My comments on The Economist (Buttonwood: Teacher, leave them kids alone)

I am not surprised by the results of the Rand study (http://www.rand.org/content/dam/rand/www/external/events/2010/11/18/financial-literacy-what-works.pdf). There is a subtle difference between "knowing" something and "understanding" it. My students "Knew" the stuff about discounting and IRR, but am not sure they really understood the concepts. They could solve exam type problems, but probably would have had problems applying the concepts in unfamiliar contexts.

I agree with their conclusion that public sector has a role to play by a comprehensive website. Something like the myplate website of USDA (http://www.cnpp.usda.gov/MyPlate.htm) for food and nutrition, I think would help.

What I find disconcerting is the Economist statement: "If so many people are mathematically challenged, it is hardly surprising that they struggle to deal with the small print of mortgage and insurance contracts."  This can have repercussions in areas well beyond personal finance. The problem I think is mathematics education in K-12 education. When my kids were in school I discovered that the first six grades were sort of taxpayer-financed day care more than schooling (at least in California, and I live in one of the better school districts in the country), at least as far as mathematics education is concerned.  While the kids were in seventh  (and eighth) grade, they were already handicapped by crummy mathematics education with the result that even though the curriculum was good it was too fast paced for the already mathematically challenged kids. In these middle school years the students were tricked into thinking that it is enough to know, not necessarily understand.

This tradition of knowledge in the sense of knowing (successful test-taking) continued in the high school years with the result students went to college with the firm belief that they had understood the stuff by virtue of a good grade. High school math curriculum was excellent, but too fast paced for the doubly mathematically challenged.

I can give one example to illustrate the difference between knowing and understanding. When I took my class in point set topology, the instructor used the well known text by Kuratowski, which we read diligently. However, the instructor (a brilliant mathematician who had earlier taught at MIT, Illinois among other schools) used an entirely different notation in teaching in the class (we searched library to find out which book he had taken the notation, but couldn't find any; we think he just made them up himself in class). We bitterly complained because it was different to understand, having read from the book. The instructor said he really didn't care what notation  Kuratowski, the important thing is to UNDERSTAND the subject matter rather than just know it. If a lesser instructor (who knew the matter) had been asked to teach the same  stuff but forbidden to use Kuratowski notation would have found the task almost impossible. And my instructor never brought any book or notes to class, but taught it ex tempore.

The first six years, I think rote learning in math is essential because it makes the rest of ones life mathematically a lot less challenging. May be that is the reason the students from Japan, China, Korea, India often do quite well. But creativity is something else. Look at the winners of Fields medals and their nationalities.