A Study of the Development of the Paradigms in Physics Program

Meeting before each class with assistant(s) to discuss their impressions of the previous class, plan the upcoming class, and discuss ways to improve those plans.

This faculty member met with assistants before each class to discuss what happened in the previous class and plan for the next class:

I have really appreciated having regular feedback from a team of people (graduate assistants and postdoc), that's been super helpful. We meet for an hour before each class, not the hour right before class but it's the day of the class in the morning. I ask them how they thought the previous class went, I tell them my plan for the day, and then they tell me how to make it better.

During these debriefing meetings, this faculty member and assistants rehearsed plans for the small group activities and interactive lectures, discussed likely student difficulties, and shared feedback about student experiences in the course:

I feel like I'm getting less feedback from the students than I did when I was younger...students talk to (the assistants) and so I feel like I'm getting some feedback indirectly through them...

This faculty member reflected on the difference between being in charge as a professor and assisting in a course:

I think there are lots of reasons, one is I'm the professor, so I think that that status is maybe intimidating...and when I was a post doc, I had infinite office hours; students used to come in and I would have long conversations with them and I don't have that now...(as a postdoc) I wasn't leading the course every day, I wasn't deciding on what the content was and so I had more brain cycles to concentrate on the students' experience. This time through I'm really thinking about the content of the course and what I'm saying to the students...it's been really hard to dedicate brain power to interpreting students' answers and getting feedback from the students. It's been surprising to me this term just how distant from direct student feedback I feel.

This faculty member wanted more feedback from the students, not only about the details of their ideas but also about their perceptions of how the course was going.

After a few weeks in the course, asking for direct student feedback with an anonymous survey.

This faculty member sought direct feedback by inviting the students to respond to an anonymous survey asking what their perceptions of the course difficulty were, what they liked about the course, and what if anything they would like to change about the course:

I did a survey of students and I've gotten a few more responses. I asked them, “can you tell me what the difficulty of the course is for you?” There is a Likert 5 point scale and the options were “very difficult, a bit on the difficult side, about right, a bit on the easy side, and very easy.” Most of the responses were “about right” and “a bit difficult”, which I think is a good space to live in; there were a couple of “very easy” and no one was willing to admit that it was “very difficult”...I'm happy with that distribution... I also asked the students what if anything they liked about the course? They like the emphasis on problem-solving; they like the emphasis on physical reasoning and doing problems that are a little more challenging than in the introductory course; and I've been getting a lot of positive feedback about the interactivity in class.

This faculty member also asked students directly about how much time they were spending on the homework:

I asked them how long they'd spent on it (the homework) and some people said that they'd spent threeish hours on it and some people said they'd spent sixish hours on it. I encouraged the students who said they were spending sixish hours on it that that was longer than I intended and that they should come to office hours and ask questions.

It is important to encourage students who are spending a long time on homework to come to office hours, especially those who may feel hesitant to seek the help they need.

As the course progresses, considering whether choices of subject matter and/or resources to include are appropriate and whether topics thought to be important for later courses are really necessary to be addressed in this one.

About midway in the course, this faculty member began to reconsider the inclusion of problems based on how rockets work:

The rocket stuff is not fitting into the course as well as I had hoped and so I'm considering in future years just dropping it completely; haven't made up my mind about it...Rockets was nice because it was an example of mass changing with time and it was also nice because it really built upon the differential equation story that we'd been telling in the course but I think those are less important goals than having a better conceptual understanding of rotational motion.

Some of the students were having a hard time making sense of the problems involving non-uniform circular motion and angular momentum because they lacked a strong background in the introductory material taught in the pre-requisite Physics 211 and Physics 212:

A surprise that should not have been a surprise is that stuff that I thought students would have a better understanding of from 21X is still difficult for some students, I think the bottom cluster of students, that's what they're struggling with... the common misconceptions that didn't seem to be addressed for these students in the intro sequence.

Omitting rocket problems in the future would allow more time to strengthen conceptual understandings for students likely to encounter difficulty in contexts involving rotational motion.

This faculty member decided not to include contexts requiring complex numbers in the current version of the course:

We decided to drop complex numbers from the course and I'm finding that to not be an issue...I was planning on talking about a particle moving in a magnetic field ...you need complex numbers to describe that trajectory and then I dropped that topic in the interest of time and so complex numbers just don't make sense...

After consultation with other faculty, the decision was to include complex numbers in the first paradigms in physics course at the beginning of the junior year.

One aspect of recognizing that students are not making enough progress is considering whether to persist in trying to develop student understanding through active engagement or simply to wrap things up by ‘telling’ information:

It's Friday and the mathematical difficulty of this problem is perhaps overwhelming for the students and so when the mechanics of doing the mathematics is overwhelming, it's hard to then on top of that engage with conceptual reasoning. So when we reconvene on Monday it's going to be five minutes of me “telling” them how to wrap this problem up and then we're going to move on to me doing more “telling” in doing a derivation (of the Euler-Lagrange equation).

An experienced colleague helped this faculty member to accept “telling” as an appropriate option as needed:

There's a space for telling and I learned this from (an experienced colleague) and the time to “tell” is when the students are not going to get there on their own. If there's some trick that they don't know, or there's some piece that they just can't invent themselves, or when students have identified what questions they have, then telling is effective. A lot of (the experienced colleague)'s instructional strategy I think, and I try to do this as well, is to give students experiences where they can figure out what questions they have and the “telling” part is answering those questions.

