A Study of the Development of the Paradigms in Physics Program

Perceiving lectures as ineffective.

This new faculty member described an ongoing process that began with realizing that the students were not learning from lectures, even when given ample opportunities for asking questions:

One seminal reason of why I shifted came during the first time I taught (a paradigms course). ...I gave a lecture (using a particular mathematical technique with spherical coordinates)...and then I asked the small groups to do the same, and I knew what I was getting into so I was very cautious with it, I asked for questions, I got a couple of questions, answered those questions and thought, “ok, now they understand it.”

Then this new faculty member asked small groups to do a simpler version of the problem. No groups, however, were able to make progress. This led the faculty member to conclude that lectures did not lead to learning.

Then in their groups I asked them to do the same derivation with cylindrical coordinates, I intentionally did the harder one myself, thinking that would help. No group was able to make significant progress on that repetition, even though my lecture had just been given, my notes were on the board... and that led me to conclude that lecturing doesn't work well, at least when I lecture; even the best students in this case were unable to reproduce what I had lectured, immediately afterwards, and I would have thought that I could just lecture through both of (the examples) if I didn't have time and they would learn the material and it would be ok.

Such experiences led this new faculty member to choose to engage students in more small group activities rather than lecturing during class sessions.

Observing increased learning from small group activities.

Shifting from lectures to small group activities only makes sense if this leads to increased learning. This new faculty member offered the following justification for making this shift:

The challenge is to know what they learn from the small group activities, but I know that at the beginning of small activities students are unable to do certain things, and then afterward I can see, usually in a later small group activity, that they are able to do those things.

And in the two hour day, the later activity where I can see that they are able to do something, could rule out homework as a learning mechanism, but even during the activity, again there is not a proof, but I would say there is an observation of learning as I see students recognizing what they are doing wrong...

...usually when I do a small group activity, it's mathematical and students without help are not able to complete the task. If they could, it should have been homework, I would say, but then with help they are able to complete it. That of course doesn't prove that they are learning because I could have given them simple instructions to follow and they could simply be following those instructions, but I don't give that many instructions; I give help occasionally when they're stuck.

The students seemed to be learning from small group activities as evident from their increased success with related activities later in the same class session, even when given only occasional help as needed rather than explicit instructions.

Learning how to manage small group activities.

A shift from lecturing to facilitating small group activities involves a shift from telling answers to listening closely while asking questions to prompt students' next step in thinking. This new faculty member had had some prior experience in facilitating such conversations as a teaching assistant as well as a new faculty member offering extra office hours while teaching a graduate course primarily by lecture:

In my first year here I introduced sort of extra recitation hours beyond the normal... homework help in which I had students work problems on the board and get advice from other students and myself.

I learned slowly, at first, doing small group activities is a lot like what I did as a TA in discussion sections, and I did have some experience with that; I just did not think of that as a way to run an entire class.

In now choosing to structure class sessions around small group activities, this new faculty member was successful in engaging members of a small group in thinking about what they were doing but had difficulty keeping other small groups from becoming stuck and bored:

And so at first I would help individual groups...what I did was I taught each group individually, I would go and say, “oh what are you doing?” and then...try to...give them hints such that they could figure out and understand what they were doing wrong and I had progressed to me circulating trying to answer all the problems, and when I first taught a paradigm by myself.. I found that I was needing to circulate too fast; I couldn't move fast enough to help everyone before they were stuck and bored, because students only remain stuck and productive for a while, and then they “well, we don't know what we're doing.”

Coaching from an experienced faculty member helped this new faculty member learn to bring the whole class back together periodically to offer guidance at an appropriate moment when the small groups were ready to hear helpful commentary:

And (an experienced faculty member) told me...that you need to bring the whole class together to answer the questions and it took me a long time to learn that, because I enjoy talking with small groups of students, and I feel like I'm doing them a good thing when I do that, and I am not aware at the time, that the rest of class is bored or stuck, and then I feel frustrated.

So now my policy is usually to answer a question for the whole class the second time I need to answer it; it's not always the second time and if it's a really unusual thing I've never seen before, I might not, in a course that I'm experienced at, because I know that ok, odds are that I've hit the only two groups that have run into this issue, but in most cases, I figure by the time the second group hits it, most of the other groups will have run into that problem and be ready to hear an answer.

Although a conversation asking questions and giving hints is not feasible with the whole group at this point, cogent commentary can offer effective guidance without giving direct instructions:

And it would be better if I gave them hints, like I would with a small group, if I were able to ask questions and give hints until they all understood it, but I can't do that with the entire class, and I can't do that with the groups fast enough to address the entire class so instead what I do is when I've seen a couple groups get to that point, where they need to hear something from me, then I call the entire class together, and I say, “some of the groups have run into this problem and if you haven't run into it yet, you probably will run into it soon, and the trouble is...” and I try to explain the trouble and explain how to get around it as well as I can and I don't have a very clear description of what “as well as I can” means, if I were teaching someone how to do this, but I want students to ideally understand the problem and be able to understand how to fix it but I don't want to give direct instructions.

The groups will differ in how they have been thinking about the problem and thus will need to make sense of these comments within their own context. If at least one group member has understood some of what was just said, that person likely will help the others make progress in figuring out what to do:

And one actual advantage of addressing the entire class is that they will all have their own notations, and so when I address the entire class I won't be using any of their notations, so there is something of an impedance mismatch, which I think is good, because it means that they are forced to translate what I'm saying into their own way of looking at it, and if I have explained things well enough what seems to happen is that at least someone in most groups understands and figures out “Oh, this is what we need to do,” and then hopefully, if the groups are working properly, explain it to the other group members and then they will all understand it.

By hearing cogent commentary rather than explicit directions, members of the small groups will still need to work things out with one another, increasing the likelihood that all members will make some progress:

At a certain level I feel like I expect that if the person who understands it best, does not thoroughly understand it, that may increase the odds of the other people, the students gaining the understanding; because the first person needs to work it out, in order to make use of whatever information I gave them, and hopefully they work that out loud in talking with their partners, as in “I think what he was saying was that we need to add these as vectors and what does it mean to add them as vectors?” or whatever it might be.

Giving such help takes time as well as skill; learning how to manage multiple groups, through both individual small group conversations and occasional whole group commentary, is an ongoing process.

Changing how one thinks about structuring a class session.

Being asked to teach in new ways can prompt changing how one structures a class session. This new faculty member, for example, offered an interesting metaphor for the relative roles of lectures and small group activities in structuring a class:

When I came here I had learned by lecture and taught by lecture, but since pretty much that very first paradigm that I taught, I have been very focused on doing group activities as the skeleton of my class. The lectures are ligaments, holding the group activities together; I don't know what the muscles are, probably the TAs.

This new faculty member now envisioned students generating the main ideas for a session through a series of small group activities. Lectures still occurred but instead of presenting the main ideas, their function was to make connections among ideas that the students had developed through their actions as well as through discussions among themselves and with the instructor during the activities.