Monday, December 10, 2007

Symbolic Manipulators Affect Mathematical Mindsets

This preprint is a rather "entertaining" reading, and you don't say that very often with things like this.

This work examines the impact of the availability of symbolic calculators, such as Mathematica, on physics students. It appears that the students are more "free" to explore the mathematical solutions using different paths. However, the study concluded that the students appears to not be able to make the connection between the mathematics and the physical meaning of the mathematics.

The students show admirable flexibility and creativity as they try different calculation strategies and representational forms. Rather, the difficulties associated with Mathematica use appears to arise from more subtle issues. They arise from a local coherence in their thinking that leads them to focus on computational aspects of the problem while suppressing the connection with the physics and with extended mathematical meanings.

I got very fascinated with several of the transcripts of the conversation between the students as they struggle to solve physics problems. I just hope they knew they were being recorded. :)



Anonymous said...

Agreed. It's just totally fascinating to read the conversation as they try to calculate the mean value :p

Really fun read. Thanks for the link.

Stupac2 said...

Well, as someone who just finished the first half of DJ Griffith's book, I can say that mathematica helps, a lot. I don't usually use it for "difficult" math, in the sense that I couldn't do it without the computer, just for "painful" math, things like finding expectations of ridiculous wavefunctions. Anything involving the uncertainty principle needs four integrals, at least, and with any wavefunction that's not from a simple system those are just murder by hand.

It's kind of funny, though, that someone is getting paid to study what I spend a few hours on every weekend.

ZapperZ said...

Well, I wouldn't say that they got "paid" for it. I think the authors are probably either instructors for the course, or someone who's doing some pedagogical research work on physics education.

I think it is interesting to consider how, with the availability of all these modern conveniences, the teaching and learning process in physics have changed. Know subtle effects such as the ones cited in this work might help instructors to pay attention to certain pitfalls.