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.

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.

Reflections on Physics 132 Spring ’22 Part III – Added this semester: A problem solving “process”

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””

Reflections on Physics 132 Spring ’22 Part II – Something that has been evolving for a few semesters: After-class broadcasts

One of the biggest challenges in any course is managing the limited time available. The UMass semester is configured so that there are always 13 Mondays, 13 Tuesdays, 13 Wednesdays, etc. For a course that meets MWF, this schedule means there are 36 class sessions of 50min each. This is a really short amount of time to cover optics, electricity, magnetism, and modern physics as prescribed by the Physics 132 official course description. One way to save a little time each day, while simultaneously making the course more equitable is through the use of daily “broadcasts.” These emails, which I have been sending after each class since the start of the pandemic, contain both a summary of the day’s material and any announcements. After five-semesters of refinement, I feel I have a sense of the key features.

Continue reading “Reflections on Physics 132 Spring ’22 Part II – Something that has been evolving for a few semesters: After-class broadcasts”

Reflections on Physics 132 Spring ’22 Part I – Updates on the use of TAs in large-enrollment Introductory Physics for Life Sciences courses

Another semester is in the bag, and, if all goes according to plan, this will be the last time I teach physics 132 for quite a while. As such, I think a deep reflection on the semester is particularly warranted. While some changes/additions such as a fully remote option, there were several attributes added or revamped for this semester’s course. These, and existing features, all need consideration for their successes and areas for improvement. This is the first post in a series taking that deep dive into reflecting on Physics 132 Spring 22.

The teaching of large enrollment courses is always a team effort: requiring not only the instructor but also support staff such as lecture prep as well as both graduate and undergraduate teaching assistants (TAs). During the Spring 2022 semester, Physics 132 had two graduate and seven undergraduate TAs. In order to optimally support student learning, I feel that, as leader of this team, my critical roles include: forming a team with diverse experiences and knowledge; leveraging each team member’s unique knowledge, skills, and perspective; promoting a culture wherein each TA feels their expertise is acknowledged; ensuring everyone feels comfortable in their role and empowered to do their best to support students.

 A successful TA team begins at its formation. When I started at UMass in 2015, I used graduate TAs exclusively as that was my prior experience. As time went on, and the level support I felt was necessary increased, I began to hire undergraduate TAs to help fill the gaps using exclusively upper-division physics majors. This preference for physics majors was not carefully considered. I am somewhat ashamed to admit this preference arose from a sort of “physics chauvinism.” I assumed that majors in their third and fourth years, with their presumably deeper knowledge of the content, would make the best TAs.

I have since discovered what, in retrospect, should have been obvious: that a more diverse teaching team that mixes in life-science majors who had previously been successful in the class was superior. While my assumption regarding the deeper knowledge of upper-division physics majors has turned out to be true, life-science majors bring several other important attributes which strengthen the team as a whole.  

The undergraduate Physics 132 alums not only bring their valuable perspective as former students in the course to the TA role, but also their life science knowledge and disciplinary mode of thinking are useful to share with the physicists on the team. Physics 132 is very much an introductory physics for life sciences course. In addition to biological applications sprinkled throughout the material, each unit has a central biologically- or chemically-authentic motivating context [link to talk]. Having biologists on the teaching team can help make these examples more authentic and can ensure that I am using the language with which my life-science students will be familiar. For example, I was using the term van der Waals interactions. However, thanks to my undergraduate TAs, I learned that the term London dispersion forces is more common. Thus, I switched to primarily using London dispersion forces while still mentioning van der Waals for those who may be more familiar with that term.

To further empower my team members, I adopted a new format for my weekly team meetings taken wholesale from Prof. Guy Blaylock in our department. In past semesters, I struggled with promoting engagement during these planning and preparation sessions. TAs would often remain quiet while I presented information about upcoming topics and would even remain reticent when I explicitly solicited their feedback on student challenges they had observed. Prof. Blaylock’s practice for these meetings involves assigning one teaching team member each week to present on the upcoming material with an emphasis on the particular challenges that they think students might face along with suggestions on how they themselves learned the material. To ensure that the presenting member was fully prepared for this role, they were notified a week in advance and had access to the prior semester’s materials.

This meeting format has, in my opinion, been a wildly successful switch. All my TAs were more engaged throughout the meeting process – not just when it was their turn to present. These presentations resulted in more feedback from the TAs on student difficulties, their own struggles with the material. I feel that giving officially dedicated space for TA insights gave them all permission to contribute as full members of the teaching team.

My role in these discussions was often became that of “translator:” explaining biological concepts to the physicist members of the teaching team and physics concepts to the biologists. This role forced me to grapple more deeply with the disciplinary differences between biology and physics resulting in, I feel, a better understanding for myself and thus a better course.

These observations are not just my own. The TAs themselves shared similar opinions in an end-of-semester evaluation of me. In the words of one TA, “I thought the structure of the team meetings each week was quite beneficial. Specifically, having each TA lead a brief discussion on the current and/or upcoming topic being taught in class often provided the rest of the team with tips on how to explain concepts students often struggle with using different approaches and perspectives that are conducive to a more wholesome understanding. Overall, the team meetings were more involved than those I attended the previous semester, which I felt made a difference in the way I engaged with students taking the course both during class and in the physics help room; there were numerous times were I employed suggestions taken from the team meetings and found that the concepts clicked with students after doing so.”

Beyond ensuring that the TAs were prepared for the material, I feel that giving the TAs the potential for ownership helped them feel more comfortable sharing other challenges with me. For example, two young women on my teaching team were comfortable enough to share some personal difficulties they were having with some students in the help room. I am very glad that I was able to create a sufficiently trusting environment that these two young women felt comfortable sharing this with me and that we were able to work together to find a solution to address the issue.   The fundamental philosophy of these meetings is, I think, beneficial to leadership in general: allow the team to have a substantial and empowered leadership role (as opposed to simply explaining their importance as I used to do). While I know that this is not at all a new idea, as a faculty member moving in to more roles of leadership, such insights are of critical importance. Perhaps a similar philosophy could be, at least partially, implemented in 691G?