We carried out several experiments in which we used sequences of physics problems to investigate students' ability to apply calculus concepts in physics problems. In this paper, we discuss an experiment which focused specifically on the concept of "area under a curve." We organized group problem solving sessions to teach students the concept of area under a curve using our problem sequences. We combined both a paper-based test and a computer-based test with online hints to assess students' ability to transfer their learning to solve new physics problems. We found that students' strategies for solving physics problems using this concept largely depend on problem type and scenario. Students' prior knowledge of area under a curve from calculus could interfere with their ability to learn a coherent model of using this concept in physics contexts.

Physics tutorials are worksheets that guide students to answer conceptual questions. Two well-known sets of physics tutorials, the Tutorials in Introductory Physics (TIP) and Open Source Tutorials (OST), are reported to emerge from distinct conceptual change principles. For example, TIP is often associated with "elicit-confront-resolve", while OST is connected with "refining intuitions." Based on the analysis of interviews with tutorial authors and of the tutorials themselves, we looked for similarities between the tutorials. We identified a pattern that is common to both sets of tutorials, which we call the "revisiting" strategy: students are asked to return to a problem they have already examined. Elicit-confrontresolve and refining intuitions can both be examples of revisiting, suggesting that revisiting is an important and general technique that illuminates the similarity between the two sets of tutorials.

Abstract:The preparation of future learning (PFL) perspective posits that transfer can be measured by how effectively students can learn to solve new problems. This contrasts with the sequestered problem solving (SPS) perspective which focuses on whether students can solve new problems unaided. We developed a tutorial to facilitate students" understanding and application of mathematical differentiation in physics problems. One group of students utilized our tutorial, while a control group received a traditional lesson on the same topic. After instruction, each group completed a SPS transfer task. Following that they received computer-based hints to aid them on same transfer task. The extent to which students successfully used these hints assessed their PFL transfer. We found that students who completed the tutorial did not outperform the control group on the SPS task, but they did outperform them on the PFL transfer task.

Preparing graduate teaching assistants (TAs) and undergraduate learning assistants (LAs) to teach in physics classrooms is a topic of great interest in physics education research. We investigate the use of role-play performances to prepare TAs and LAs to teach students in introductory physics tutorials, labs, and SCALE-UP classes. Each role-play addressed specific pedagogical knowledge and specific disciplinary content. We find that our role-plays helped TAs and LAs to express their ideas about discursive teaching methods and fostered productive discussions about teaching physics.

Recent research has highlighted the need to explore the propagation of innovative teaching strategies. SCALE-UP (StudentCentered Active Learning Environment with Upside-Down Pedagogies) is one such innovative strategy that requires transforming the learning space to support small group work. SCALE-UP is both well-propagated and frequently sustained within departments once it is implemented, possibly due to the investment in a transformed learning space. However, not all instructors and departments reach the significant learning gains typically documented in the literature. In this study, we use interviews to explore the extent to which individual instructors implement and sustain specific features of SCALE-UP, like reduced lecture time and group composition, because such features may be more easily modified over time than the classroom space. We report on instructors' perceptions of the extent to which their courses align with the SCALE-UP model and whether deviations from the literature-based model result from intentional or unintentional changes.