John G. Kemeny, a Dartmouth College mathematics professor, dealt with all of these issues first hand in the 1960's and learned a lot in the process. The questions you ask led him and his colleague Thomas Kurtz to transform the entire institution during the 1960's and 1970's, well ahead of the trend. The following quotes are from "The Computer and the Campus: an Interview of John Kemeny" (an interview by Ken King of EDUCOM performed in 1991, a year before Kemeny's death). They address your questions very closely, and the rest of the interview is relevant too. This excerpt starts at about 13:05: *KK: How do you deal with [resistance of faculty to resist tradition by adding computing to the curriculum]?* * * *JGK: I think the question that would have to be asked of the administrators at the institution is: "How would you evaluate a faculty member who teaches a completely obsolete course superbly?" I would think, I would *hope* they would give low grades. And in certain types of courses, teaching it without using computers is teaching a completely obsolete course.* And this is at 14:10: *JGK: In a calculus course, Taylor series is a fairly difficult topic. The thought that you add up a bunch of polynomials, which are terribly nice functions, the sum of them will be very close to some very weird function that you started with, the transcendental function, is very difficult for a student to understand.* * I followed the mathematics in college, but I had absolutely no feeling deep down about what was going on. On a computer, you can have the original function drawn, and show step by step as you add up the polynomials, you draw the graphs, and you see it getting closer and closer to the original function.* * I learned things about Taylor series I had not known after twenty years of teaching calculus just by looking at the graphs that appeared on the computer screen.* The entire interview is here: http://www.dartmouth.edu/comp/about/archive/history/kemeny/ or on Youtube, here: http://www.youtube.com/v/HHi3VFOL-AI - Robert
From: Anna Johnston [jannaston@gmail.com]
Subject: math fun and calculus
Hi Rich,
I wanted to ask you a question (and perhaps get a gage through mathfun) --
old though it may be -- that's come up in my current circle: calculus in
high school. I've read MAA articles dating back 11 years on the
questionable nature of teaching calculus in high school, talked to high
school teachers, mathematician parents, as well as my former colleagues at
WSU. The basic thread of these conversations is that calculus should not be
part of the high school curriculum. Instead there should be more breadth
with a stronger emphasis on discrete concepts (combinatorics, number theory,
probability, set theory, logic, proofs, etc). The reasons are:
(1) First and foremost, there are other areas of mathematics that would help
students think logically while giving them knowledge far more useful in
everyday life. [...]
(2) Secondly, society's need for calculus has been surpassed by the need for
discrete math. [...]
(3) Thirdly, the linear push to calculus is a turn off to many students.
The style of teaching most HS calculus teachers are forced into teaches
students that advanced math is not about thinking but memorization.
Though this idea seems to be old, the only math AP exams are Calculus and
stats. [...]
The question is: Why is calculus still the perceived linear end point to HS
math and what is the best way to change perceptions and curriculum?
-- Robert Munafo -- mrob.com Follow me at: fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com- youtube.com/user/mrob143 - rilybot.blogspot.com