For example, in the context of this project and what students should learn in today's crowded curriculum, consider this quote from Benjamin Crowell [1]:
In many subfields of physics these days, it is possible to read an entire issue of a journal without ever encountering an equation involving force or a reference to Newton's laws of motion. In the last hundred and fifty years, an entirely different framework has been developed for physics, based on conservation laws.
The new approach is not just preferred because it is in fashion. It applies inside an atom or near a black hole, where Newton's laws do not. Even in everyday situations the new approach can be superior. We have already seen how perpetual motion machines could be designed that were too complex to be easily debunked by Newton's laws. The beauty of conservation laws is that they tell us something must remain the same, regardless of the complexity of the process.
[1] Benjamin Crowell, Light and Matter, chapter 14, retrieved from
http://lightandmatter.com/html_books/lm/ch14/ch14.html
Hello Christian,
Yes, and thank you for bringing in the children.
Once, giving a talk to my son's fourth grade class, 9 years old, I asked the students what numbers could be divided by two, and gave the list 1,2,3,4,5,6,7,8,9,10. All the students said 2,4,6,8,10, very proudly. I remarked that any number can be divided by two. For example, I explained, if you give a little 3 year old girl a cookie, who never went to school, and ask to share with her sister, she will divide it in half, and give half to the sister. What is lost in school, I asked. The wrong intuition is given to kids, under the guise of simplication. Then, we started to talk, and their attention amazed me and their teacher.
I just presented a comment in RG, that fits the first part of your comment, on physics. To avoid duplication, please refer to it (third answer) in the link: https://www.researchgate.net/post/In_a_physics_context_what_do_students_find_difficult_in_using_Lagrangian_and_Hamiltonian_methods
Cheers, Ed Gerck
CONCLUSION: Yes, it would it better for students to learn conservation laws first, and avoid non-covariant descriptions such as Newtonian mechanics.
Rather than vectors (forces) in Newtonian physics with F = ma, students can focus on the Euler-Lagrange equation, or Lagrangian, where one does not use vectors because the equations of motion are based in scalars (energy).
Further, in probably most physical situations, the Euler-Lagrange equation has been superior, for about 250 years, to using F = ma (even when F = ma is valid) and especially where it is not, such as inside an atom or near a large mass.
More at Preprint New Physics with the Euler-Lagrange Equation: Going Beyond Newton
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