Re: Mathematica as a New Approach to Teaching Maths

*To*: mathgroup at smc.vnet.net*Subject*: [mg127512] Re: Mathematica as a New Approach to Teaching Maths*From*: W Craig Carter <ccarter at MIT.EDU>*Date*: Mon, 30 Jul 2012 22:15:37 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <9573433.50612.1343288228908.JavaMail.root@m06> <jv01n2$hds$1@smc.vnet.net> <20120730074544.4B4916847@smc.vnet.net>

I teach a class on the subject of mathematics applied to materials science and engineering. I use mathematica as a tool to emphasize the application of mathematics, visualization, simulation, and programming. http://pruffle.mit.edu/3.016/ I find that it serves as excellent reinforcement to concepts that they have only learned once in their mathematics curriculum. Furthermore, believe mathematica is an excellent vehicle for doing a broad survey of many maths topics and encourages students to browse, explore, and experiment with "untaught" mathematics material. I felt strongly that the "M"-like programs will play fundamental part in the students' future professions. Of the several choices, I picked mathematica because I felt that the mathematica skills were more natural with regard to mathematics. I believe that the learning curve being steeper was a net benefit as the students pick up other languages. As a final observation, I note that students who have taken my class do use mathematica as a tool in their subsequent classes, and I do hear from graduated students that they appreciated the skills that they have learned. W Craig Carter Professor of Materials Science, MIT On Jul 30, , at Mon Jul 30, 12 @3:45 AM, Richard Fateman wrote: > On 7/27/2012 11:43 PM, Ralph Dratman wrote: >> David, >> >> I agree that Mathematica is quite difficult to learn, but I also think >> a good teacher could make the learning process significantly easier by >> going carefully over certain key points which are not emphasized in >> the documentation. > > I think the point that is easy for enthusiasts to miss (and this > pertains not only to Mathematica but its competitors) is that students, > by and large, will (mostly correctly) view the introduction of > Mathematica into their courses as "extra work", "more homework" and > irrelevant to testing (will there be a computer on exams?). > > In point of fact, the difficulties of Mathematica are orthogonal to the > material in courses in numerical analysis, calculus, and probably other > topics. I have, for a number of years, been the "go-to" person for > instructors teaching calculus at UC Berkeley, when students using a > computer algebra system get what appear to be wrong answers from such > systems. While the number of such instances has decreased, they have > not disappeared, and some are "features". > > It is also important for enthusiasts to realize that many students do > not want their classes to be "enriched" by the introduction of a > peculiar computer program which they are forced to learn. Many students > simply want to get a passing grade so they never have to take another > math class. > > There are, of course, some set of students who are interested and > curious and enthusiastic. For example, students who ask, "How do > you write a computer program that does integrals?" These are perhaps > the same students who realize that the calculus textbook fails to > describe an algorithm for doing integrals, and may even understand > that there are some integrals whose closed form does not exist. > > Publications which address the question of "how does the introduction > of computer labs (etc) affect the student learning level" rather > consistently come up with a conclusion that is roughly, "they learn > about the same." >> >> For example, one of the most fascinating features of the language -- >> its ability to mix symbolic and numeric quantities -- can also be a >> source of great confusion for the neophyte. > > This is confusing only because they have learned another, more > restricted, language first. Ab initio, why can't > the mixture of symbolic and numeric calculations work? To a > mathematical sophisticate totally unaware of programming, it is > a big disappointment that BASIC (etc) cannot deal with uninitialized > variable x by computing x+x resulting in 2*x. > > > > >> >> I would also go very carefully over what one must do to keep the front >> end and/or kernel from going out of control, and how to recover when >> that does happen. >> > > This is of course totally irrelevant to the subject matter at hand, and > disappointing in the extreme that one must spend any time on this. > >> I have a number of related ideas to help students get the feel of the >> Mathematica environment before plunging in to accomplish serious work. > > Unfortunately, serious work encounters, fairly often, serious barriers. >> >> I would love an opportunity to teach Mathematica to a small group of >> smart high schoolers or beginning undergraduates. > > Tell us when you figure out how to market such a course. > >

**References**:**Re: Mathematica as a New Approach to Teaching Maths***From:*Richard Fateman <fateman@cs.berkeley.edu>