An Important Paper on Math-As-Language

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.

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:

  1. Let students try to translate the physical concept themselves into mathematical language.
  2. Allow them to collaborate as a team to form a communal definition.
  3. Have each team write their definitions on the whiteboards.
  4. 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.

A Quote that I think Applies to the Different Problem Solving Schemas of Novice and Expert Physicists

In the beginner’s mind there are many possibilities, but in the expert’s there are few”

Shunryu Suzuki

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?

  1. 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.

Adding Biological and Chemical Authenticity to the 131 Textbook

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:

  1. 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.
  2. 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.

Toggerson Awarded Commonwealth-wide award for work on OER

Brokk Toggerson has been awarded 3rd Place (Bronze) / $500 prize from the first-ever Department of Higher Education Open Educational Resources Olympics for his work on the Physics 131: Forces, Energy, Entropy and Physics 132: What is an Electron? What is Light? open-source textbooks. These awards were established to honor the extensive accomplishments of of public higher educators statewide. Winners were selected by a sub-committee of the OER Advisory Coucil. The first and second place winners were from community colleges meaning that Brokk Toggerson was the only awardee from a research university.