Mortal Math

Photo © Anon.

Few would disagree that the above math or science question has now gained deadly relevance or importance in this year’s cruel summer, especially during this week’s abnormally hot weather.

EcoMath 4 Everyone

Is it apt for math teachers to use this week’s extreme weather condition plaguing some parts of the planet to help some middle-school students brush up their Celsius-Fahrenheit conversion skills, and to challenge them with some real-world problems in the aftermath of climate change? 

A typical grade nine (or secondary three) ecomath question is the following:

On a certain day, the Celsius thermometer and the Fahrenheit thermometer registered the same numerical value for the temperature. Given that 86°F = 30°C and 104°F = 40°C, what was the temperature that day?

Post-Pandemic Holeydays 

Guesstimate how many tourists regret flying to some parts of the US and the EU at this time of the year—when popular tourist attractions are closed during the hottest hours to protect visitors from dehydration or to reduce the odds of their visiting an emergency room.

How much would tourism-related businesses in heat-stricken regions suffer financially this summer?

What percents of unlucky tourists would need to extend their “holidays” due to prolonged heat-related hospital stay?

The Polluters Preaching to the Poor  

Estimate the number of deaths in the animal kingdom resulting from our hotter planet, which is primarily driven by materialistic consumers in the developed world, who now hypocritically want to lecture the developing world about human-induced climate change and to some extent the naturally-occurring weather pattern known as El Niño.

Why should China, India, Indonesia, and other emerging economies listen to the West, which are historically responsible for the dire climatic situation we’re in today? Why must much-maligned totalitarian China and undemocratic others donate to international climate funds set up by “guilty” high-GDP big polluters to help poorer nations struggling with climate change?

With the world paying lip service on cutting down on oil and gas for alternative sources of renewable or clean energy to grow their economies, low yield of crops and the increasing risk of wildfires and floods, not to say, frequent electricity blackouts in poorer or corrupt developing nations, are likely to be the new (new) normal.

Heat Kills

According to the Centers for Disease Control (CDC), more than 700 people in the US lose their lives to extreme heat each year, with close to 68,000 people being sent to emergency rooms.

Guesstimate how many locals and foreigners, especially the homeless, the migrant workers, and the refugees, in all the global regions now experiencing a heatwave would find it hard to avoid a heat-related hospital visit this year. How many of them might fail to cheat death simply because of their helplessness or others’ indifference?

The Dodo Effect

The world has already warmed by about 1.1°C since the industrial era began and scientists forecast temperatures will keep rising unless governments and businesses around the world have the (political or moral) will to cut greenhouse gas emissions.

How many fish in rivers and canals, or seabirds and whales, would disappear or starve thanks to “global warring”? How many animal and plant species are going the way of the dodo in coming years and decades?

Singapore’s First Winter

Way back in 2016, I’d tweeted tongue-in-cheek about Singapore’s experiencing her first winter:

Singapore's 1st Winter: Will fine dining up and more folks aspiring to be middle-class cause Singapore to witness its #Singageddon? #climate (1/25/16)

Fake News: Singapore experienced its first winter this week—tens of thousands of Singaporeans took no-pay leave when the temperature dropped to zero degrees! #climate #humor #zero #winter Source Photo: © Anonymous (1/14/18)

At the current rate in the global rise (or drop) in temperature, the chances of those of us (who’ll be blessed to live beyond the three-scores-and-ten lifespan) seeing snow in Singapore are anything but zero.

Environmentally & morally yours

© Yan Kow Cheong, July 16, 2023.

A Grade 3 Singapore Math Question

Not too long ago, a mother posted the above grade three question on Facebook, and sought help from fellow parents: “Hi all, can anyone advise this P3 qn? Thanks!”

Before you read some of the replies or suggestions below, if you’re a parent or tutor, how would you solve this fraction question (with the mathematical knowledge of an average grade three student)?

A parent’s reply was: “This is a question that wants u to compare the fraction with half. Whichever fraction is smaller than half is the answer.

“To compare against half, take the denominator and divide by 2. If the numerator is less than the divided value, it is smaller than half.”

The mother replied, “蔡锦森 oh ic! Nv thought of that! Gosh, how to explain to a P3 ? 😝”

Another parent or tutor joined in: “So for such questions, there are 2 types. One type requires the student to compare against half. The other is to compare the difference with 1 whole. E.g. Which fraction is closest to 1? 7/8, 3/4, 6/7 etc”

Later, another member commented: “Normalize all the denominators and compare.”

Would you use any of the suggested strategies to solve the problem?

An Apt Question for Grade Three Students? 

In the Singapore math curriculum, the guidelines for elementary school students (or primary school pupils) learning fractions at different grades are as follows:

Primary 2 (Grade 2): Add and subtract like fractions whose sum is less than 1.

Primary 3 (Grade 3): Learn equivalent fractions; add and subtract related fractions whose sum is less than 1.

Primary 4 (Grade 4): Along with improper and mixed numbers; add and subtract related fractions whose sum exceeds 1.

As I’ve zero idea about the source of this test question, I leave it to the reader to decide for themselves whether or not this grade three question is in line with the local syllabus. If not, why? Or do you think this question is somewhat ill-posed?

