Is Overly Fundamental Understanding of Physics Concepts Hindering Learning?

[anorlunda]

I have noticed a surge in questions in the physics forums from people tying themselves up in knots trying to understand fields, electrical and electronic devices, and especially Ohm's Law, by reasoning one electron at a time. They get themselves tied up in chicken-egg issues and circular definition loops. IMHO their struggles are needless and caused by attempts to understand things at an overly fundamental level.

Ohm's Law V=IR, is a very simple and incredibly useful. But that is a bulk (averaged) form of the law. Ohms Law can also be expressed in terms of fields distributed in time and space, but only after the student has sufficient calculus to accurately describe it. I do not believe that attempts to understand the distributed form by intuition alone is fruitful. One can study how to make use of resistors without learning how resistance arises on the molecular level. Students who have not yet learned the math should IMHO be encouraged to explore V=IR in all it's glory while never trying to visualize it one or two electrons at a time.

The same applies to magnetic fields, generators, motors and the electric grid. It is not fruitful to study those without calculus and differential equations.

The same applies to particle mechanics. Temperature is a 3D scalar field that at the particle level expresses kinetic energy. Wind is a 3D vector field that at the particle level expresses kinetic energy. If one starts visualizing one particle at a time, he/she might come to the absurd conclusion that temperature and wind must be the same thing. Without calculus, these topics should be studied only at the bulk level, forgetting particles.

Perhaps the surge in such questions is in my imagination. I have not done statistical analysis. But perhaps it results from a change in elementary/secondary science education methods that believe that science is most easily understood at the fundamental level and working up. Is that the case?

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

 

[martane]

As someone who has also noticed an increase in these types of questions, I completely agree with your assessment. Trying to understand complex concepts like Ohm's Law or magnetic fields by visualizing one or two particles at a time can definitely lead to confusion and frustration. It's important to have a solid understanding of the fundamentals and the math behind these concepts before attempting to visualize them on a smaller scale.

I think part of the issue may be the way science is taught in schools. Many times, the focus is on memorizing formulas and equations without truly understanding the underlying principles. This can lead to students trying to make sense of things at a fundamental level without having the necessary knowledge or tools to do so.

It's also important for educators to emphasize the importance of calculus and differential equations in understanding these concepts. While it may seem daunting to some students, having a strong foundation in these mathematical concepts is crucial in truly grasping the complexities of fields and other physics topics.

In conclusion, I agree that it's important for students to focus on the bulk form of these laws and concepts before delving into the more complex, distributed forms. It's also important for educators to stress the importance of calculus and differential equations in understanding these concepts. Hopefully, with a stronger emphasis on these fundamentals, we can see a decrease in the number of confused and frustrated students in the physics forums.