Many introductory calculus-based physics students have difficulties when solving physics problems involving calculus. This study investigates students’ retention and transfer from calculus to physics. While retention is the ability to recall your knowledge at a later point in time, transfer of learning is defined as the ability to apply what one has learned in one situation to a different situation.

In this dissertation we propose a theoretical framework to assess students’ transfer of learning in the context of problem solving. We define two kinds of transfer – horizontal transfer and vertical transfer. Horizontal transfer involves applying previously learned ideas in a problem. Vertical transfer involves constructing new ideas to solve the problem. Students need to employ both horizontal and vertical transfer when they solve any problem. This framework evolves through this research and provides a lens that enables us to examine horizontal and vertical transfer. Additionally, this proposed framework offers researchers a vocabulary to describe and assess transfer of learning in any problem solving context.

We use a combination of qualitative and quantitative methods to examine transfer in the context of problem solving. The participants in this study were students enrolled in a second-semester physics course taken by future engineers and physicists, calculus instructors and physics instructors. A total of 416 students’ exam sheets were collected and reviewed. Statistical methods were used to analyze the quantitative data. A total of 28 students and nine instructors were interviewed. The video and audio recordings were transcribed and analyzed in light of the aforementioned theoretical framework.

A major finding from this study is that a majority of students possess the requisite calculus skills, yet have several difficulties in applying them in the context of physics. These difficulties included: deciding the appropriate variable and limits of integration; not being clear about the criteria to determine whether calculus is applicable in a given physics problem, and others. This study also provides a detailed understanding of students’ difficulties in terms of our theoretical framework. Instructional strategies are suggested at the end to facilitate the transfer from calculus to physics.