A Study of the Development of the Paradigms in Physics Program

Thinking about what will happen during Week 1.

In an interview about two weeks before the start of the course, this faculty member commented upon how much effort was going into planning the first week of class:

I'm finding myself spending a lot of time thinking about Week 1. I don't think that's a bad thing; I think that's an especially good thing, because it sets the tone for the rest of the course.

The focus was on thinking about how to engage students in doing physics as well as on how to convey specific physics content.

I don't think about my instruction in terms of “noun-like learning objects.” I generally think about my instruction in terms of verbs, of what are students doing and what experiences are they having, and that I think changes how I'm interacting with the students.

Often the students would be working in small groups of two or three, talking with one another as they wrote or drew on large white boards lying on the tables. This faculty member and assistants would move among the groups and pause to listen to what the students were saying, view what they were writing or drawing on their large white board, and sometimes make a comment or ask a question. This faculty member had gleaned insights from the research literature about ways to interact with students in such small groups:

I am planning on employing Alan Schoenfeld's metacognition coaching strategy in class, so making a core expectation that instructors can at any time ask the three questions “What are you doing? Why are you doing it? How will it be helpful?” (((schoenfeld92)))

Schoenfeld (1992) found that students often continued working in unproductive ways near the beginning of his mathematics problem-solving course. By asking the three questions as he circulated among the small groups, Schoenfeld coached students to step back occasionally and think about what they were doing, why they were doing it, and how it would help them solve the problem. Eventually his students began asking these questions of themselves, thereby prompting themselves to change direction as needed while figuring out an effective way to solve a problem.

This faculty member also expressed appreciation for the insights offered by several graduate students and a postdoc about ways students might perceive this focus: “Having the students' perspective at this early stage is really helpful.” Underlying these conversations was the decision to schedule the course in a studio classroom (http://scaleup.ncsu.edu) with students sitting around tables where they could work together writing and drawing on the large white boards; such collaborative activities would be easier in such a classroom than in a lecture hall with students sitting in chairs lined up in fixed rows.

During first day of class, attending to administrative details related to using such active engagement strategies.

This faculty member had previously taught several of the upper-level paradigms in physics courses but had not remembered to take care of some of the details related to the active engagement strategies typically used in those courses:

So there's a lot of administrative overhead that I...just forgot to say or only occurred to me in the moment that I had to say it, I hadn't planned to say it, so the fact that these are pre-paradigms students has been an adjustment for me. They don't know about 304 F (a room for majors to work together in outside of class) and don't have Mathematica (software for graphing functions) on their computers. I need photos of them so I can learn their names..,

Establishing a collaborative environment had involved some unanticipated extra time and effort such as having an assistant take pictures of the students to help in learning their names, downloading to students' computers software needed for small group work and homework, remembering to ask students to pick up small whiteboards, pens, erasers, and a large white board for their group as they entered the classroom so they already had these materials at hand when they needed to use them later in class, and informing students of department resources for fostering a sense of community among majors, such as a room where they could study and work together on homework.

Being aware of and planning ways to mitigate as well as utilize a wide range of experience and preparation among the students.

Because the course was to be offered only once each academic year, some of the students were still completing the introductory series whereas others were transfer students already enrolled in the upper-level paradigms in physics courses. Thus the students varied widely in what they knew and could do:

I'm certainly noticing the range in the students' experiences; there are some students who clearly are not very proficient with the 211 material (from the first term of the introductory physics sequence); and then there are other students who are in the paradigms (junior-level courses) and are proficient... it's hard for me to decide what level to pitch my statements at, so I'm finding myself bouncing all over the place in terms of level of sophistication of the explanations that I give.

At least one of the students had not completed the pre-requisites; such inappropriate enrollments might be avoided by asking the department advisor to make sure students have course pre-requisites before they enroll. Also helpful would be to clearly state the course pre-requisites on the first day of class.

This faculty member had put a lot of effort into identifying the knowledge and skills students would need for undertaking the topics and activities being planned as well as into considering how to provide for those who had not learned about these topics and techniques previously. A visual display of post-it notes on the office wall acted as a reminder of the many aspects that needed to be addressed. One choice this faculty member had made was conducting an initial small group activity based on a problem in a familiar context, a challenging problem but one for which even the least prepared students likely had resources for doing the kind of sense-making intended. Also emphasized in class was the importance of asking immediately for clarification by those who heard a word or idea expressed that they did not understand.

By using class time for small group activities and large group discussions, this faculty member created many opportunities for students to express their ideas. Some of these ideas were intentionally elicited but needed multiple conversations:

(During the previous session, we had) started with a daily question that we're trying to get the students to stumble on, a common stumbling block, and discuss it explicitly and it came up beautifully and I talked about it; and then disappointedly it happened again today...

Other student ideas were not anticipated. This faculty member made a list of those learned by listening carefully while assisting small groups, engaging students in interactive lectures, and answering questions after class:

...that list behind you are student ideas that I did not anticipate and I wanted to talk about today; I didn't get to talk about all of them...(I noticed them) by talking with student groups and... (during an interactive lecture) I did part of the set up of the problem, and I got to the part where I wrote down the differential equation for the velocity in the s direction and in that discussion some of these ideas came out but it (noticing new student ideas) was primarily talking with students in groups and answering students' questions outside of class.

The wide range of student ideas was reflective of the wide range in backgrounds and preparation.

