MATH - January 13, 2011

Close to the center of the rage about the adequacy of teaching in US K-12 schools is the difficulty in reaching students in Mathematics, even elementary Arithmetic. This is due in part to the fact that most students, their parents and their teachers think of Math as the art of carrying out calculations, and these have been reduced to carrying out certain memorized procedures. Indeed, the art of teaching the procedures has been sharpened specifically to eliminate almost all need for a deep understanding, which can command time and attention. In the process, we rob our students of the intellectual adventure that has been so central in creating the growing discipline of commanding the artificial intellectual structure we call Mathematics. When we attempted to improve the students’ understanding in the 1960s and 70s by teaching what became known as the New Math, we ran into a block by parents and teachers who thought that what they knew was all that it was required to know, and resented the idea that they would need to learn some “new” ideas to improve that understanding. The belief in Mathematics not as an adventure in human knowledge of this intellectual structure, but as just the art of getting the answers without being “burdened” with comprehension infects our understanding even well into graduate study. Meanwhile, almost all of the intellectual world (excluding the portion that speaks English) has adopted the New Math and has left us behind while it caters to those who can handle the development of this discipline. Attempts by the universities to expand those theoretical limitations has been rejected by the students, their administrators and parents, who seem to prefer a world of authoritarian rules that can be applied with rote ease and without mental strain. The history and philosophy of this voyage out of ignorance are dismissed as luxuries, with the mechanical extraction of calculation being thought of as the true meaning of the study. Since this end is available without the “philosophy” and can be increasingly built into machines, the human content is eliminated. Meanwhile, the rest of the world is not standing still.