I have experience in teaching in Europe (France and Ireland) and in the US. The ways of teaching physics doffer quite a bit. In the US, Calculus is not required. Therefore, a Physics teacher has to teach physics using algebra. While in France, Mathematics courses incorporate calculus, even basic calculus. Also Physics courses implement some 'maths tools' like derivatives and so on, which makes the physics course a mixture between conceptual physics and calculus based physics. Some French teachers might say that the level dropped significantly, may be, but this is still another approach much more calculus based. Landau's famous textbooks use calculus, while Feynman's lectures are more intuition based (even though one cannot object that calculus is also a part of the lecture, at a second level of reading, I agree). Some teacher say, we don't need calculus as one can 'feel' the concepts. Some others will say that we should use calculus to solve problems, as one uses a screw driver for DIY at home. I think this is an interesting debate (less controversial, or may be not) and as usual your opinions are more than welcome!
But what do we do with concepts ? Physics is a predictive and quantitative science, therefore, what can we predict quantitatively without calculations ? I ask the question without condescending attitude, it's a real question. How can you teach student predictive and quantitative physics without calculus ?
“Physics is essentially an intuitive and concrete science. Mathematics is only a means for expressing the laws that govern phenomena”. Albert Einstein
Physics for non-majors is taught without calculus. Yet, learning a formula for a concept is considered essential. Physics for majors is often taught with an excruciating level of mathematics to the detriment of concepts.
It is necessary to calculate an outcome. Mathematical models are necessary. It is necessary to emphasize that models are not physics and the limitations of the models must be understood. Models do not tell us anything about concepts, but concepts explain the models.
Physics instruction without calculus can impede understanding the concepts because the model is constrained to algebra. Nevertheless, an instructor that understands the concepts knows how to explain the concept and the mathematics. Physics instruction that emphasizes calculation and derivation of models can fail to teach the concept and elevate the model to be the concept.
A good instructor must understand and teach the concepts. A good instructor must understand the model that represents the concepts. Teaching physics to non-majors is all about the concepts. Teaching physics to majors and engineers is all about the concepts and the models of the concepts. The models of the concepts require calculus.
Isn't this dependent on the age of the students? Basic physics concepts can be taught to younger children but by the time they reach post compulsory education, in the UK A level, then they need to be able to use calculus. If not what is being taught is not physics, or arguably any science since they are not being given the tools to derive from first principles, but Physics Studies.
From my experience, both are essential and reinforce each other. Concepts should be pushed forward by use of maths in order to introduce more advanced ones. This is how a science is built. I believe the teaching should follow the same path.
Joseph L Alvarez , I appreciate your lucid explanation, as follows:
" Joseph L Alvarez added an answer on June 28, 2018
Physics for non-majors is taught without calculus. Yet, learning a formula for a concept is considered essential. Physics for majors is often taught with an excruciating level of mathematics to the detriment of concepts. It is necessary to calculate an outcome. Mathematical models are necessary. It is necessary to emphasize that models are not physics and the limitations of the models must be understood. Models do not tell us anything about concepts, but concepts explain the models. Physics instruction without calculus can impede understanding the concepts because the model is constrained to algebra. Nevertheless, an instructor that understands the concepts knows how to explain the concept and the mathematics. Physics instruction that emphasizes calculation and derivation of models can fail to teach the concept and elevate the model to be the concept.A good instructor must understand and teach the concepts. A good instructor must understand the model that represents the concepts. Teaching physics to non-majors is all about the concepts. Teaching physics to majors and engineers is all about the concepts and the models of the concepts. The models of the concepts require calculus."
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I studied physics, and before that, algebra, geometry, trigonometry, calculus, number theory, boolean algebra, topology, probability theory, biology, geology, and chemistry all in separate courses. All of your statements strike a chord with me. I attained the "excruciating level of mathematics to the detriment of concepts"; however, I took "physics for non-majors," which is "taught without calculus." Thank you so much for showing the logical pathway in your lucid flow-chart!
Nancy A. Watanabe
Ph.D., Comparative Studies in Literature
Certified: Teaching Technical and Professional Writing
College of Engineering
University of Washington
Course Taught: Technical and Professional Writing for Engineering Majors
University of Alaska, Fairbanks
University of Oklahoma, Norman
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