Need for Math to Study Econ – Excellent Description – But…

The post, http://www.theatlantic.com/business/archive/2013/08/the-complete-guide-to-getting-into-an-economics-phd-program/278773/#comments , in The Atlantic gives a careful description of how much math is needed in econimics, except for one flaw.  The authors conflate “course” with “content”.  I discussed that in my comment, which I copied below.  Still, I think it is an excellent and enlightening article.

”

I am a math professor who has experience teaching the math courses that you mention. (This was at Washington University in St. Louis.) If your advice about the appropriate math background involves content, not just courses, then I am deeply concerned that students will be misled into thinking that they have the right background, and have acquired the right skills, by just doing well in the courses. Equating courses with content is only valid at a few universities that still maintain high standards; or, in the pre-1980 world before Clark Kerr observed the “…shift from academic merit to student consumerism is one of the two greatest reversals of direction in all the history of …higher education…” We have now traveled the road from adopting consumer strategies like “grade inflation” to adopting “content deflation”.

You mention that math can be learned through hard work. That is absolutely true, but with content deflation, the material isn’t even there to learn. (See the excellent book “Academically Adrift” where it is documented that studying has decreased from 25 hours a week in 1965 to 13 hours now. Critical thinking improvement, over the first two years, has gone from one sigma to less than .2 sigma.)

I am commenting here because I want to point out to students the difference between “content” and “course”. To make it clear, here are some examples. These examples are from Calculus One courses. At SUNY Binghamton the first test has many questions on limits, including questions requiring a working knowledge of the epsilon-delta definition. At the U. of Michigan, the course web page explicitly says that even continuity will be touched on lightly. At CalTech, the course page says, “…The typical high school courses, and the AP tests themselves, are woefully inadequate in explaining, or testing, why things work and how to justify one’s propositions…”

At my own institution, the Chairman of the Math Dept wanted me to change the differential equations course from one based on MIT’s to what he referred to as their standard “cookbook” course. It seemed the engineering school was concerned about “retention”, which seemed to be retention of all students. They even forwarded a “complaint” from an upperclassman who wrote that he tutored a few of my students and that he could hardly ever do any of the MIT problems, though he “…made an A [in the cookbook version] and an A in the next course”. My students laughed when I read that to them.

I hope these are enough examples to encourage the authors to clarify what skills and knowledge they want the students to have. I think it would do a service, not only to potential grad students, but to everyone who needs to understand economics and all of the other areas that need quantitative thinking. I believe that once students understand what they really need, they may acquire the power to reinflate course content.

(For anyone who wants to know more about the reality of today’s university mathematics, you can go to my blog inside-higher-ed.com. You can also find a paper there that explains most of differentiable multivariable calculus in an intuitive, but rigorous way.)”