Redish, Edward F., and Eric Kuo. “Language of Physics, Language of Math: Disciplinary Culture and Dynamic Epistemology.” Science & Education 24, no. 5 (July 1, 2015): 561–90. https://doi.org/10.1007/s11191-015-9749-7.
I recently finished this paper on the differences in the use of mathematics between physics and mathematics as viewed from a linguistics/semantics standpoint and it was quite informative. Often folks discussing undergraduate curricula (including here at UMass Amherst) speak of the need to simply require physics majors to take more math courses. This paper provides an interesting counter perspective. This paper may also be an interesting addition to P691G.
I also think that this paper, along with several of the references therein that I would like to read, has further reinforced my idea that the prep for 131 should be reconsidered. I really think that it should be, to quote the paper, “without the equations.” I will, of course, keep the mathematical reviews as needed because we will do math but a strong conceptual stance in preparation is the way to go. In class, we can then focus on the translation to mathematics as an explicit skill.
Yesterday, I met with Theresa Austin, of the College of Education’s Language Literacy, and Culture program, and Adena Calden of the Department of Mathematics, about this issue. The goal being to determine what insights from the teaching of English to ESL students could perhaps be employed to teach my students their second language of mathematics. The conversation was productive. In particular, she provided an excellent procedure for the in-class translation exercise:
- Let students try to translate the physical concept themselves into mathematical language.
- Allow them to collaborate as a team to form a communal definition.
- Have each team write their definitions on the whiteboards.
- Do a gallery walk activity involving critique and voting for the best one.
For step 4, I will need to think more about how to facilitate constructive criticism. Perhaps Chris Ertl, who has done some neat work on poster sessions for the labs, can provide some good suggestions.
“In the beginner’s mind there are many possibilities, but in the expert’s there are few”
While this quote is meant to encourage folks to keep the sense of open mindedness in the face of advancing knowledge, I think an alternative interpretation works well for physics instruction.
As Chi et al discuss in their work1, novice and expert physics students approach analyzing problems in wildly different ways:
- Novices tend to focus on the surface features of the problem: ramps, friction, pulleys, ropes, etc. In their “beginner’s mind” these are all simply different types of problems – there are “ramp problems,” “friction problems,” etc.
- In the “expert’s mind,” however, there are a lot fewer options: all problems begin from a small set of universal principles: Newton’s Laws, Conservation of Energy, etc.
Perhaps this quote can help students cement their knowledge?
- Chi, Michelene T. H., Paul J. Feltovich, and Robert Glaser. “Categorization and Representation of Physics Problems by Experts and Novices*.” Cognitive Science 5, no. 2 (April 1, 1981): 121–52. https://doi.org/10.1207/s15516709cog0502_2.
Another year has past and with it a lot of changes to my 131 efforts. This year has represented the first time I have taught P131 since Spring 2017 and coming back at it with fresh eyes has been very illuminating. There will probably be a lot of discussion on what I did this past year and how it can inform where I am going in the next iterations during the 2023-2024 school year.
One thing, which has become apparent as I publish my 132 Textbook: What is an Electron? What is Light? to the Living Physics Portal has been the inclusion of sections from OpenStax Biology, OpenStax Chemistry – Atoms First 2e, and the occasional selection from some of my peers in the disciplines here at UMass Amherst into that text. These sections are, almost by definition, authentic representations of the language and modes of thinking which characterize these disciplines. Including them in the physics text serves a two main purposes:
- Such sections help ensure that students see the physics material as connected to their majors’ courses. After all, right there, in the text, is some information straight out of a biology or chemistry class.
- Such sections also provide an equity role: not all students in 131/132 have the same major background; some students may have not been required to take certain classes for example while others may, due to the differences in the semesters in which different majors take physics, have taken these courses several years ago. By including them in the text, I am making sure that the needed biology or chemistry information is fresh in each person’s mind.
As I said, such sections are already exist in the 132 textbook, and submitting it for review has re-impressed on me the importance of such materials. Also important are homework questions that test the material. I remember as a student skipping these introductory/motivational chapters in my intro texts (Young and Freedman’s Sears and Zemansky’s University Physics with Modern Physics 13th ed.). Simple economic factors were at play: I had a limited amount of time and the material in these sections was never assessed in any way. Thus, I skipped them. Recalling this economic thinking shows the importance of having homework assessment of the material.
So, what am I thinking with regards to such biology/chemistry sections? Which should I perhaps include? Well, I am sure that this list will change as I go this summer developing the materials for fall, but a few already come to mind:
- Entropy – Some discussion on the importance of entropy to biology and chemistry? Perhaps more on the Gibbs Free Energy? Also some comments about some of the examples we work such as the alignment of cytoskeletal fibers in cell division?
- Energy – Some overview of the ideas of energy from a biology text?
- The ATP reaction – I use this a lot in my discussion of microscopic energy and during the past semester a few students’ comments demonstrated that a review of this material would probably be beneficial.
- Some discussion on ground reaction forces for when we get to simulations etc from a kinesiology resource? A discussion of force plates could also be good.
Just a few thoughts I figured I would get down.
I am currently reading a book entitled Get Better Faster: A 90-Day Plan for Coaching New Teachers by Paul Bambrick-Santoyo. While a more detailed review will come later, there is one point that is of particular interest. The author suggests that, when monitoring student work, the monitors (in my case myself and the TAs) should go to the fastest groups first. At first glance, this seems counterintuitive: shouldn’t the in-class assistants spend the most time with those groups who struggle the most? Bambrick-Santoyo, however, points out that going to the fastest groups first has two benefits:
- The in-class assistants get a good sense of where the students are likely to struggle and what alternative conceptions students have. While I always encourage my TAs to work the problems in advance and while we discuss them in our weekly meetings, these efforts are not always sufficient. By attending to the fastest groups first, TAs in particular get a in-the-trenches sense of where students are likely to stumble.
- Attending to the fastest groups first gives those groups who need a little more time the time they need to progress to the point where they are in a position to ask a question or get feedback.
Again, I am sure there will be more to come from this book, but I wanted to share that out.
Another addition this semester was a “problem solving process.” While most physics textbooks include problems solving processes, I have a fundamental disagreement with the philosophical underpinnings implied by these published sequences. Many of these processes implicitly suggest that students should be able to look at a problem and see all the steps before beginning work; that they should be able to “outline a solution” before even beginning the math. In my experience, this is not how physicists solve problems. Frankly, a situation is not really a problem if you know all the steps upon setting out. I want students to learn to sit with the discomfort of not knowing all of the steps at the outset and to develop the confidence needed to figure out problems as they go.
Continue reading “Reflections on Physics 132 Spring ’22 Part III – Added this semester: A problem solving “process””