On Tue, Dec 24, 2013 at 8:09 AM, Robert Hansen <email@example.com> wrote:
<< SNIP >>
> There are a number of issues with this statement. > > 1. I realize that it became common practice for students with little or no > prerequisite success in academics to continue forth and choose an academic > major, regardless. Those students are now working at Starbucks and sitting > on a pile of tuition debt that they will struggle to repay for decades. > Except for the most exceptional circumstances, a math major does not > (should not) be majoring in math, if by college they are still struggling > with the notion of ?mathematical thinking?. Being unsure of what your major > might be is entirely not the same thing as being unsure what the major is > or what the subject is. It is the later that has landed students in finical > ruin. It is an issue that is easily fixed if we stop marketing college > degrees to unsuspecting and unknowing students as if we were selling them a > car. > > You seem to always shoulder students with the burden of suffering a math deficit, whereas it may be the school's curriculum and/or teachers and/or the whole culture of a high school that starts closing these doors.
"Math dependent degree" includes a lot of them, including just about anything healthcare related. Maybe 3% want to be math majors, whereas 40% seek a math-dependent major.
Some students have just never had the benefit of an optimized learning environment. They have every potential to catch up and surpass, and yes, that potential is as yet unfulfilled. Not unusual.
That doesn't mean it's wrong to ill advised to steer them to courses like Devlin's.
Indeed, we may want to propose course like Devlin's *instead* of a local school's.
2. Devlin describes ?school math? as focusing on learning procedures to > solve stereotypical problems. Nothing new here. Just the usual > mis-characterization by reformers of school math. Devlin goes on to say > that pure math (this is what his course talks to) is designed to solve real > everyday problems. I am not sure how he got pure math and applied math so > mixed up. He seems to understand what pure math is so I have to assume that > he doesn?t understand what applied math is. Nonetheless, I like pure math, > and I solve everyday technical problems, every day. My ability to do so did > not begin with nor does it have anything to do with pure math. It began > with algebra and continued on through the topics of precalculus and > calculus. The bulk of it is simply really good algebraic reasoning. >
Making sharp distinctions between pure and applied mathematics is not essential.
Textbooks are very often formulaic, having you find roots of this and that polynomial, slopes of this and that line. What may not fall out of such formula-based learning is any confidence of being able to solve "generic problems" that life my pose.
At some point in a student's career we let them know about "numerical recipes" and the fact that whole books of them are out there for consultation.
Those who use mathematical techniques to grapple with problems are less in need of great memorization skills than great research skills.
Where are the cookbooks? How do you match a problem to an algorithm? Those are skills too, beyond proving.
Finding the theorem and realizing it's relevance, locating the right recipe in the library, is all part of what one needs. Good road maps. Overviews. Most K-12 textbook math is fairly bereft of such concept maps.