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Singapore Math

Wednesday, October 15, 2014

Stamping Up Singapore Math


Even if you are just an amateur stamp-collector, much less a professional philatelist, it won’t take you long to realize that not many people in this world are fond of collecting Singapore stamps, as compared to, say, stamps issued by other countries.

SingPost seems to have somewhat cheapened the value of Singapore stamps, by issuing First Day Covers, as if they're selling parking coupons—Singapore issues, on average, a dozen sets of new stamps every year.

Semi-circle stamps of yesteryear

In general, most Singapore stamps have an uninteresting theme or design; SingPost's commemoratives seem to have been issued more as a means to generating extra revenue from stamp collectors, with little attention paid to aesthetics and beauty.


Numeracy via Singapore Math Stamps

In general, although philatelists don't have a positive view of Singapore stamps, however, not all is bleak for our postal department. To promote mathematics and mathematics education in Singapore, in particular Singapore’s mathematical achievements locally and internationally, it wouldn’t be a bad idea if SingPost considers issuing commemoratives with a mathematical flavor. For instance, it can issue First Day Covers on the following themes:

· A set of three stamps featuring Singapore’s triple firsts at the Third International Mathematics and Science Study (TIMSS), which has since put Singapore on the Mathematics Education World Map—an economic by-product of this would be to produce more localized adaptations of Singapore math textbooks, hopefully from some politically unstable, resources-rich developing countries;

· Another set of three stamps featuring Singapore’s emphasis on the concrete-pictorial-abstract model in primary (or elementary) school mathematics, which arguably has contributed to our students’ better understanding of mathematical concepts, especially when it comes to solving word (or story) problems;
                                                       
· A set of stamps highlighting Singapore’s model (or bar) method, which has prematurely empowered tens of thousands of local pupils to solve nonroutine and challenging word problems, which traditionally used to be set only at the secondary (or middle-) school level;

· A set of stamps depicting famous (dead or living) Asian (or Singaporean) mathematicians and mathematics educators—few as they may be—who have contributed much to raising the mathematical standards in Asia;

· A set of stamps celebrating special Math Days like the AbacusDay, Statistics Month, Metric Week, and Pi Day;

· A set of stamps debunking Asian superstitions, myths, and legends, related to annual festivals like the Lunar Seventh Month (or Ghost Month); or exposing pseudoscientific beliefs involving so-called auspicious and inauspicious (or lucky and unlucky) numbers, feng shui numbers, and I Ching;

· A set of stamps on the different types of abacuses, including those used in divination and superstition;

· A set of stamps featuring magic squares used by Asians in numerology and astrology;

· A set of stamps featuring Asian achievements in mathematics, whether at the International Mathematics Olympiad (IMO) or in regional contests and competitions;

The pentagonal framework defining
Singapore's math curriculum
· A set of stamps featuring the five components of the mathematical problem-solving model (attitude, metacognition, processes, concepts, and skills), which forms the framework of the mathematics curriculum in Singapore;

· A set of stamps featuring the most commonly used (or misused or abused) heuristics (e.g., draw a diagram, make a list, guess and check, look for patterns, work backwards) and some artificially forced thinking skills (e.g., classifying, comparing, sequencing, identifying patterns and relationshipsanalyzing parts and whole, induction, deduction, spatial visualization);

· A set of stamps commemorating the Singapore's Ministry of Education (MOE) visions:
1998: Thinking Schools, Learning Nation
2006: Teach Less, Learn More
2014 and beyond: ?!?!


Glocalizing Singapore Math via Philately

To promote an interest and appreciation of Singapore's (or Asia's) mathematical history and heritage in philately, traveling exhibitions may be held locally and regionally. For instance, rare philatelic gems such as mistakes, fakes, and forgeries—how mathematics can help detect forgery and fraud in philately—may be showcased.

So, issuing Singapore stamps with a mathematical flavor would go a long way to marketing and glocalizing Singapore math, while recognizing the contribution of local math educators, on leveraging the power of mathematics to help alleviate poverty, or lessen the economic gap between the haves and the have-nots. Let’s stamp mathematics firmly on Singapore postage stamps—glue is halal. Stamp up, Singapore!


For further reading
Wilson. Robin J. (2001). Stamping through mathematics. New York: Springer-Verlag.


© Yan Kow Cheong, October 15, 2014.

