Re: Mathematica as a New Approach to Teaching Maths
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- Subject: [mg127497] Re: Mathematica as a New Approach to Teaching Maths
- From: Richard Fateman <fateman at cs.berkeley.edu>
- Date: Mon, 30 Jul 2012 03:45:44 -0400 (EDT)
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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.
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