Response on " Was Pythagoras Chinese?"

•  Does it make a difference to our students' learning if we acknowledge (or don't acknowledge) non-European sources of mathematics? Why, or how?

Since I was born and raised in China before coming to Canada at age of 12, the foundation of my mathematical knowledge was learned in China. This includes arithmetic operations, integer operations, fraction operations, solving algebraic equations and system of equations. Because of the difference in mathematical curriculums, I was ahead of my class for several years since grade 7. In Canada, I learned pre-calculus in high school and more advanced mathematics in university. Hence, I have the experience learning math from two different cultures.

In China, elementary school math is taught with a blend of Chinese and Western sources. I remember learning how to use an abacus and we have our own version of Pascal’s triangle we call it “Yang Hui triangle”. Also, as mentioned in Gustafson, we learned right triangle theory as “gou-gu” theorem. Nonetheless, we also use Arabic numerals, and we call our variables x, y, z. Even though we have Chinese names for sine, cosine, and tangent, we write using the Western notations in problem solving. As a matter of fact, using various sources of mathematics have little impact on student’s learning. What made a huge difference between Canadian school and Chinese school is the way of teaching the knowledge. As mentioned in Gustafson’s work, memorization serves as a ground for knowledge building in Chinese education. Students are required to memorize definitions, theorems, as well as ways to solve problems. Moreover, no calculator is ever allowed in exams. In my opinion, this way serves well on building a good foundation but when students become more mature, I’d like being taught by Western approach more. When in advance level, students should use tools to aid achieving the purpose of understanding. Time should not be spent on doing arithmetic by hand, yet knowing how to do arithmetic by hand is also important. 

•  What are your thoughts about the naming of the Pythagorean Theorem, and other named mathematical theorems and concepts (for example, Pascal's Triangle...check out its history.)

I would say, the way of naming mathematical theorems after the founder is sometimes bit misleading. Nowadays with the advancement in technologies, the development of knowledge are watched closely by academic society across the world. It would be easier to identify the source of a new idea. However, when communications cannot be done efficiently in the past, the validity on awarding one (or more, for co-founding) person for the contribution is questionable. Different people can independently come up with breakthroughs (e.g. Newton and Leibniz). In my opinion, the naming should be referring the knowledge instead of referring the person who come up with it (e.g. intermediate value theorem). Of course the acknowledging of the inventor is also important, but that can be done separately. Another benefit for not naming after a person is to remove the culture bias and barrier in knowledge. For example, when we look at the theorems in math courses, we get the Eurocentric feeling in mathematics because most of the theorems are named after European mathematicians. However, mathematics has been developed across different countries and cultures for quite a long time. Instead of fighting for who did it first, people should pay more attention on the evolvement of the knowledge.