Pre-calculus is one more indicator of the linear view most people in the US have of mathematics. They added a course filled with largely unrelated topics just to advance students to the next point on the line. High schools hurry students to get them through calculus, instead of really focusing on what maths they need in the world. In this rush some mixture of trig, functions, logic, analytic geometry, functions, sequences and series, modeling, complex numbers are covered in a single course, forcing most teachers into the cookbook style of teaching. A great example of this cookbook style is in teaching logarithms to secondary students. During a course in "teaching secondary ed math", I was told the ONLY way to teach logarithms is to have students memorize the rules of logarithms. I had no desire to teach public school secondary ed math after that. One of the main points of my original note was that discrete math is NOT just for computer scientists (or every student who needs to be more computer literate), with the trend of science heading towards the discrete. Biology, for example, has become far more discrete with the discovery of DNA/RNA. Though the double helix was discovered in the 50/60's, we're still trying to figure out exactly how it encodes and handles other information theoretic jobs. Course work continues to change. The course I took in the 80's at university looked nothing like the course I took in the 2000's to support DNA/RNA and protein folding research -- combinatorics had its place in enumerating codons and everything seemed far more logical. Physics, one of the bigger beasts pushing calculus, is even heading in discrete directions. Some of the newer approaches in physics treat the universe as an information theoretic problem, though some physicists have issues with this. On 11 Mar 2011, at 18:54, Dan Asimov wrote:
P.S. One more comment to what Anna wrote:
<< A solid understanding of discrete math concepts (for example, more familiarity with summations than the brief introduction they get in calculus, or the binomial expansion) would make calculus far less threatening.
The fact that in the past many students came to calculus without adequate preparation has been appreciated years ago, and for this reason the oddly named "pre-calculus" course has appeared in many, many H.S. and college curricula. It includes trigonometry and other subjects, and has replaced what used to be a full year of trig in many H.S. curricula.
--Dan
________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun