Category Archives: Stack Modeling

Calculus for Cats

Bar Modeling, Humor, Mathematical Humor, Problem Solving, Recreational Math, Singapore Math, Singapore Model Method, Stack Method, Stack Modeling, , , , , , , , , , , , , , , , , , , , ,

If you had to choose between cat and calculus, which one would you save, especially if you happened to be a cat-and-math lover?

A math meme that pokes fun at the MAGA cult

Unlike dogs that are faithful, loyal, and obedient, cats are unpredictable, independent, and creative.

Yes, you can rely on a dog to unconditionally love you back even after you’ve scolded or even ill-treated them. The same treatment could hardly be said of or expected from a “never-forget” cat, who’s often the master (or lord) of their owner.

Know who’s the boss at home. Art stolen from “Kitty Corner” on FB.

It’s probably not a coincidence that a title like Calculus for Cats doesn’t just sound catchy (or even sexy), but it’s also apt for the feline family for a number of reasons.

Arguably, most dogs and puppies could handle algebra and trigonometry (or even pre-calculus), but cats and kittens, blessed with a “higher IQ” than their canine counterparts, could apparently manage calculus as well—or even intuitive topology in the hands of a geeky trainer.

Why aren’t more people christening their cat “Newton”?

Philosophically, dogs are peasants; cats are poets.

Singapore’s Cat Problem Solvers

It’s said that most dogs solve elementary math word problems religiously using algebra, without much appreciation (or comprehension?) of what they’re doing, unlike [lazy] cats—who’re always on the lookout for a shorter or creative way—that are prone to using the intuitive bar or stack model method to solving them.

Based on TIMSS and PISA rankings, it’s probably not an exaggeration to say that zero resources Singapore has done a relatively good job vis-à-vis other high GDP nations (with a much higher education budget) in nurturing its students (and teachers) into cat problem solvers.

Are You a Cat or Dog?

As a mathematical problem solver, are you more cat than dog? Or, to play safe, would you rather not rock the boat, by reluctantly being a dog math educator? Besides, you probably feel safer to sticking to routine algebraic methods than exploring nontraditional strategies in solving brain-unfriendly questions.

The “lazy” one does nothing; the “bees-zy” one does anything and everything.

No Sacrificial Lamb

Coming back to the dilemma between cat and calculus, if you’re a geeky cat lover, which one would you choose?

Assuming that no dog would be made the scapegoat to substitute the “unlucky” one, which one would you sacrifice or die for to keep one over the other?

Wisely yours

© Yan Kow Cheong, December 22, 2024.

Art by Rina Piccolo. @RinaPiccolo

Algebra for Babies & Toddlers

Bar Modeling, Math Publishing, Problem Solving, Recreational Math, Singapore Math, Stack Modeling, , , , , , , , , , ,
A math definition that appeared to have been hijacked by Al-Qaeda or the Taliban

An unspoken commandment among parents and homeschoolers is: Thou shalt not introduce algebra to young kids without close adult supervision.

Looking at the unhealthy number of pre-school math titles in local bookstores, some Singapore math authors have set questions that directly or indirectly help promote algebraic thinking among toddlers and kindergarteners, particularly via the bar model method and number patterns, whether they’re pedagogically conscious of it or not.

Kiasu parents or tiger mums would buy assessment (or supplementary) math titles (often disguised as “parents’ guides”) to give their kids an “unfair advantage” over their peers.

On closer look, disappointingly, these preschool “enrichment math” books are often mere rehashed primary one (or grade one) assessment math titles.

Fr: Cartoon from Judy Smith Hallett

I decided not to showcase any covers of these oft-drill-and-kill kindergarten math titles here to avoid any perception that I’m endorsing some local authors or their publishers.

Notion, Not Notation

Debatably, it’s no harm getting preschoolers to start thinking algebraically long before they’re formally taught generalized arithmetic. Yes to pre-algebraic thinking but no to algebraic notation or equation for kindergarteners.

Personally, I’ve yet to see any decent locally published K–2 Singapore math titles in bookstores (other than through some questions in children’s puzzles books), which creatively or systematically promote algebraic thinking skills.

In the last two decades, there had been a number of journal articles and a few NCTM (and even some AMS) titles that feature activities or nonroutine questions that champion pre-algebraic thinking at the kindergarten level.

It’s a pity that Pre-K and kindergarten teachers (and mathepreneurs) haven’t leveraged on these rich resources to come up with supplementary math titles to evangelize the algebraic gospel to K–2 students.

The raison-d’être of premature algebra teaching

In Singapore, a mecca for brain-unfriendly, budget-friendly assessment (or supplementary) math titles, it looks rather surprising that local Singapore writers have so far not come up with an “Algebra for Babies or Toddlers” when local libraries already carry catchy foreign titles like Bayesian Probability for Babies and Pythagorean Theorem for Babies.

Ripe Harvest but Few Workers

The time is ripe for creative math educators, local or foreign-born, to publish a creative algebra series for toddlers and kindergarteners of kiasu parents, but it looks like the writers who’d help pluck up the fruits are few. An untapped market for publishers that want to move away from canned or drill-and-kill preschool math titles.

Opportunistically & creatively yours

© Yan Kow Cheong, August 27, 2023.