A Singapore Grade 4 Geometry Question

On Facebook, someone recently posted the above primary 4 (or grade 4) geometry question, asking for help from fellow parents. How would you do it (without calling on ChatGPT)?

If you’re a parent, homeschooler, or tutor, how would you explain it to an eight- or nine-year-old child, who’s struggling with non-drill-and-kill questions on area and perimeter?

Give It a Try First!

Try figuring out the answer on your own first before peeping at two parents’ quick-and-dirty solutions below. Better still, could you present an idiot-proof or peasant-friendly solution that even a smart dog or cat could understand?

 

Solution:

6 width and 6 long = 3units  of the rectangle.

1 rectangle -> 16cm.

3 rectangle 

16x3 = 48cm.

Stretch Your Mind!

Many moons ago, I was commissioned to write Mind Stretchers 2*, a grade 5 problem-solving math book, which was popular in a number of local schools and tuition centers—disturbingly, they’re guiltlessly or blatantly photostating entire chapter questions as part of their worksheets.

And I still recall that on the topic of Perimeter, I’d posed a number of routine and nonroutine questions. What surprised or tickled me then was when the Managing Editor asked me whether or not some of these questions are solvable, because at first glance, they look like there are missing information to solving them.

These geometry questions can give students (and probably their oft-math-anxious parents and teachers) some goose pimples out of fear or panic if they can’t figure out the answers offhand. 

Understandably, without a cool mind and some patience (or perseverance), even perimeter and area questions at the elementary (or olympiad) level can prove to be a challenge to math educators if they’re not trained to tackling them using the right approach.

Frustration and fear usually set in, especially for nonroutine questions that don’t normally appear in drill-and-kill school textbooks and workbooks.

Premature Testing

The danger of setting these types of brain-unfriendly questions too early, or having them prematurely in a class test, especially when most students have yet to fully grasp the concepts of area and perimeter, could be detrimental to the mental health of most average math students.

Parents who freeze at the sight of these questions would often exhibit a knee-jerk reaction, by getting a tutor for their child, if they’d afford it.

Tuition or No Tuition?

Most stressed parents often reason that if they couldn’t even solve these grade 4 questions, things would only get worse in later years, as the higher-grade topics get more complicated and the questions become more challenging. They just don’t want to see their child struggle in math, especially when they themselves had had a negative experience of the world’s most disliked school subject.

Even for math teachers and tutors, there’s nothing to be ashamed of if at first or second reading, they’re clueless how to tackle these nonroutines. Yes, they do appear in mid- or final-year exams arguably as a social filter to separate the nerd from the herd, but once math educators and homeschoolers know how to approach these questions from the right angle, before long, these math problems would become routine to them.

The 4F’s of Mathematical Problem Solving

Few math teachers and writers would admit that (school or olympiad) math involves lots of fears, false starts, frustrations, and failures. The sooner parents and homeschoolers (and their children and grandchildren) are aware of this oft-unspoken problem-solving process or ritual, the pressure or expectation level for all parties ought to go down significantly in reducing any unnecessary mental or mathematical stress.

Pain is (always) part of the joy of creative mathematical problem solving—the no-pain-no-gain mantra is axiomatic in math at all levels.

Geometrically & perseveringly yours

© Yan Kow Cheong, October 16, 2023.

* When the wallet-friendly title was out of print, a senior editorial staff emailed me that he’d pay me a cosmetic S$150 to buy the copyrights. I never bothered to reply to his laughably ridiculous suggestion. I wouldn’t be surprised that they’d since plagiarized the content to be used and reused for other purposes.

20 Things You Probably Didn't Know about Singapore Math

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!

© Yan Kow Cheong, November 2, 2011.

Mathophobia is curable!

Mathophobia is curable!

Although millions of people suffer from mathophobia (fear of mathematics in all its forms and degrees), however, it was not too long ago that more attention had been given to this disease, fueled partly by the influx of self-help math books to tap on the huge market of mathophobics and mathematically challenged citizens.

I believe that in a-not-too-distant future books on mathophobia and its related symptoms will be shelved under the Health Section in the library. There may also be titles written on numerical phobias or conditions, such as triskaidekaphobia (irrational fear of the number 13) and acalulia (inability to do basic arithmetic).

Once mathophobia is recognized as a psychological illness that affects workers' performance, perhaps doctors will henceforth issue a medical certificate that may look as follows:

CERTIFICATE

To Whom It May Concern

This is to certify that Aziz Salamat is suffering from Mathophobia (Graphobia).

She has been granted medical leave for 2 days, starting from Monday 2 April 2015 to Tuesday 3 April 2015.

Dr. Adrain Gan

MBBA, FRSE, HISM, DDFT

The best cure for mathophobia is prevention; the best antidote is math confidence. Every child can learn math successfully, and every teacher can teach math successfully. In fact, no one is “math-dumb”. Learning math is both logical and emotional. So, treating any math anxiety must include both affective and cognitive elements, as mathematics is both logical and psychological.

What is needed is not a one-for-all syllabus, but rather a curriculum that is challenging, yet at the same time catering for children's different cognitive developments.


Mathophobia: A disease transmitted by parents and teachers to children.

© Yan Kow Cheong, February 28, 2010