Foundations On how to best introduce the concept of differential in Physics

AI Thread Summary
The discussion revolves around understanding the concepts of differentials and differentiation in mathematics education. A participant seeks guidance on a specific article by Artigue and Viennot regarding students' misconceptions about these topics. The conversation highlights the challenges of teaching differentiation, with some contributors expressing concern that didactic methods can complicate rather than clarify the subject for students. They emphasize the importance of both intuitive and rigorous approaches to understanding differentials, suggesting that modern methods, such as differential forms, may be too advanced for high school students. Various resources, including academic papers and textbooks, are shared to aid in comprehension, but one participant ultimately decides to return to foundational calculus materials due to the complexity of the provided links.
mcastillo356
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Hi, PF

Here is the text I've taken a look at

file:///C:/Users/usuario/Desktop/2001_JMT_Girep.pdf

And the article I'm looking for:

Artigue M. and Viennot L.
Some aspects of students' conceptions and difficulties about differentials,
Misconceptions and Edu. Strategies in Sci&Math. Cornell, Ithaca, USA (1987)

To further understand the text. Don't know where to start from.

Love.
 
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mcastillo356 said:
Hi, PF

Here is the text I've taken a look at

file:///C:/Users/usuario/Desktop/2001_JMT_Girep.pdf

And the article I'm looking for:

Artigue M. and Viennot L.
Some aspects of students' conceptions and difficulties about differentials,
Misconceptions and Edu. Strategies in Sci&Math. Cornell, Ithaca, USA (1987)

To further understand the text. Don't know where to start from.

Love.

The first link is to your computer's hard drive.

I'm able to find links to the PDF for the article you are asking about with a Google search. Are you not getting the same search links?
 
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Hi, @berkeman, how are you?
This page:
https://iopscience.iop.org/article/10.1088/0143-0807/11/5/002/pdf
Three options: access through my institution (I am not enroled now), purchase or rent.
I will purchase.
Best wishes!
PD I would like to write you on April. Would you allow me? Things on track, thanks God, but still have an important meeting with a specialized doctor.
 
mcastillo356 said:
Here is the text I've taken a look at
Which is on your computer. We can't see it.
 
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mcastillo356 said:
PD I would like to write you on April. Would you allow me? Things on track, thanks God, but still have an important meeting with a specialized doctor.
Of course, feel free to contact me anytime. :smile:
 
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mcastillo356 said:
Are these people really serious that one should explain differentiation and differentials in this way? I'm sure that I'd have been utmost confused, if somebody had tried to explain it to me like this.

Often didacts make things much more difficult for the student in their confused attempts to "simplify" or "elementarize" a subject.

I think as a physicist you need both an intuitive understanding of expressions like ##\mathrm{d} x## as a difference in the limit of zero distance and in a rigorous sense of taking the appropriate well-defined limit (using the "##\epsilon##-##\delta## description".

Another more modern approach is also that of differential forms (Cartan), but that's for sure too advanced at the high-school level.
 
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vanhees71 said:
Are these people really serious that one should explain differentiation and differentials in this way?
The goal should be to have a non-infinitesimal transfer of knowledge about infinitesimals.
 
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Possibly enlightening:
(Dray and Manogue) Using differentials to bridge the vector calculus gap
https://bridge.math.oregonstate.edu/papers/use.pdf
(Dray and Manogue) Using differentials to differentiate trigonometric and exponential functions
https://bridge.math.oregonstate.edu/papers/trig.pdf
from Tevian's site:
https://sites.science.oregonstate.edu/~tevian/onid/cv/pubs.html#vector
and https://bridge.math.oregonstate.edu/

UPDATE:
https://blogs.ams.org/matheducation/2016/05/31/thick-derivatives/
 
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Hi, PF
@robphy, @DaveE, @caz , that's hard work! I've decided to turn back to the textbook Calculus. The links are very interesting, but too difficult for me at this moment. Anyhow, I will keep them on mind.
Greetings!
 

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