Thousands of students around the world celebrate Pi Day today, but local math students in Singapore can only dream of being part of this annual mathematical event. Singapore math students, teachers, and parents don’t (and can’t) celebrate Pi Day, as long as they officially follow the British style of writing their dates (DD/MM/YY).
What makes matters worse is that this year, Pi Day falls on the first day of the one-week school break, which makes it almost impossible for hardcore math teachers, who want to buck the calendrical trend, to get their students excited about the properties and beauties of the number Pi.
Until Singapore switches to the American style of writing dates (MM/DD/YY), which may not happen, at least during my lifetime, however, this shouldn’t prevent us from evangelizing the gospel of Pi among the local student population.
Here are seven e-gifts of the holy Pi, which I started musing about 314 minutes ago on this Pi Day.
Christmas is a golden and joyful opportunity for number enthusiasts and math geeks to sharpen their creative mathematical problem-solving skills.
Here are 12 CHRISTmaths cookies that may help you shake your brain a little bit in the midst of Christmas festivities.
Warning: Refrain from forwarding this post to relatives or friends living in countries, which are intolerant of Christmas and Christianity, such as Brunei, Saudi Arabia, and Somalia, as it’s haram for “infidels” to take part in any kind of Christmas celebrations. And I assume that includes reading any on-line materials deemed un-Islamic or un-Mohammedan, which might lead believers astray from the faith.
1. Unlucky Turkeys
Estimate the number of turkeys that make their way to the supermarkets every year.
2. A Xmas Candy
Mary wanted to buy a candy that costs 25 cents. A dated vending machine would take one-cent, five-cent, and ten-cent coins in any combination. How many different ways can she use the coins to pay for the candy?
3. The Dimensions of a Cross
A square of side 25 cm has four of its corners cut off to form a cross. What is the perimeter of the cross?
4. The Number of Crossings
Two lines can cross one time, three lines three times, four lines six times, and five lines ten times. If there are 25 lines, what would be the maximum number of crossings be?
5. An Eco-Xmas
If all instances of the word “CHRISTMAS” were replaced with “XMAS,” how much ink and paper (or Xmas trees) could you save every year? How much money could be channelled back to feeding the poor and the hungry during the festive season?
6. Number of Xmas Cards
In an age of Xmas e-cards and video cards, how many Christmas greetings cards are still being sent worldwide? How many trees are being saved every festive season?
(a) Without a calculator, how would you verify whether the number 25! has precisely 25 digits or not.
(b) Which positive integers n (other than the trivial case n = 1) for which n! has exactly n digits?
8. Xmas Trees
Guesstimate how big a forest would 25 million Christmas trees occupy.
9. Folding papers
Fold a single piece of paper perfectly in half, from left to right. How many creases will there be after the 25th fold, when you continue folding so that all the rectangles are folded into two halves each time?
10. Pre-Xmas Tax
Imagine Singapore were to implement a pre-Christmas tax on all kinds of Christmas marketing before the first week of December. Estimate how many extra million dollars would the Income Tax department collect every festive season.
11. A Xmas Quickie or Toughie
What is the sum of the last two digits of 1! + 2! + 3! +⋯+ 24! + 25!?
12. An Ever-Early Xmas
Show that as one celebrates more and more Christmases (or, as one gets older and wiser), Christmas seems to come earlier every year.
Gould T. (2013). You’re all just jealous of my jetpack. New York: Drawn & Quarterly.
Math educators, especially stressed [often self-inflicted] local teachers in Singapore, are always on the look-out for something funny or humorous to spice up their oft-boring math lessons. At least, this is the general feeling I get when I meet up with fellow teachers, who seem to be short of fertile resources; however, most are dead serious to do whatever it takes to make their teaching lessons fun and memorable.
It’s often said that local Singapore math teachers are the world’s most hardworking (and arguably the world’s “most qualified” as well)—apparently, they teach the most number of hours, as compared with their peers in other countries—but for the majority of them, their drill-and-kill lessons are boring like a piece of wood. It’s as if the part of their brain responsible for creativity and fun had long been atrophied. A large number of them look like their enthusiasm for the subject have extinguished decades ago, and teaching math until their last paycheck seems like a decent job to paying the mortgages and to pampering themselves with one or two dear overseas trips every other year with their loved ones.
Indeed, Singapore math has never been known to be interesting, fun, or creative, at least this is the canned perception of thousands of local math teachers and tutors—they just want to over-prepare their students to be exam-smart and to score well. The task of educating their students to love or appreciate the beauty and power of the subject is often relegated to outsiders (enrichment and olympiad math trainers), who supposedly have more time to enrich their students with their extra-mathematical activities.