One way to handle the disparity in preparation was to encourage the more advanced students to spread out among the small groups, rather than to cluster within one group. With coaching, the more advanced students could serve as informal mentors within their small groups, thereby deepening their own understandings by facilitating learning by the other members of the group. Also important was making clear to the students that all members of a group needed to understand a problem's solution, that the success of a group would depend on every member being able to report and discuss the group's solution:

We talked explicitly about the rules for giving presentations in my class...when you go up with your board, that all the group members go, that I can ask any one of the presenters to answer a question...and that the audience members are responsible for asking questions.

The intent was for group members to make sure everyone in the group participated in producing and understanding the details of the group's work and for all the students in the class to attend closely to and learn from each small group's presentation.

Being aware of language issues for students who are not native speakers.

This faculty member became concerned about a group of students who were not doing well:

There is this group of students who are not doing very well and I'm really trying hard to think about how can I help them, both these particular students right now and also in future iterations of the course, how do I give them more support in the beginning of the course so there isn't so much of a gap between the students?

Many of these students seemed to be non-native English speakers:

Some of my frustrations about this low performing group of students, many of them seem to be non-native English speakers, so I'm wondering how I can clarify some of the language issues for them; my instincts are write more sentences on the board that mirror what I'm saying to the students, my difficulty with that is that the boards are hard to see in the classroom that I'm using...

There were reading assignments in a textbook but apparently many students had not purchased the textbook nor were accessing copies available in the department:

I could lean more heavily on reading assignments for the students; I have noticed that many students have not purchased the textbook and are not following the reading assignments I've posted on the course website, which I think is the problem with this generation of students, but having a written text for the ESL students might be helpful for those students...

Most of these students were not asking questions in class nor coming to office hours:

Additionally...I don't feel like I have a lot of access to what is confusing them; they are not asking a lot of questions in class; they are not, most of them are not coming to my office hours. I think they are intimidated by my professorial rank so I'm really trying hard to think about how can I give them opportunities to ask questions; my fear there is that they are so confused they don't even know what questions to ask; so how do I help them get to the stage where they can ask questions?

A colleague suggested requesting students submit written questions that could be answered in class:

... maybe if they have more time and they're not in the pressure of a situation where I'm demanding a question right now, that might loosen up some questions, but again I think these students may be tripping over the language; the topics we talk about have a specialized language. It's so tough to communicate when you're not comfortable with the language.

An extra review session may have helped or may just have been more overwhelming:

I had this review session yesterday where I went over the solutions to the exam and also did some more discussion about topics around the exam that I thought might help the students work faster on the (next) exam because I got feedback from students who had low scores who felt like they didn't have enough time and also (they needed to know) more about coordinate systems and so I did; some of that material is new material that is stuff that I didn't talk about in the course but I thought might give more context and be helpful and I'm not sure how that went. Some students said yes it was helpful and some students looked overwhelmed “oh my god there's all this extra stuff I need to know!”

One possibility would be to arrange for students to have a longer time to take an exam in a quieter room. This faculty member also realized that better communication with the instructors of the introductory course would help clarify to what topics the students might, or might not, have had prior exposure:

I'm also realizing that I need to have a lot more conversations with the introductory instructors about exactly what conversations they have with students about specific topics that are related to my course like angular momentum and moment of inertia and polar coordinates.

As the course progressed, this faculty member became more aware of the experiences of these students and concerned about how to meet their needs.

Readjusting plans after finding out how students are having trouble and what their questions are.

Planning a course involves deciding what to do when, based upon one's estimate of how much time teaching each topic requires. When lecturing, one can control the pace but engaging students in interactive discussions and activities introduces many uncertainties. The time required depends upon what students say, ask, and do. Midway in the course, this faculty member reflected on getting about a week behind, because of becoming aware of and responding to student difficulties:

I think I'm experiencing what happens in interactive classrooms, which is you have a schedule that you think is reasonable but turns out to be extremely ambitious and along the way you figure out what students are having trouble with and have questions about and so that just expands time in the schedule...

The students' difficulties may involve not making connections to topics taught in earlier courses or not monitoring well what they are doing:

The students who are struggling...I'm having some specific conversations but I'm still trying to work out what the difficulty is. Some of it is just not making connections with 211 and 212 (the introductory physics courses), like that material is in cold storage and they're not accessing it; some of it is not being able to monitor their problem solving process, so I'm trying to use Alan's questioning techniques (Schoenfeld, 1992) to help them...

The length of the problems as well as the extensive use of symbols and unfamiliar coordinate systems added to the confusion that some students were experiencing:

They probably do not have a lot of practice solving problems of this length and they probably don't have a lot of practice solving problems with just symbols only...dealing with curvilinear coordinates, they're doing it for the first time it feels like and so they're going the long way around whereas the more advanced students are just able to write down the answer...I just think that there are these pieces that they haven't had practice with and so it's going to take them longer and there are more opportunities for mistakes in that way

The increased length of the process for these more complex problems also affected timing issues:

The challenges are the typical ones, how to respond in the moment to students who are struggling because I'm encountering their difficulties perhaps for the first time, trying to find these metacognitive prompts that are a little bit more productive for individual students in the moment, and one challenge is now that the problems are getting longer, I'm wishing I had the longer class period for doing problem-solving, that was a big compromise that I made to have the room that we have and so I'm hoping that maybe when we have the new classroom, that I'll be able to get two 85 minute blocks instead of these three one-hour blocks.

This course met for an hour three days a week, but the upper division courses junior year meet every day, for an hour on Monday, Wednesday, and Friday and for two hours on Tuesdays and Thursdays. The double hours on those days allow for longer small group work followed by extended whole group discussions, or sometimes a series of small group work followed by a whole group discussion at different stages of solving a complex problem. Although scheduling a course in an atypical format may be difficult, this faculty member recommends two longer class periods instead of the typical one hour three days a week schedule.