Purpose 2

Below is my new purpose going into the doctoral program at Columbia University TC.

“Poets do not go mad; but chess players do. Mathematicians go mad, and cashiers; but creative artists very seldom.” This quotation from G. K. Chesterton highlights the supposed danger that hides its claws in the shadow of logical and numerical structures of mathematics that could devour one’s sanity. While I grieve such an erroneous perspective towards mathematics, unfortunately, I find similar beliefs from student responses that I observed throughout the six years of my experience as a mathematics tutor.

In my tutoring sessions, whenever students complete their tasks, I would ask them, “How did you get that answer?” regardless of the correctness of their solutions. Students’ responses to this question would vary. Sometimes they would try their best to explain their strategies or recognize patterns (just like the aforementioned metaphor of chess players). Other times they would tell me they used the formula (Because that’s just how it works! they would exclaim – the case that reminds me of the cashier metaphor). They also may confess that they had guessed or that they do not know. What had startled me was that many of these remarks, especially those from the students who were not familiar with my way of teaching, were accompanied by deeply troubled faces asking, “Am I wrong?” 

I would be heartbroken every time I encountered such a reaction. It almost seemed that these students were afraid to face the consequence if they got their answers wrong. Such reactions could be explained by math anxiety, “a feeling of tension, apprehension, or fear that interferes with math performance”¹. Indeed, many of these students would immediately show worrisome faces just as they encounter questions that require more than a procedural application of the taught algorithms. As I studied more about mathematics education, I came to believe that researching the difference between perspectives of students in South Korea and students in the United States could enable scrutiny in math anxiety. This belief was further bolstered in discussions of fractions.

In the United States, the representation of fractions is one of the culprits of triggering math anxiety. The presence of fractions in math problems would discourage many students from even trying, presumably due to the entailed multi-stepped arithmetics. Many of them seemingly prefer decimals, as calculators could immediately resolve the complication. Contrarily, many students in Korea prefer fractions much more than decimals. Arithmetics with decimals involve a tedious procedure comparable to that with multi-digit integers, while fractions are often simplifiable if an appropriate strategy is utilized. Of course, such a difference in how students perceive fractions is probably directly affected by calculator usage, as Korean schools prohibit calculators in math classes. However, I believe there must exist deeper reasons for the phenomenon.

Many challenging math tasks in Korean schools, for example, encourage strategic reasoning in a way that there usually exists a strategy to approach solutions to questions involving seemingly complicated numbers (especially fractions) without encountering tedious calculations. I conjecture such task designs may reduce student math anxiety provoked by fractions, as students pay more attention to looking for strategies rather than the representation of numbers.

Another conjecture is the linguistic difference. The word fraction, given its prefix, means a part of a whole, which highlights the quantity of rational numbers, whereas the Korean translation of fraction, 분수 (pronounced “bunsu”), renders the meaning of the division of two numbers with an emphasis on the relation of the two integers. Notice how, for students who first learn fractions, the word fraction requires arbitrary learning of a new system of rational numbers, while bunsu connects more to the known idea of integers. I suspect such subtle linguistic differences in understanding the term impact how students perceive fractions or other mathematical concepts – and thus impact math anxiety. 

Though, I do not wish to compare the two nations and determine that one nation is better at coping with math anxiety than another. Rather, my research interest is to study the difference in how and why math anxiety is provoked in different nations and cultures depending on their language, history, and curricula. As different nations, cultures, and languages have vastly different ways of thinking and understanding mathematics, such research would help isolate factors that trigger math anxiety through the analysis of various trends of math education, through which the ways of perceiving mathematics to mitigate math anxiety can be identified.

Revolving back to Chesterton’s quotation and my observation in student beliefs, many of the cases of anxiety seemingly come from the fear of getting answers wrong. Chess players and cashiers should not get their answers wrong, as they would face immediate consequences, whereas there exist no correct answers for poets and creative artists. While Chesterton argues mathematicians are more similar to the former two cases, I believe otherwise. With numerous ways to perceive mathematics, even the wrong ideas could expand discussions, potentially branching out to other new ways of understanding certain mathematical topics. A quotation from Karl Weierstrass, the father of modern analysis, bolsters my belief: “A mathematician who is not somewhat of a poet will never be a complete mathematician.” I believe that this element of mathematics, the one so explorative and creative that it is even comparable to poetry, is essential in mathematics, therefore must be essential in mathematics education. With such an educational setting, students could divorce from the anxiety of finding correct answers and focus on the aesthetic experience that the mathematical journey renders.