One of the reasons that I love this work is that I am continually learning. My students are always forcing me to thing about physics more deeply and in new ways. In the past few weeks, I have come to a new way of articulating what all I am expecting my students to learn in my class. I do not claim that these ideas are in any way new; I am simply articulating these ideas for myself. In this paradigm, there are at least three aspects of learning physics:
- The physics concepts themselves: This can be done completely without math. Here I am looking at questions such as, “can students describe the difference between temperature and heat?” or, “can students describe what a force is and what it does?” I know from talking to students that many students skip over this particular aspect, and suspect (hope?) that exercises such as asking students to write will help students develop competency in this area.
- Problem solving skills: This is a somewhat standard aspect of learning physics that I think my students are expecting and involves not only mathematical skills but also being able to apply the physics ideas to new situations. The ability of students to learn to solve physics problems while still being unable to answer questions such as those above indicates to me that these problem solving skills can be, to a point, developed separately from physics conceptual knowledge. However, I think it is clear that strong conceptual knowledge is critical to having students be the most successful problem solvers possible and is essential if students are make sense of their results.
- Learning to read mathematics as a language: As E. Redish and other have often pointed out, the use of mathematics in science is different than the use of mathematics in math. In science, we use mathematics more as a language (albeit a very useful and powerful one!) to describe real-world phenomena. Furthermore, as again Redish and others have pointed out, our students are not good at seeing the difference and reading math. I have seen this in my own classroom with students’ initial reluctance to use superscripts and subscripts claiming that they find them “overwhelming.” Giving sufficient practice problems that are sufficiently complex, where the super and subscripts are critical to success, seems to help. Another example of students struggles with mathematics as a language is the all too common mistake of students calling W the work when, in the context, it actually represents the number of microstates. Therefore, designated exercises to help with this are clearly important.
Without all three of these skills, I do not think that I can expect students to be able to comprehend and apply the material to the degree that I would like.