THE SIMPLICITY IN MATHEMATICS

“A camel is a horse designed by committee.” - Sir Alec Issigonis, a British automobile designer who created the best-selling, economical Mini and the perennially popular Morris Minor.

The horse is a domesticated one-toed hoofed mammal. It belongs to the taxonomic family Equidae and is one of two extant subspecies of Equus ferus. The horse has evolved over the past 45 to 55 million years from a small multi-toed creature, Eohippus, into the large, single-toed animal of today. While a horse is tame, can run fast, and can take a rider on its back with comfort, a camel can only trudge along, has humps that make riding it difficult, and is stubborn with a bad temperament. A camel is an even-toed ungulate in the genus Camelus that bears distinctive fatty deposits known as "humps" on its back. Camels have long been domesticated and, as livestock, they provide food such as milk and meat and textiles like fiber and felt from hair. Camels are working animals especially suited to their desert habitat and are a vital means of transport for passengers and cargo.

This “design by committee” concept tries to incorporate so many suggestions into an output. But when they are all taken together, they make the final product quite bad.

I have observed this in several US math textbooks where they combine so many thoughts, methods, and notions that the novel sense gets lost. The finest way of solving problems gets suppressed under layers of pointless material.

In a standardized math test, American students scored below the world average while Singapore students scored consistently high. In fact, according to an international benchmarking study, Singapore ranked as the #1 country to have students performing their best in Mathematics.

The Singapore math method is a highly effective teaching approach originally developed by Singapore’s Ministry of Education for Singapore public schools. The method has been widely adopted in various forms around the world over the past twenty years.

I studied at the exercises and problem sets in Singapore math textbooks, and they were much simpler and direct to the point. There were no peripheral layers that cluttered the lessons. The instructions and exercises were very clear and concise, and I saw how it would be much easier for a child to learn.

The Singapore math method is focused on mastery, which is achieved through intentional sequencing of concepts. Some of the key features of the approach include the CPA (Concrete, Pictorial, and Abstract) progression, number bonds, bar modeling, and mental math. Instead of pushing through rote memorization, students learn to think mathematically and rely on the depth of knowledge gained in previous lessons.

An attitude that math is important and approachable are essential. Students perform at a higher level when their potential for understanding and success is assumed.

In typical U.S. math programs, students get a worked example, and then solve problems that very closely follow that example, repeating all the same steps with different numbers. In Singapore math, students must think through concepts and apply them in new ways from the very start. Since they can’t rely on simple replication, students are pushed to greater engagement and broader thinking. In U.S. math programs, concepts and skills are more compartmentalized within and across grade levels than in Singapore math, where a strong sense of connectivity to past learning is woven throughout.

Singapore math not only helps students become more successful problem solvers, it helps them gain a sense of confidence and resourcefulness because it insists on conceptual depth. This naturally prepares students to excel in more advanced math.

Design by committee overthrows the original objective of a product or service. It makes a problem more complicated than it should be, thus requiring more complex solutions. Wouldn't it be smarter to simplify a problem instead of making it more complicated?

“I have just three things to teach: simplicity, patience, compassion. These three are your greatest treasures.” - Isaac Newton


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