It is commendable for people like John Barber to show interest in the way mathematics is taught but his guest opinion of Dec. 4 merits some corrections.
If we want to discuss any topic, then offending general statements like “not teaching them anything” are not a good opening.
The “discovery,” sometimes also called “problem,” methodology of teaching mathematics is the most efficient way to do so. Mathematics is not “handling numbers”; mathematics is an art of reasoning (proofs), understanding of logical substance (definitions) and making logically consistent statements (theorems).
To minimize the well-known fact that the majority of kids “don’t understand mathematics” the new methodology tries to follow the history of mathematics where first there was a problem, then a solution and finally formalization (theorems, definitions, axioms).
The main purpose of teaching mathematics is not to create a work force for Microsoft or Boeing, nor is it to prepare kids for tests, but to equip young people with sound reasoning, giving them also some insight into how situations in the real world (physics, economy, medicine) can be modeled by mathematical means. The “instructional” curriculum, using drill and trying to mentally subdue the student to the teacher, is unlikely to achieve that.
Peter C. Dolina