Investigating and improving introductory physics students’ understanding of electric field and the superposition principle: The case of a continuous charge distribution

We discuss an investigation of the difficulties that students in a calculus-based university introductory physics course have with electric field and the superposition principle for the case of a continuous charge distribution and how that research was used as a guide in the development, validation, and evaluation of a tutorial on these topics to help students learn these concepts. The tutorial uses a guided inquiry-based approach to learning and involved an iterative process of development and validation. During the validation process, we obtained feedback both from physics instructors who regularly teach introductory courses in which these concepts are taught and from students for whom the tutorial is intended. Then the final version of the tutorial was administered in several sections of a calculus-based introductory physics course after traditional lecture-based instruction in relevant concepts. We discuss the performance of students in individual interviews and on the pretest administered before the tutorial (but after traditional lecture-based instruction) and on the post-test administered after the tutorial in three sections of the introductory physics course. We also compare student performance in several sections of the course in which students worked on the tutorial with another section in which students only learned the material via traditional lecture-based instruction. We find that students who used the tutorial performed significantly better compared to those who learned the material only via traditional lecture-based instruction.

Figure 1

A sample response from a student for pretest questions (1) and (2) for the direction of the field at the points shown.

Figure 2

A sample response from a student for the post-test question (4).

Figure 3

A sample drawing from a student for pretest question (1) showing the direction of the electric field at points $A$, $B$, and $C$.

Figure 4

A schematic diagram from the tutorial designed to help students learn to transition from the case of the electric field due to a discrete distribution of equidistant identical charges in a straight line to the field due to a continuous charge distribution.

Figure 5

A schematic diagram for the pretest questions (1) and (2).

Figure 6

A schematic diagram for the pretest question (3).

Figure 7

A schematic diagram for the post-test question (1).

Figure 8

A schematic diagram for the post-test questions (2) and (3).

Figure 9

A schematic diagram for the post-test question (4).