Re: learning calculus through mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg108082] Re: learning calculus through mathematica
- From: Murray Eisenberg <murray at math.umass.edu>
- Date: Mon, 8 Mar 2010 06:11:25 -0500 (EST)
One reason is very simple: by using a CAS to do many long symbolic calculations, students can focus on modeling and the resulting and relevant mathematical concepts and methods -- not the details of carrying out long chains of algorithmic, algebraic steps. My 45 years of teaching make perfectly clear that, for most students in calculus, e.g., they are so involved in trying to get the symbolic manipulations right, they have little or any idea of why they're doing them. They totally miss the forest for the trees. The other side of this situation, I regret to say from my experience, is that the lazier or intellectually weaker students are often incapable of rising above merely carrying out mechanically the symbolic manipulations -- many of which they get wrong anyway -- to have much of an understanding of the higher-level concepts involved. On 3/7/2010 4:06 AM, Andrzej Kozlowski wrote: > I have never seen or heard any convincing reason why using a CAS should > make it possible to understand and learn better those areas of > mathematics which are fully accessible to a student with only a pen and > paper. In fact I can see a few reasons why the opposite might be the > case. In many situations I can see clear advantages in performing > algebraic manipulations "by hand" or even "in the head", which is, in my > opinion, the only way to develop intuition. The same applies to > visualisation - while being able to look at complicated graphics can > often be a big advantage, I always insist on students developing the > ability to quickly sketch simple graphs by hand on the basis of > qualitative analysis of analytic or algebraic data. This is again > essential for developing intuition and I am not convinced that doing all > this by means of a computer will provide equivalent benefits.... -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305