Math = Logic?

Suppose you’re in a dungeon with two doors. One leads to escape, the other to execution. There are only two other people in the room, one of whom always tells the truth, while the other always lies. You don’t know which is which, but they know that the other always lies or tells the truth. You can ask one of them one question, but, of course, you don’t know whether you’ll be speaking to the truth-teller or the liar. So what single question can you ask one of them that will enable you to figure out which door is which and make your escape?

Stumped? Don’t worry, you’re not alone. It’s not a trick question though; in fact the answer is fairly straightforward:

You ask either of them: “If I asked the other person which door is the one to escape, which would he point to?” Then you take the other door.

According to Nicholas Kristoff, a New York Times columnist, those with mathematical training are more likely to figure out this problem. Why is that? Kristoff explains that math isn’t just math — it’s logic. The skills utilized when studying and learning math are the same logistical skills you use for everyday things like brain teasers, statistics, or economics; even if you don’t realize that’s what you’re doing.

Questions like the one mentioned above, however, are often puzzling to Americans. For example, studies show that only 37% of American kids could correctly answer the question below whereas 75% of our Singapore counterparts answered correctly.

What is the sum of the three consecutive whole numbers with 2n as the middle number? (Answer: B)

  1. 6n+3
  2. 6n
  3. 6n-1
  4. 6n-3

It is not uncommon to hear stories of America’s poor performance in reading and math on an international scale. While this is a common misconception considering our scores have actually been improving over the past years, some of our counterparts in other advanced countries are indeed progressing more quickly. This is not due to an overall higher intelligence of other countries though. If we revisit the Singapore comparison we can learn that this kind of thinking is not innate. Instead, this logic is taught. Some may be familiar with the concept of “Singapore Math”, a model constructed upon child development theory that relies on student mastery of a limited number of mathematical concepts each year. The end result is that these students have a deeper level of comprehension and are therefore more prepared for problem solving. This enables them to master more difficult topics, like fractions and ratios, at much earlier ages than American students.

So if this is true, why then are Americans “avoiding” math? I’m sure we all know someone, or have been guilty ourselves, of copping out with: “Oh, I’m just not good at math”. But why do we have these outlooks on our math abilities when they can indeed be taught?

The answer may lie in our early foundations in mathematics. Unlike Singapore’s focus on mastery of limited concepts, American mathematics often focuses on memorization and drilling of concepts, such as multiplication. This can result in a lack of understanding about the meaning and function of numerals. And since mathematics continuously builds on itself, if a student doesn’t master the basic foundational concepts they will progress slowly and often fall behind. In fact, a study by researchers at the University of Missouri found that: “Children who don’t grasp the meaning and function of numerals before they enter first grade fall behind their peers in math achievement, and most of them don’t catch up”. This contributes to the alarming 22% innumeracy rate among adults in the United States. This early exposure and mastery of basic mathematical concepts is crucial for future arithmetic abilities.

This comparison is not to dishearten educational efforts in the United States, however. In fact this should encourage the public that the solution may be more straightforward than we imagined. Tools such as The Quantile® Framework for Mathematics can aid in this transformation by providing learners with resources for their individualized mathematical levels. Tools like these can be personalized for each student and provide additional means for gaining mastery of specific concepts.

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