Singapore Math via Humor
A prisoner of war in World War II, Sidney Harris is one of the few artists who seems to have got a good grasp of math and science. While school math may not be funny, math needn’t be serious for the rest of us, who may not tell the difference between mathematical writing and mathematics writing, or between ratio and proportion. Let Sidney Harris show you why a lot of things about serious math are dead funny. Mathematicians tend to take themselves very seriously, which is itself a funny thing, but S. Harris shows us through his cartoons how these symbol-minded men and women are a funny awful lot.
Angel: “I’m beginning to understand eternity, but infinity is still beyond me.”
Mathematical humor is a serious (and dangerous) business, which few want to invest their time in, because it often requires an indecent number of man- or woman-hours to put their grey matter to work in order to produce something even half-decently original or creative. The choice is yours: mediocrity or creativity?
Humorously and irreverently yours
Adams, D. S. (2014). Lab math. New York: Cold Spring Harbor Laboratory Press.
Harris, S. (1970). What’s so funny about science? Los Altos, Ca.: Wm. Kaufmann, Inc.
Check out an inexpensive (but risky) way to make a Singapore math lesson less boring: The Use of Humor in Mathematics. The author would be glad to visit local schools and tuition centers to conduct in-service three-hour math courses for fellow primary and secondary math teachers, who long to bring some humor to their everyday mathematical classrooms—as part of their annual 100 hours professional upgrading. Please use his e-mail coordinates on the Contact page.
Based on the average number of questions contained in an assessment (or supplementary) math book these days, it can be estimated that most students in Singapore would have solved some seven thousand math questions by the time they had graduated from elementary school. Indeed, an awful lot, to say the least.
I try to understand why local math writers feel that they’ve to provide such an unhealthy number of these drill-and-kill questions or routines for students to practice. Surely, their publishers are behind this “numerical obscenity,” arguing that many kiasu parents would feel that they’re buying a value-for-money book. Imagine the emotional or psychological harm it could do to a child who barely has any interest in the subject.
Even for those with a fluency with numbers, wouldn’t a thousand (or even half of that number) questions bore them to death? Many would end up getting a distorted picture of what elementary math is all about—imitate-practice-imitate more-practice more.
The Junk Food of Singapore’s Math Education
Drill-and-kill math questions are like the junk food of math education. Every now and then, we all visit these fast food outlets, but to grow up on a diet that consists mainly of burgers, French flies, and Coke for most days of the week, that can only be a good recipe for unavoidable obesity and all sorts of preventable diseases that would pop up sooner than later. Likewise, over-exposing students to these math drills would only produce an army of drill-and-kill specialists, who wouldn’t be able to think critically and creatively in mathematics—and later in life.
The Baby [Math] Gift for Singapore’s Jubilee
For Singapore’s Golden Jubilee, when the nation celebrates its 50th year of independence in 2015, other than giving items like a special medallion, a multi-functional shawl, and a set of baby clothes, one of the suggested gifts by the mathematical brethren to be given to Singaporean babies born next year should be a check amounting to not less than a thousand bucks. This would help defray the average cost incurred by parents who would need to buy those elementary math supplementary titles during the child’s formative years—it’s a rite of passage for every child studying in a Singapore government school to expose himself or herself to these drill-and-kill questions. Even if parents are opposed to these math drills, school teachers or tutors might still recommend the child to buy one!
Drill-and-Kill Specialists or Innumerates
Of course, it’s better to produce tens of thousands of drill-and-kill specialists than an army of innumerates. In the short term, this raises the self-esteem of the children, as they feel that they can solve most of these routine questions, by parroting the solutions of the worked examples. We all learn by imitation, but at least the questions need to slowly move from routine to non-routine. We can’t afford to have hundreds of questions that test the same skills or sub-skills almost without end. We need a balanced percent of drills, non-drills, and challenging questions—not a disproportionate unhealthy number of drill-and-kill questions, which would only affect our long-term mathematical health.
The Good Part of Drill-and-Kill
One good thing about these wallet-friendly drill-and-kill math titles is that they can easily replace a lousy or lazy math teacher, or even a mathophobic parent. After all, we can’t expect too much from a mathematical diet that could help sustain (or even strengthen) us for a while. At best, they’re like Kumon Math, which subscribes to the philosophy that more practice and more drill could eventually help the child to become self-motivated, and to raise his or her self-esteem in the short term.
Are You a Disciple of Drill-and-Kill?
If mathematical proficiency is credited to be achieved through practice and more practice, would you buy a few of these math practice titles for your child? Or, as a teacher or tutor, would you recommend one for your student or tutee? Don’t you think that this is a case of “more is less”? Could the child end up being mathematically undernourished when it comes to creative problem solving and higher-order thinking? Or maybe the child could even be numerically constipated by an overdose of these drill-and-kill questions?
In my formative years, I don’t recall any elementary school teachers sharing some mathematical puns with us. I suppose that the arithmetic of yesteryear was often taught in the most uninteresting way by many who probably didn’t look forward to teaching it to a bunch of noisy kids.