Re: decoding inbuilt function
- To: mathgroup at smc.vnet.net
- Subject: [mg121054] Re: decoding inbuilt function
- From: "David Park" <djmpark at comcast.net>
- Date: Thu, 25 Aug 2011 07:05:41 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <201108221003.GAA22469@smc.vnet.net> <4592974.8304.1314168104259.JavaMail.root@m06>
Mathematica is not directly a tool for teaching mathematics, nor so much a tool for doing mathematics. It more a meta-tool for constructing the tools you need for doing these things. Almost any field such as pedagogy or application to specific areas of engineering, mathematics or science will require that someone construct the needed tools. WRI provides basic, and powerful, algorithms to do many things and auxiliary tools such as the notebook interface with sectional grouping and Text cells, which provides the ability to write literate documents. It is not reasonable to expect WRI to flesh out all the possible applications. There are just too many and they wouldn't even be the best people to do it. Mathematica is poor at teaching basic mathematical ideas. Rather, it has extensive and maybe "messy" algorithms to do various things such as limits and integrals. If you want to teach these things you have to bypass the Mathematica routines and provide routines or rules, probably in the form of axioms, that can be directly applied to expressions to carry out calculations and derivations. I have an example of this for limits in one of the essays in the Presentations application. Somewhere in the Mathematica Book there is an example of writing rules for evaluating a limited kind of integral. Again Presentations has a StudentsIntegral section for manipulating single variable integrals by various basic techniques before evaluation from a table, or handing them over to Mathematica. No one knows how to use Mathematica (including me)! It is too new a medium with such new powerful capabilities. One can't just mechanize old approaches. There is A LOT of work and development to be done, and not just by WRI. How can you get more students to actually do mathematics on their own? To take off and fly solo? One thing that I feel fairly certain of is that humans understand actions better than static diagrams or lists of equations. Just seeing a notebook evaluated step by step (even if it is rather minimal) is better than looking at a pre-evaluated notebook. And moving sliders or pushing buttons might illustrate a point but it is a long way from DOING mathematics. That's why I question the utility of CDF and use of single Manipulates. It's a diversion from better solutions. (And besides, the development of CDF seems to be corrupting regular Mathematica in use of system functions such as saving notebooks.) Just get regular Mathematica - early - and start learning how to use it. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Ralph Dratman [mailto:ralph.dratman at gmail.com] If a student comes to your office saying she cannot seem to understand this "limit" thingy, I wonder if you would wish to say, "Don't feel too bad, Ms Liddell. No one in our department understands limits much better than you do! Anyway, not enough to program a computer to do them. Only Wolfram has the algorithm for that." This seems unconscionable to me. But then, I didn't realize taking limits was so difficult. In order to differentiate something, obviously you have to take a limit. Yet I never heard of anything one couldn't manage to differentiate. And then having the derivative of a function would surely help in taking other limits involving that function. What's the big difficulty? Ralph
- References:
- decoding inbuilt function
- From: student <ragamadhuri.24@gmail.com>
- decoding inbuilt function