Friday, July 11, 2014

The Mathematics of 7Eleven®


The chain of 7–11 convenient stores is so called because these family-friendly outlets used to be open from 7:00 a.m. until midnight, but now they're open all the time in the least expected locations: 24/7/365. 

Other than munching and gulping at odd hours at 7Eleven stores, these franchise outlets also provide a fertile ground for math educators to come up with some creative math questions to enhance their students' mathematical problem-solving skills. Here are a sample of eleven non-routine elementary and middle-school math questions that may appeal to your students.


With prizes ranging from games t-shirts Oakley sunglasses figurines autographed posters and...
7-eleven.com
1. Number of Convenient Days 

In the U.K., 7/11 is abbreviated as 7th November; in the U.S., 7/11 is written as July 11. How many days are there from the U.S. date to the U.K. date?


2. The Recurring 711

What fraction represents the recurring (or repeating) decimal 0.711711711…?


3. The Day of the Week in 711 Days 

If 7/11 (July 11 in the United States) is a Friday, which day of the week was 7/11 in 2011? What day of the week will it be 711 days from now?


Clock 7:11
Source: Clipart ETC



4. The Acute Angle at 7:11


What is the angle between the minute hand and the hour hand at 7:11?





5. The Likeliest 7/11 Day of the Week

Which day of the week is 7/11 most likely to fall in a 400-year calendrical cycle?


6. Tangram-izing 7/11


Use three sets of the seven-piece Tangram to form the numerals 7 and 11.


7. Number Freaking 7/11

(a) Estimate the average revenue generated by all 7Eleven outlets in the United States every day.

(b) What land or area space is occupied by all 7/11 convenience stores in the world?


8. Are There 711 Digits or More?

How many digits do these indexed numbers have? (a) 711 (b) 7711


9. The 711th Digit Is…

What is the 711th digit of the decimal expansion in the reciprocal of 711?


10. 7Eleven Are Closed …

7Eleven outlets are open 24/7/365. However, on a few occasions some stores had to be closed. Suggest some possible reasons for the closure of these convenient outlets.


11. What Are the Prices in 7-11?

Mr. Yan went inside a 7–11 store and selected four items. When he reached the counter to pay for the goods, the cashier took his calculator, pressed a few buttons and said: "The total price is $7.11."

Mr. Yan replied, "Are you sure? Do I have to pay $7.11 because the name of your shop is 7–11?"

The half-embarrassed cashier answered, "Of course not! I've multiplied the prices of these four items and I've just given you the total."

The puzzled Mr. Yan laughed and said, "Why did you multiply these numbers? You'd have added them to get the total price!"

The cashier said, "I'm sorry; I've pressed the wrong button!"

The cashier then repeated all the calculations, by adding the prices of the four items, and to his surprise, the total was still $7.11.

What are the prices of these four items?





Selected Answers

1. 120 days

2. 79/111

3. (i) Monday (ii) Tuesday.

4. 149.5°

8. (ii) 601 digits

9. 9


10. $3.16, $1.25, $1.20, $1.50.


References
Michalewicz, Z. & Fogel, D. B. (2004). How to solve it: Modern heuristics. New York: Springer-Verlag.
Yan, K. C. (2011). Christmaths—A Singapore math creative problem solving title. Singapore: MathPlus Publishing.

© Yan Kow Cheong, July 11, 2014.


Postscript: This writer isn't sponsored in any way by the 7Eleven brand to write this blog article. However, he won't turn down any cash donations or vouchers, if his e-article has helped challenge and benefit tens of thousands of 7Eleven math fans around the world.

Friday, June 13, 2014

13 E-Cards Worth Sending on a Friday the 13th

Here are 13 lucky e-cards (stolen with zero acknowledgements on social media) you may wish to send to triskaidekaphobic or semi-superstitious friends, fiends, or foes on this most unluckiest day of the calendrical year.



























Why not make your own Friday the 13th e-cards, and share them with the mathematical brethren? Happy Friday the thirteenth!

Superstitiously yours


References

Yan, K. C. (2013). 13 Math Tidbits on Friday 13. Singapore Math, Dec. 13, 2013.

Yan, K. C. (2013). Hungry Ghosts Don't Do Singapore Math. Yan's One Minute Math Blog, Oct. 12, 2013.

Yan, K. C. (2012). Halloween MathSingapore Math, Oct. 31, 2012.


© Yan Kow Cheong, June 13, 2014.