Dr. Courtney said:
Students who learn intro physics like this both master the essential concepts in physics as well as quantitative problem solving. The light goes on for them regarding "The Unreasonable Effectiveness of Mathematics in The Natural Sciences." The quantitative problem solving skills carry over into many other areas. "Conceptual Physics" is an oxymoron. Physics does not exist apart from the ability to make quantitative predictions and measurements. Once students have the algebra skills to handle it, teaching them that Physics is only qualitative and conceptual is dishonest.
I think we are both in error in our assumptions of the other. I am in no way arguing for the removal of mathematics from physics education (or even an introduction to physics course). Perhaps i will have to abandon the use of the term
conceptual physics instead of asking the community to view it differently. I am arguing for a revamp of the problems we assign and the topics we cover in our general physics classes.
Consider the following two questions.
1) A block is at the top of a frictionless, flat ramp. When the block is released from rest, what energy changes does the block undergo as it travels to the bottom?
2) A 0.50 kg block is at the top of a frictionless, flat ramp, that is 1.0 m high. The block is released from rest. What is the block's speed at the bottom of the ramp?
Now, the first question will come under a lot of fire from physics teachers and professors alike. "By not applying a mathematical model, you are not doing physics!" I would wholeheartedly agree with this sentiment.
I do not want to defend the first question. But, why does the second question not come under much fire? Partly because we require more from the student than just to provide an answer. We want them to show their work and, as you have your students do, assess their answer. Now, i want to introduce a third question to the fold.
3) A block is released from rest at the top of a frictionless ramp that concaves inward. An identical block is released from rest from the top of a frictionless ramp that concaves outward. Which block will be moving faster upon reaching the bottom?
This question requires a mathematical response, like the first question. However, this question, unlike our second question, does not end at a result. It is the start of more questions. "Why do i receive the same result, despite two differently shaped ramps?" Question one lacks a result. It is hard to discuss results in physics if you are not generating any! Question two ends at the result. Question three takes me beyond the result.
Now, let's look at the topics covered in a general physics course. Generally, these courses are mechanics heavy. You start at the beginning of the text, and you go as far as you can before time runs out. In my old school, another reason for our general physics course being mechanics heavy was to prepare students for the now defunct AP Physics B curriculum. This frustrates me because all students are being treated as future physics majors.
The problem with this kind of course is twofold. We promise to open their eyes to a new way of seeing the world, but we cover far few phenomena (whether that phenomena is suitably explained classically or not). In my first year teaching, our school's general physics course spent over two months covering the motion of a ball, whether thrown or dropped in a vacuum (i.e. kinematics). We then revisited that same motion of a ball in terms of energy, for another few weeks. For a third of the school year, my class looked at the motion of a ball (that doesn't even roll!).
Secondly, mechanics is perhaps the most abstract part of the curriculum. You deal with definitions (force, momentum, and energy) that will serve useful in the rest of physics. In creating those definitions, modelling all sorts of objects as a point suffices. Well, it suffices for us, but not for the students. We are supposed to be wetting their feet in modelling, not drowning them.