Xref: utzoo sci.math:13891 comp.sys.handhelds:3973 Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!samsung!zaphod.mps.ohio-state.edu!rpi!sarah!leah.albany.edu!hb136 From: hb136@leah.albany.edu (Herb Brown) Newsgroups: sci.math,comp.sys.handhelds Subject: Re: The use of calculators in teaching calculus Keywords: Calculators, calculus Message-ID: <1990Dec4.134720.28772@sarah.albany.edu> Date: 4 Dec 90 13:47:20 GMT References: <4608@umbc3.UMBC.EDU> Sender: news@sarah.albany.edu Organization: State University of New York at Albany Lines: 62 In article <4608@umbc3.UMBC.EDU> rouben@math13.math.umbc.edu () writes: >Here are a few thoughts and ideas on the role of calculators >and computers in teaching freshman calculus. I am interested >to find out if there are others who share these thought, or if >there are some who disagree with me. Comments from both >teachers and students of calculus are welcome. >-- >Rouben Rostamian Telephone: (301) 455-2458 >Department of Mathematics and Statistics e-mail: >University of Maryland Baltimore County bitnet: rostamian@umbc >Baltimore, MD 21228, U.S.A. internet: rostamian@umbc3.umbc.edu At The University at Albany, the Mathematics Dept created a Computer Classroom (not a lab, but a classroom; we also have several computer labs sprinkled throughout the campus) whereby we offer several different mathematics courses including Calculus. This was the first semester of operation. I taught two courses in the Computer Classroom: Calculus I and a course called Basic Analysis. (There were two other Calc I courses, a Classical Algebra course, a Lin Prog & Game Thy course, one in Numerical Methods, and a Stat course.) The classroom is designed so that no computer is physically between the student and the instructor. The students SIMULTANEOUSLY interact between their computer, the instructor's computer, the blackboard, and their fellow students. My experience thus far has been one of excitement and jubilation. (I have been in this business for nearly 20 years and remember these feelings when I first received my doctorate and began teaching.) Let me give you an example of what became possible in this Calculus course that I did not do (or even attempt to do) in previous ones. I like to discuss (briefly) the concept of an inverse function, although I am aware that it is a difficult concept. I've always attempted to convey the concept visually by drawing (or attempting to draw) both the function, it's inverse, and the identity function (y = x) on the same set of coordinates. In order to maintain a semblance of interest I would pick an 'easy' function to deal with, i.e., one that would permit me to compute its inverse by hand before ALL students nodded off. This semester, since we are using Maple software, I chose the function x^3 + x + 1 Now, solving a cubic in class is, well, how should I put it ..... However, we had MAPLE! So, after discussing the ideas of an inverse, I presented this example and asked for help in solving for the inverse. More than one student said "Let Maple do it!" That's exactly what I wanted to hear. We asked Maple do some dirty work. It did, giving us three answers. After analyzing each answer we discovered the inverse function. (P.S. They were ALL AWAKE!!) We then plotted the three functions I mentioned above and got to SEE what an inverse function looked like. I think most of those students now know something about an inverse function and its graph. One additional comment needs to be made here. When I say "We did this and we did that" I literally mean WE. Each student has access to his/her computer and does the calculation or plot on that machine and gets to SEE the results immediately. Herb w -- ---------------------------------------------------------------------------- Herb Brown Math Dept The Univ at Albany Albany, NY 12222 (518) 442-4640 hibrown@leah.albany.edu or hibrown@cs.albany.edu or hb136@ALBNYVMS.BITNET ----------------------------------------------------------------------------