A Study of the Development of the Paradigms in Physics Program

Meeting multiple goals.

In designing the course, this faculty member wanted to emphasize sense-making goals but also recognized the need to address content goals, both in terms of what physics to teach and how to provide the mathematics support likely to be needed:

The primary challenge is there are too many goals...there are three categories of goals: there are physics content goals, there are the supporting math goals and then there are the sense-making goals... (I'm) thinking about how those goals are related to each other, so interleaving them in sensible ways, but then also figuring out how to make the sense-making goals central and not just peripheral.

The intent was to enhance students' ability to use sense-making strategies while also developing physics knowledge and mathematical fluency that would help students make the transition to the more mathematically sophisticated upper division physics courses.

Selecting content when combining multiple courses into one.

One aspect of the designing process involved being aware of and accommodating the decisions the Paradigms 2.0 committee had made with respect to changing the curriculum for the upper-division courses:

Another concern I have is the amount of physics content that I will cover. On the one hand, there are only ten weeks, and we're combining multiple courses into one, so something has to go and on the other hand, I'm trying to think carefully about what content is going to be relied on later. So for example I've promised to do power series and that will be useful later in the paradigms (upper-division courses for majors) and I've also less strongly agreed to do some complex numbers.

Conversations in the Upper Division Curriculum meetings helped build such awareness as illustrated in Figures 3a, 3b, 4 and 5 of Part 3 (pages 14, 15, 21, and 22). During several meetings, the faculty members mapped connections made among the upper-division courses. Important aspects to consider included what content would be relied upon in subsequent courses, what content would be motivating for students, what combination of content would make a coherent story, and what content could be omitted. Having also participated on the Physics 2.0 Committee, this faculty member fortunately had a good grasp of the changes underway in other courses to help guide these decisions.

Building on prior courses and preparing for later courses.

This faculty member was interested in consulting with other instructors to find out what language, if any, they used to foster sense making. The hope was to begin developing a common language around sense-making strategies to be fostered in all of the courses for majors. The faculty member stated this long term goal:

I think sense making is a theme that should be an instructional goal that is curriculum wide because it is so rich and often so context dependent. One of my goals is for students to have this habit of “I need to understand what my answer means, I need to reflect on whether or not I think it's right, and how it's connected to other knowledge.”

Finding out what other instructors are doing has involved both research and informal conversations with faculty during curriculum meetings:

In terms of research, (a graduate student) interviewed a bunch of faculty about what they do in their classroom around sense making and she is also looking at how students complete a reflection prompt on a homework rubric in introductory physics. The other source of information is conversations in the curriculum group, so for example (another faculty member) once suggested that we have a common homework rubric that includes an evaluation step that would be curriculum wide.

The purpose of explicit sense-making prompts would be to help all students to develop a habit characteristic of successful students:

Some students do that (evaluate their answer) and those are often the very successful students. I think some students don't know that that's what they're supposed to do. Therefore my interventions are in making these kinds of reasoning routine, through repetition, every problem they're asked to do it, by showing them how powerful it is that they can catch their own mistakes, and by talking about a breadth of strategies so that they have lots of tools.

By choosing to participate in both the introductory and upper-level curriculum meetings, this faculty member was able to contribute to conversations about such ways to foster student success across the span of undergraduate physics courses for majors.

Assessing sense-making skills.

Asking students to respond to an informal ungraded assessment near the beginning and end of a topic or course has become common in the physics community, with many research-based assessments available. These focus on content knowledge, problem-solving, scientific reasoning, lab skills, or beliefs and attitudes (See https://www.physport.org/assessments/). This faculty member wanted to design and use such an assessment for a different purpose, to document sense-making skills at the beginning and end of the course. Creating such an assessment would include designing an appropriate format:

Right now, I'm working with a team to come up with a sense-making assessment that I'm hoping to give at the beginning and at the end of the class, so that's been a big challenge to think about what format that's going to have...the approach that we're currently taking is we're trying to design GRE (Graduate Record Exam) type questions where students are not expected to explicitly solve the problem but to use other strategies for selecting an answer from several choices.

This assessment of sense-making skills would ask not only for the selection of an answer from among provided options but also would request written responses in which the students would describe the strategies they used to select an answer.

Embedding sense-making goals in all aspects of the course.

A typical physics course proceeds by moving through a series of topics embedded in a variety of tasks. This suggested a possible structure for designing a course emphasizing sense-making strategies:

I've been thinking about a structure to help me make that happen, but I think it's pretty similar to how we think about teaching physics content, which is you provide example, you let the students practice the skills of doing the task, you provide students with opportunities to perform the task in context, you incentivize doing the task, and then you give feedback on doing the task. This seems pretty mechanical, but it is helping me think about how to embed the sense-making goals in all aspects of the course, in class, in homework, in lecture, and in small groups.

The challenge was to create ways to make explicit those aspects of sense-making that often are implicitly assumed to be occurring, such as that students will check their answers by considering extreme cases. The intent was to emphasize sense making in all aspects of the course -- during interactive lectures and small group activities in class as well as an expected part of problem-solving responses on homework and examinations. This included sense-making at the beginning of a problem in orienting oneself to the physical system portrayed, monitoring progress while working on the problem, and evaluating an answer at the end, to understand the answer and to have confidence that the answer is correct.

Designing ways to scaffold and fade instruction in sense making.

Because sense-making is not formally required in most courses, the plan was to request sense-making explicitly in class, on homework, and the first exam, such as “Consider special cases: Does your result for the maximum range of a projectile on an incline make sense if the ground is horizontal? If the ground is vertical (like right up against a cliff)?” Exam instructions would state that credit would be given for sense making about an answer, such as why an answer was correct or if a student realized something was wrong and explained why it was wrong. In the middle of the course, the instructions would be more general in format, such as “Utilize at least two sense-making strategies to evaluate an answer.” Near the end of the course, instructions would fade to an even more general format such as “Be sure to do some sense-making around your result.”