By Johnny Duda
A revealing article in The Atlantic Monthly attempted to tackle the widespread disparity between Americans and other countries when discussing math. Many adults simply ignore mathematical tasks by claiming to be bad with numbers. A similar article in the New York Times also discussed how American adults stack up with counterparts from around the world, and the results are startling:
“A 2012 study comparing 16-to-65-year-olds in 20 countries found that Americans rank in the bottom five in numeracy. On a scale of 1 to 5, 29 percent of them scored at Level 1 or below, meaning they could do basic arithmetic but not computations requiring two or more steps.” (NYT)
But like many knowledge gaps, the problem doesn’t begin in adulthood. American students are outpaced by their international peers at a very early age, the disparity developing as young as elementary school. Students in Asian countries can spend as many as 240 days per year in classes (compared to 180 for American students). As students age, this disparity widens to a chasm by age 16. (NYT, Atlantic).
Why the downward trend? And what can we do about it?
Whereas the data (and the Atlantic article) might suggest that Americans are simply innately inferior to mathematical and conceptual skills, the actual reason lies more in how the subject is taught rather than how it is perceived. Discomfort surrounding math stems from an intuitive disconnect. From an early age, students are taught math in an algorithmic sense––a rigid set of codes and formulas to follow in an effort to arrive at an expected answer. As a result, we’ve taken the joy and discovery out of math and learning.
An example of an algorithm is the approach taken to solve the following question:
How do we solve this?
If you’re like most former math students, you may have said something like “Well, when there are two exponents like that, you’re supposed to multiply them!”
(X2)3 = X2x3 = X6
While this may get you to the right answer, it’s a rule easily forgotten. Remembering to multiple exponents is simply an algorithm, aka a shortcut used to know how to solve a problem like this rather than how to understand it.
Instead, let’s recognize that exponents simply represent repeated multiplication, same as multiplication represents repeated addition. When teaching multiplication for the first time to young children, it’s easy to use the visual moniker of “times-ing” something to indicate how many “times” we see it.
For example, in the case of:
3 + 3 + 3 + 3
We can ask — How many times do you see the number 3? The answer is 4 times. Therefore, this problem can be spoken as “Three TIMES four” and written numerically as “3 x 4.”
The same goes for exponents.
The exponent on the outside of the parenthesis let’s us know that whatever is inside is being multiplied by itself 3 times.
______ x ______ x ______
We see from the problem that in this case, we’re dealing with X2, and can rewrite the problem as:
X2 x X2 x X2
Let’s let 3 stand in for our X.
32 x 32 x 32
9 x 9 x 9
9 x 9 x 9 = 729
36 also equals 729. How about that!
Instead of dividing the wide world of mathematics into easily forgettable rules and processes, let’s instead use what the world gave us in the first place — a myriad of relationships that are already defined and codified in their own unique language. A more intuitive understanding of fundamental concepts provides a solid foundational understanding that will carry students through their courses, entrance exams, and beyond.
Dr. Duda graduated from Harvard University in 1999, and received his doctorate in Education from UCLA in 2011. Johnny has over a decade of experience as a teacher and mentor to middle school, high school and college students. In addition to developing original programs for Vault Prep, Johnny advises select U.S. and international students on their college applications and essays and specializes in working with students with special learning needs.