualties, atrocities) of the Cambodian people when Kherme Rouge changed the calendar back to Year Zero, as part of a Multicultural Math elective in a college quantitative literacy course.

13. Preach on the costly or deadly consequences of disobeying the eleventh commandment: Thou shalt not divide by zero!

12. Come up with ten creative ways to help a mathematically challenged public for often mistakenly taking the letter “O” for the numeral “0.”

11. Set up a Facebook page for fans of the “Zero Fiends.”

10. Advocate a zero-tolerance policy for drugs and debts among disadvantaged kids and hardcore gamblers in poor neighborhoods.

9. Conduct public talks to the young that they and their offspring wouldn’t be paranoid of millennium years: 2000, 3000, ….

8. Promote the idea of zero pets at food courts and shopping malls as a sign of good hygiene.

7. Be a Carbon Hero, by embracing a “carbon zero” lifestyle, by using public transport and ordering e-books.

6. List down no fewer than ten sociological or psychoanalytical uses of zero.

5. Set a 2020 goal of achieving near-zero innumeracy as an educational goal among elementary school students.

4. Start a Zero Digest zeroing on the mathematical, philosophical, and spiritual zero, and place advertisements as a way to reduce the price to $0.00.

3. Come up with a number of rebuses related to the number zero or expressions about zero.

2. Campaign for a zero-situational-ethics working environment.

1. Follow K C Yan on Twitter as @Zero_Math and share your “zero” tweets with the zero-math brethren.

The Lighter Side of Singapore Math (Part 2)

2010-09-25T06:30:00.000-07:00

In Praise of Models

A K-8 Sample of Singapore Math Questions

Grade 1
Use the [Singapore] model method to show that (a) 2 + 3 = 5, (b) 9 – 4 = 5.

Grade 2
Use a model to show that 3 × 6 = 6 × 3.

Grade 3
Use a model to show that ½ × ⅘ = ⅖.

Grade 4
Use a model to show that 2 ÷ ⅖ = 5.

Grade 5
Use the model method to evaluate the value of 3½ × 4⅚.

Grade 6
Use a model diagram to show that the infinite series converges to a finite number.

½ + ¼ + ⅛ + ⅟₁₆ + ... = 1

Grade 7
Use a model to show that (2x)² is not equal to 2x².

Grade 8
Use a model method to solve these equations.
(a) x² – 3x (b) x² + 3x + 5 = 0

Singapore World Records

Most participants in a ribbon-cutting ceremony (3,238)

People wearing balloon hats at one time (1,491)

Most people caught jumping queues at one time (?)

The first (or fastest) one to board a train at a newly open train station (? sec)

Most number of people solving a word problem using the model method (n!?)

The world's gigantic math model cut on grass (?)

Wittgenstein’s Ghost

Math educator: Let one unit represent the number of Singapore Math books.

Homeschooler: But, Dad, suppose one unit doesn’t represent the number of Singapore Math books.

New math titles in the pipeline

1. The Singapore Model Method for Those with Zero Sight
[By a Singapore-born blind math educator]

2. A Bluffer’s Guide to the Singapore Model Method

[Pending approval from the Censorship Board of Adult Education]

3. Singapore Math for SENIORS

[A CHRISTmaths gift for grandparents & godparents]

4. China Math vs. Singapore Math: Which is Better?

[Does this include Taiwan Math?]

5. Singaporeanizing Math
[What on earth is that?]

An Evolution of Grade 5/6 Singapore Math Word Problems

Teaching Math in 1970 (Traditional Math)

Mr. Yan has three cows and eight chickens. How many legs are there altogether? [Ask a next-door neighbor for the answer.]

Teaching Math in 1980 (Model Method)

Mr. Yan has twice as many cows as chickens. If there are 64 legs in all, how many cows are there? [Ask a neighborhood school teacher for the answer.]

Teaching Math in 2000 (Problem Solving)

Mr. Yan has cows and chickens. If there are altogether 28 legs, how many chickens and how many cows are there? [Ask a full-time tutor for the answer.]

Teaching Math in 2010 (Challenging)

Mr. Yan has almost twice as many chickens as cows. The total number of legs and heads is 184. How many cows are there? [Answer a math coach, or a volunteer from the Ask Dr. Math Website.]

The Core of the Singapore Math Student

What the most-disliked subject means for the average or above-average Singapore student (in spite of TIMSS):

K1-K2: Math is a lore.

Grades 1-2: Math is a score.

Grades 3-4: Math is a bore.