Having worked hard on the problem, students likely would be receptive to listening to the faculty member present the solution:

So the end of this problem, will be a telling; they know what questions they have but they're just fried on finishing it off, so my telling them I think will have some value. Then the derivation “telling” will be the students would not be able to do that on their own; they need to see it done once by a professional first.

Another issue this faculty member faced was whether to use the Mathematica software in class:

One thing that I have learned and will do in the future is I will not ask students to do Mathematica in class; it's way too distracting; they can't let it go, so I will in the future off load all of that to homework and offer lots of office hours because that sort of thing benefits from having one-on-one interaction.

In designing the course, this faculty member had planned to scaffold sense making early in the course with very specific prompts and then to fade to more general prompts toward the end of the course. What happened, however, was that the nature of the subject matter taught near the end of the course, special relativity, changed in ways that caused changes in the types of sense making that were appropriate:

My original plan was to at this stage to be really fading the sense-making prompts from the homework and expecting the students to be engaging in sense making on their own. I'm thinking I'm going to abandon that plan and still try to prompt for a lot of sense making because the sense-making activity is just different. I expect the students won't know what to try...

A sense-making strategy called visualization, for example, is different for classical mechanics and special relativity:

So in terms of the sense-making goals for the course, I'm struggling to see a continuity in the sense-making stuff...I'm struggling to find sense-making prompts for the students...so with visualization, before I would have asked “draw a diagram of the situation, draw a plot of position versus time,” and now it's “draw a diagram of...before and after events,” and draw “space time diagrams,” which has position and time on the axes but you're not drawing, you're not plotting a function, you're drawing points and just trying to figure out what the coordinates are of those points on different axes. So they're both visualization but it's different, the tasks are different

With classical mechanics, students are starting with a life-time of intuitions to build upon in making connections to the formal physics description; with special relativity, students are starting with the formalism and developing new intuitions:

and in classical mechanics, I like visualization because I think it, or I hope, it connects more to the students' intuition about what's physically going on and in special relativity, they're now trying to develop new intuitions and so the direction of how intuition is playing into their sense making is different. In one (classical mechanics), you have intuitions and you're trying to connect the formalism to that, and in the other (special relativity), you're starting with formalism and then you have to refine your intuitions based on that; it's kind of a different direction.

Such differences created the need for continuing with specific rather than general sense- making prompts in this context.

Recognizing one's own limitations in launching a new complex endeavor.

During the interviews, this faculty member was thoughtful about the difference between doing everything envisioned and accepting what was feasible under the circumstances.

The last third of the course involved teaching relatively new content, which meant multiple stresses in making sure to be correct in class, in devising elegant ways to say things clearly, in becoming aware of and responding to student difficulties, and in creating a coherent narrative where there was a strong progression of ideas and everything fit well together:

This is content that I haven't taught very much; I've only taught it last year and this year and so I'm still trying to make sure that I'm not saying wrong physics, which means that I haven't found the most elegant words to say around the content to help students understand...With special relativity, I don't feel like I've got a strong narrative for the students yet...I don't think they see an arc of a progression of ideas, a strong progression of ideas, and that's something I'd like to improve for next term

Such multiple stresses reduced the cognitive resources available to help students:

One of the challenges for me is that...I only have a certain amount of cognitive activity ability and so if there is a challenging problem with a lot of parts and I want to keep in my brain the stuff that I want to talk about, it's really hard for me to engage with students and see what their ideas are because I just can't hold it all in my brain at the same time. So I feel like today I wasn't able to get around to groups and talk to groups because I was really trying to keep my brain around the problem and so maybe next year I'll be able to interact with students more and help them get through the problem more efficiently or at least stop them from spinning their wheels and give them more direct support.

This faculty member found it difficult to accept not being able to help students to the extent needed:

I'm oscillating between this “not every student is going to understand everything in the course” and “I really care about every student in my course and I want to help each and every one of them” so that's the tension.

Although the new course was helping students learn in ways that would prepare them for the upper level courses, some of the students were encountering substantial difficulties in this setting, which was discouraging both to the students and the faculty member.

Reflecting often and keeping a record for oneself.

This faculty member kept a binder, with plans, handouts, and commentary for each session:

I really tried hard to keep my binder up-dated so I would have some notes and then after class I would try to change my binder so that I would have a record of what I thought would be a better course through next time

Such binders were part of this department's instructional culture. Because the upper level paradigms in physics courses were so different from traditional physics courses, each faculty member kept a record of each session of a course in a binder, with notes about what happened, copies of any handouts, descriptions of any activities, and homework assignments. When teaching assignments changed, the new instructor for the course would receive a version of the binder, along with suggestions for making changes for improvements.

Also important for this faculty member in designing and teaching the course was informal mentoring by an experienced colleague:

...other advice that I've been getting from (an experienced colleague), the first time through a course, you're not setting it in stone and so remember that the next time through will smooth over some of the rough edges.

What this faculty member found particularly helpful were their excursions “to go to get frozen yogurt together about every other week.” Reflecting often, both alone and with a thoughtful colleague, helped this faculty member to gain perspective and insights about these challenging ways of teaching and learning.