What If?

Imagine if the same question were to be assigned to a group of grade five students. How would they approach it? 

Would most of them resort to a knee-jerk solution by finding the LCM of the four fractions, before comparing their numerators, rather than thinking whether a less-tedious or shorter method might do the job?

Or would they conveniently convert the fractions into decimals (with or without a calculator)?

The Art of Problem Posing

I wonder whether rephrasing the above question might make it mathematically (or fractionally?) more meaningful for students to apply their knowledge of comparing fractions. Say, what if we asked them to compare a set of fractions vis-à-vis a base fraction like 1/2?

Which of the following fractions is greater than 1/2?

A. 2/5     B. 3/7    C. 6/10     D. 4/9

Again, here too, the aim is to discourage students from religiously applying the fraction-decimal conversion, or from tediously converting these fractions to a common denominator.

At higher grades, we’d use larger fractions that would make finding equivalent fractions painfully tedious or time-consuming.

Meanwhile, may I encourage you to share how you’d tackle this fraction question without adding more pressure on students (who might already be suffering from some form of “fraction trauma” as a result of being subject to premature abstraction and procedural methods)?

Methodically & meaningfully yours.

© Yan Kow Cheong, June 29, 2023.

Is a Pythagorean Ban or Bill in the Pipeline?

Is the above geometry question a “trick” question to check whether the “anti-woke” curriculum censors in some red states are awake or not?

Or just pro-Disney critics trying to poke fun at some pro-DeSantis “math specialists” (or ultra-MAGA patriots and puritan parents), who’re hell-bent to ban any deemed questionable or objectionable math questions that could potentially add unnecessary stress to math-anxious students and their parents?

If a poem promoting national or racial unity could “cause confusion and indoctrinate students,” a nonroutine math question from an alien or foreign source might also inflict twice as much psychological harm to the self-esteem (or mental health) of students who’re not born or blessed with the “mathematical gene.”

In the name of mathematical wokeism, what would qualify as a “worst [math] question”? One that could lead to a temporary mental blackout or a three-second-long stroke?

Or one that would trigger common symptoms like faster heartbeat, sweaty palms, and dry throat, which unspokenly affect all of us to a certain degree, when faced with a time-based brain-unfriendly or fiendish math question?

Should polarized politics or racial puritanism be allowed to triumph over mathematical problem solving and critical thinking? When “holy votes” from a significant proportion of the population dictate the direction of math education, curricular or educational decisions that would benefit the nation would be rarer than perfect numbers.

Questionably & critically yours

© Yan Kow Cheong, June 4, 2023.

Creativity or Stupidity?

This week, I saw this attached (grade one?) test item or math meme on Facebook, which was initially posted by “The Language Nerds” group.

Based on the multiple comments to this ill-posed math question, it’s amusing, yet also disturbing, to read that most responders are praising the student for his “creative” answer, or criticizing the “uncreative” teacher for penalizing the poor child.

In this postmodern or polarized world we’re living in, you’d think that maybe only someone who’s a “very stable genius” would rationalize or argue that the student’s response qualifies as one of the equally valid answers. And if the biased teacher insisted on marking the creative child wrong, the parents might consider suing him or her for giving their son an undeserved zero.

Creative or Uncreative Comments

Below are some netizens’ replies to the math question from “Maths Jokes Daily,” which range from the hilarious to the ridiculous to the preposterous.

I think because the circles weren't closed properly 🤔

honestly think its possible for most people to understand what you are supposed to do here, so I would definetely argue that this is not a badly formed question :)

Were the correct answers 1.39, 2.17 and 3.96 ?

He got it wrong because he marked 3 numbers, and the question only asked for one, so the right answer is 15

He provided 3 right answers. He identified the smallest number in each row disregarding the periods and commas. LOL !

He circled 3 numbers. Number 1 is the smallest number and therefore should have only selected the 1 single number.

Also, why did the teacher put 3 lowercase "alpha" symbols?🤣

it’s evident smallest number and not smallest numberS so he should have circled only 1

Because he only circles 1 but not 1.39 Same with others

The fault lies entirely with the fool that numbered the questions with Roman Numerals and then used 1, 2, 3 instead of a, b, c

That kid is already smarter than the teacher.

Thats at least .5 for thinking outside the box

? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! 

Would you side with the teacher or the student? How would you respond to the “wrong” answer to this ill-posed or improperly posed question?

Creatively or uncritically yours

© Yan Kow Cheong, May 19, 2023.

Book-Smart Math vs. Street-Smart Math

 

Based on the picture and text, who do you think got a better deal? Which party ended up happier: Customer or Seller?

Would you agree that the young exam-smart customer was outfoxed by the old street-smart fruit seller? 

Aren’t we all guilty of this “book- or exam-smart syndrome,” when we’d buy more than what we needed because we thought we’re getting a good deal, or we didn’t want to be taken advantage of?

In the end, isn’t the supermarket or shop owner or fruit seller who’s having the last laugh, while the customer thinks they’re the “smarter one”?

Isn’t it a case of “more is less”? When A-students are being outwitted every day by C-students in the marketplace!