Grades 5-6: Math is a chore.

Grades 7-10: Math is a sore.

Grades 11-12: Math is no more.

Nine Daffynitions of 999

2010-09-02T23:16:00.000-07:00

Anyone of you ever thought of dialing 999 for help in solving some of your elementary math problems? Well, you never know! There might be some bored police personnel on night duty longing for a change in handling the usually boring calls related to ambulance, fire, and robbery.

In fact, in the name of productivity it's not a far-fetched idea to recruit policemen and women who can also render numerical assistance to their mathematically challenged callers, especially in the middle of the night when there're fewer emergency calls, and when these bored (or boring?) staff tend to doze off often.

Traditionally, a number of developed and developing countries have inherited a mathematically challenged police force. May each country or county be blessed with better-educated police personnel who are confident to handle complex real-life problems, whose solutions often requiring an above-average logical and rational mind.

Here are nine extra-definitional meanings of 999.

9. Police on fire calling for ambulance

8. Police firing at stolen ambulance

7. Police chasing ambulance on fire

6. Ambulance ferrying police on fire

5. Ambulance on fire injuring police

4. Ambulance and police both on fire

3. Police in stolen ambulance on fire

2. Police looking for fired ambulance

1. Fired police in ambulance on fire

What's your definition (or daffynition) of 999? Share yours with the rest of us.

Nitely yours

© Yan Kow Cheong, September 2, 2010

The Abacus as a Divination Tool

2010-08-26T19:03:00.000-07:00

For generations of Chinese traders and shopkeepers, the abacus (called suanpan) has been an indispensable tool for calculation and for finding the financial health of their business – the profit and loss of their trade.

Two Chinese and two Japanese abaci

Less well known is that the suanpan is also used as a divination tool among many Chinese migrants. If you go to Chinatown today, you can still see old folks (who are usually the owners of their businesses) strike the beads of their abacuses before opening their shops in the morning. Striking the abacus is perceived to be a good omen: This primitive calculator will be used often throughout the day, indicating brisk business. And the louder they strike the beads, the better the business.

The choice of the beads (sizes, shapes and types) matters. The common beads are made of wood, stone, silver or gold, each serving a different purpose. For example, some beads are chosen as they allegedly help to secure a faster job promotion, while others to gain health and wealth.

Moreover, the placement of the abacuses (or abaci) at home or in the office is important to ensure that there is no bad feng shui (meaning “wind and water” in Chinese). Furthermore, the positioning of the abacus also changes with each Chinese zodiac year – twelve animals which repeat themselves every twelve years.

A 4 cm by 2 cm Soroban

Some years ago, I bought a small key chain that comes with a tiny golden-looking soroban (Japanese abacus). It never occurred to me then that this little ornament could serve as a divination tool for good luck. Today, it is not uncommon to see souvenir shops selling abacus-pendants (silver or gold bracelets, earrings, and the like) – some kind of amulets to thwart off any evil spirit, or some divination tool to attract success and prosperity.

So, the next time a friend gives you an ornament that comes with a cute-looking abacus as a gift, think twice before wearing it. You may unknowingly be the recipient of some superstitious or irrational belief that good luck is yours to come; or worst, if it's from some fiend or foe, you could be under the curse of some object of worship.

For reflection

0. How would you reason with (or respond to) someone who faithfully believes that abacus-pendants are to be worn for good omen?

1. Give five reasons why people use the abacus as a symbol of prosperity and wealth.

2. What are some dangers in using the abacus as a divination tool?

3. How can you educate the public that wearing abacus-pendants as a sign of good omen will only promote pseudoscience and innumeracy?

For Mathepreneurs ONLY

1. Design an abaculator.

2. Improvise a solar-powered soroban.

3. Invent an electrified suanpan.

Aptitude Test for Math Editors

2010-08-11T21:55:00.000-07:00

Senior and managing editors in local publishing houses have always lamented how hard it is to recruit decent mathematics editors, because CV’s and interviews often fail to filter the good from the mediocre candidates. On the other hand, few senior editorial staff dare to look in the mirror to see whether they themselves have what it takes to mentor or guide their editors. There is a Chinese or Japanese saying that says: "An editor shames her managing editor." The less-than-desired-quality of a published math book often reveals much about the competency of those behind its production.

Many years ago, I suggested administering a quantitative test to shortlist potential math editors interested in making publishing a career, in the hope that this may help reduce the relatively high attrition or casualty rate in the industry.

