Newspapers and professional journals are replete with discussions of the mathematical performance of U.S. students compared to other nations internationally. The discussions report dismal results and raise alarms, but tend to avoid getting into explanations of these differences via cultural distinctions.
One person who tried to examine these cultural differences was Ichiei Hirabayashi, professor at Hiroshima University (Japan), has passed away in May, 2011. A prime example is his paper "A Traditional Aspect of Mathematics
Education in Japan" (2006), published in a ICMI text.
In this interesting paper, Hirabayashi examines mathematics as GEI (art), JUTSU (technique), and DO (way). He argues that technique cannot stand alone, as the mind is needed for both sustance and support (from the inside)....and that the combination of the two develops each student's mathematical "personality."
He writes: "If mathematics can be seen as an activity of the human mind, it could not be taught or learned merely through a mechanical procedure, because it would be a very complex and delicate activity. Certainly mathematics is a cognitive subject, but to learn it we need to have a good emotion toward it...It may be possible only through the whole personality and humanity of the teacher. For instance, can a teacher really help their pupils to like mathematics if he/she hates mathematics?"
Unfortunately, these brief comments do not do justice to Hirabayashi's argument and welcome perspective. I suggest you get a copy of the paper and read it.
One final item. Professor Wim Kleijne (Netherlands) shared his reaction to the paper: "It is most interesting and 'out of my heart'. He was able to formulate his thinking in a very convincing way, conform what are also my own intentions in math education. What he described embedded in Japanese culture is in my opinion directly applicable to many other countries."
So, your thoughts...? Do you examine mathematics as GEI? And, do you help students see the DO?