It’s probably no wonder that most exam-smart A-students around the world end up working for street-smart C-students. The former have so much to lose, compared to the latter who’ve far more to gain (if they do make it!).

If you’re a “math educator” (teacher, tutor, writer, editor, ghostwriter, lecturer, “moonlighter,” …), do you have what it takes to venture into the business of math or math education? 

Smartly yours

Photo © Anon.

Stole the attached picture from ex-colleague-and-friend WeePing Chun on Facebook.

© Yan Kow Cheong, May 9, 2023.

Math à la Japonaise

We need to thank Mrs. Marie Kondo for advocating that tidying up needn’t be obeyed as an eleventh commandment, especially for a significant number of us who can’t afford to live sans a mess, or who just refuse to be Konned by her enviable minimalist lifestyle.

Since the tidying consultant has been in the limelight recently after her long overdue admission that the art of tidying up could be an optional activity for those who can’t stand the sight of all kinds of oft-dated, sentimental, or hoarded items lying around the house (and in the office), I thought it’s apt to share about “KonMari Math,” which I christened two years ago, to show that even math educators too haven’t been spared by the gospel or philosophy of the organizing goddess.

Math word du jour

Photo from math prof @mathematicsprof on 17/2/19

Personally, I’m dazzled by most things Japanese: origami, sushi, wasabi, not to say, soroban (Japanese abacus—square-rooting, cube-rooting, differentiating, and integrating), Kumon math, Sakamoto math, Sangaku, and Wasan.

After being introduced to Mr. Kenji Wakabayashi by my ex-colleague and friend, Mr. O.K. Heng, to learn about the ABCs of the Sakamoto Maths Method, I was later offered the opportunity to attend a months-long series of math talks on the Japanese problem-solving heuristic (or “problem-solving strategy” as it’s known in some parts of the globe).

To certify that I’d mastered Sakamoto math, I reluctantly had to take an exam with fellow participants who’re much younger than me. I was already around forty then, and needless to say, by then, it’d been a while since I last sat for a math proficiency test or exam.

Front cover of the manual

Today, I’m thankful to Mr. Wakabayashi who gave me an opportunity to get a strong foundation on Sakamoto math, which has proved to be a more advantageous or intuitive problem-solving strategy than the bar model method in a number of problem situations.

What is even more amazing is that I attended all these Japanese math lessons without forking out a penny. Talking about being blessed mathematically (and financially), when other participants or franchise sponsored trainers have to pay hundreds of dollars to attend these twice weekly and weekend classes.

Indeed, Sakamoto math offers paid, sponsored, or guest attendees another method of solution to solving brain-unfriendly word problems. I think a Singapore math educator-turned-trainer ought to be versed with not only the bar model method, but also with the stack model method and the Sakamoto math method—a trinity of problem-solving strategies.

Recently, while working on a bar modeling manuscript, I accidentally came across some Wasan (or Japanese math) materials, which further solidifies my knowhow of Nippon math, especially some of the techniques I learned in Sakamoto math moons ago.

May I encourage all of you to expose yourself to the richness of Wasan, which would help broaden and deepen your appreciation and knowledge of multicultural math, if you’re open to learning different problem-solving strategies (or heuristics) commonly used in countries with a rich mathematical heritage.

Of course, to learn Sakamoto math effectively, do it preferably under a master-trainer from Japan—never mind their accent—rather than merely reading the notes of your child or nephew who’s signed up for a Sakamoto math course.

May the learning of Nippon math and multicultural math (Vedic math, bar model method, stack model method, line model method, …) spark mathematical joy in your life.

Wishing you many blessed joy-sparking or aha! moments.

Mathematically & multiculturally yours

References

Kondo, M. (2022). Marie Kondo’s Kurashi at home. New York: Ten Speed Press.

Yan, K.C. (2016). Sangaku — Japanese temple geometry. Geometrical quickies & trickies. Singapore: MathPlus Publishing.

© Yan Kow Cheong, March 10, 2023.

A New Yorker cartoon by Evan Lian.

Freedom from Crypto Addiction

Cure from crypto addiction needn’t be costly!

Help is now dearly available for those who’re hard hit by the recent crypto winter.

For those who can’t afford the nouveau-riche treatment, or who’re thinking of following Anthony Bourdain’s or Jeffrey Epstein’s template, because there seems to be no way out, know that there’s a (better) way to come out of that hell.

A better and faster (or cheaper) solution for crypto addicts would be to attend a counseling-and-praying session or two so that they’d be delivered once for all from the spirit of gambling.

Complete deliverance and healing is a mere prayer away if they’d turn to the Deliverer-and-Healer who has the power to free them from their short- or long-term addiction or affliction or persecution.

The Miracle Worker who turned water into wine, or who used five loaves of bread and two fish to feed five thousand people or families, is waiting and willing to deliver them from their gambling or years-long bad habit or addiction if only they agree or humble themselves to be delivered.

May their pride (or unbelief or negative faith or ignorance) not be a stumbling block to their being freed from crypto addiction, massive debt, or financial ruin.

Freely yours

© Yan Kow Cheong, February 8, 2023.