Below is a sample of questions we may pose to applicants keen on becoming word doctors in charge of mathematics titles, up to pre-university level.

A Test to Identify Math Editors

1. A writer approached two publishing houses for a manuscript she recently completed. The royalty rates are as follows:

Publisher Royalty rate

A 10% published price

B 12% net price

Net price is the price after 40% discounts to the bookstore.

(a) Which publisher should she choose?

(b) Another writer wants to know what percentage of the net price from Publisher B would yield a royalty equal to the published price from Publisher A. What percentage will this be?

2. Two publishing houses have the following mode of payments:

Publisher Mode of payment

X $5000 + 5% royalty on published price

Y 8% published price

Which publisher gives a better deal?

3. Due to the many errors in a geometry book, a printer had to replace pages 28, 29, 109, 130, and 131. How many sheets of paper did the editor have to reprint?

4. Mathematics Digest, which has a special 16-page feature in the middle, is incomplete. The third page of the supplement (page 15 of the newspaper) is missing. What other pages must also be missing?

5. Four pages of one section of a newspaper are missing. One of the missing pages is 13. The back page of this section is 40. What are the other three missing pages?

6. When asked by her editor to add the page numbers of the section on Random Numbers he wrote, Mr. Goon said it was either 216 or 256. Which was it?

7. Ricky tore out several successive pages from an algebra book. The number of the first page he tore was 143, and the number of the last page is written with the same digits in some order. How many pages did Ricky tear out of the book?

8. The middle sheet is removed from a manuscript, handwritten on both sides of the paper. If the two sides are numbered 6 and 7, how long is the script?

9. Pages 6 and 19 are on the same double sheet of paper. How many pages does the newspaper contain?

10. A 60-page newspaper, which consists of only one section, has the sheet with page 7 missing. What other pages are missing?

Time limit: One hour 45 minutes for foreign applicants, or two hours for Singapore citizens and permanent residents.*

If 75 percent were the passing mark for the above quiz, what would be the probability that half of the applicants who took the test would be shortlisted? How many could be considered a true-blue math editor or senior editor?

Two Standard Deviations from the Norm

In recent years, one recurring complaint among seasoned and prospective writers in academia and in schools, keen to write fertile math titles, is that we lack the local expertise or know-how in publishing quality or decent math titles other than locally approved school textbooks and workbooks. In fact, current editorial standards seem to be one or two deviations from the mean, as compared to what they used to be in the nineties.

The future of publishing decent math titles other than school textbooks looks uncertain, to say the least, as fewer ex-teachers are joining the publishing industry due to better job opportunities in other industries, where pay and promotion are much more attractive. Besides, there are few role models for novice editors to emulate should they choose to make publishing a career. Few math majors, if any, are in charge of math titles these days, and the editorial standards in a number of local small publishing houses (which churn out assessment titles like they're selling iPhones) leave much to be desired.

Self-publishing on the Rise

Across the industry, editors' weak mastery of math concepts and poor linguistic skills would only aggravate an already-declining editorial quality of math titles. Most proofread instead of edit, or simply take care of the grammar instead of rewrite. In recent years, it isn’t surprising to witness many writers and authors switching to self- or vanity publishing, because few writers and teachers believe that there will be added value to their manuscripts, other than cosmetic improvements, going by the influx of assessment or supplementary titles inundating the local market every year.

A Third-class Industry in a First-class Economy

A common-sensical step in addressing the often-decried “Singapore-has-a-third-class-publishing-industry-in-a-first-class-economy” issue for its educational titles is to bring in better editors on board the editorial ship, or to recruit foreign talents who have worked no fewer than three years in established foreign publishing houses. Because little attention is given to the pay and remuneration, and to the opportunity to upgrade oneself professionally, the dearth of decent [math and science] editors isn't likely to reverse any time soon. A lack of passion and professionalism seems to be the currency of many editors these days.

Singapore, a Publisher of Choice

As Singapore aspires to become a key player in math education publishing, local houses can’t afford to have math editors with an average knowledge of the subject matter and a below-average command of the English language. Having math editors with a mastery of the subject matter and a working fluency of linguistics isn’t an option if the country wants its math titles to graduate from a third- or second-class quality to match its first-class economy. And producing quality math titles other than school textbooks is the first sign or step to position Singapore in becoming an Asian publisher of choice in producing first-class math and math education titles.

* This apparent inequality is in line with the recent government's policy that Singaporeans come first, especially when it comes to providing jobs for locals and foreign residents.