Re: The audience for Mathematica (Was: Show doesn't work inside Do
- To: mathgroup at smc.vnet.net
- Subject: [mg102167] Re: The audience for Mathematica (Was: Show doesn't work inside Do
- From: Helen Read <hpr at together.net>
- Date: Fri, 31 Jul 2009 05:55:38 -0400 (EDT)
- References: <h4m4ca$ecg$1@smc.vnet.net> <h4p3g1$itm$1@smc.vnet.net> <h4rq4o$m34$1@smc.vnet.net>
- Reply-to: HPR <read at math.uvm.edu>
David Bailey wrote: > Helen Read wrote: > >> You can teach them both at the same time, using one to reinforce the other. >> >> I teach my (university) calculus students *calculus*, using Mathematica >> >> - as a tool for graphing and visualization >> - as a tool for carrying out numerical calculations >> - to check work done by hand (integrals, derivatives, algebra, etc.) >> - to carry out such work (integrals, derivatives, algebra, etc.) after >> we have done the thinking / setting up >> - for discovery learning, where the students can explore and learn by >> looking at examples, and build or re-inforce concepts >> > > Your teaching style sounds really effective - certainly in comparison > with the courses I attended as a student - in the days of chalk! > > My only query is, how do you set homework problems where you want the > student to solve the problem by hand - say an integral that requires a > substitution. Some students will inevitably get the answer with > Mathematica, and then fill in the intermediate steps! That's actually not a bad way to learn. The "skill and drill" type homework that I assign is for practice, and isn't collected or graded. The students know that they will have to do some integrals by hand on quizzes / tests, so it makes no sense for them to "cheat" on the practice homework. In fact, I often tell the students to do the skill problems by hand for practice and use Mathematica to check their work. As an example, when learning integration by partial fractions, students will often try a problem, check the answer in the back of the text and find that they did something wrong. Now, what went wrong? Did they goof up the algebra in finding the partial fraction decomposition, or did they get that part right and integrate incorrectly? They can use Apart[] to check their partial fraction decomposition, then try to correct their own algebra if it is found to be wrong. Once that's all OK, they can check the actual integration with Mathematica, and try to hunt down and fix any mistakes. -- Helen Read University of Vermont