Force Concept Inventory-based multiple-choice test for investigating students’ representational consistency

This study investigates students’ ability to interpret multiple representations consistently (i.e., representational consistency) in the context of the force concept. For this purpose we developed the Representational Variant of the Force Concept Inventory (R-FCI), which makes use of nine items from the 1995 version of the Force Concept Inventory (FCI). These original FCI items were redesigned using various representations (such as motion map, vectorial and graphical), yielding 27 multiple-choice items concerning four central concepts underpinning the force concept: Newton’s first, second, and third laws, and gravitation. We provide some evidence for the validity and reliability of the R-FCI; this analysis is limited to the student population of one Finnish high school. The students took the R-FCI at the beginning and at the end of their first high school physics course. We found that students’ $\left(n=168\right)$ representational consistency (whether scientifically correct or not) varied considerably depending on the concept. On average, representational consistency and scientifically correct understanding increased during the instruction, although in the post-test only a few students performed consistently both in terms of representations and scientifically correct understanding. We also compared students’ $\left(n=87\right)$ results of the R-FCI and the FCI, and found that they correlated quite well.

Figure 1

A theme is a set of three isomorphic items (differing only in their representations).

Figure 2

Corresponding multiple-choice alternatives of theme 4 (T4) in the R-FCI. The representational formats of the alternatives are a bar chart (item 2), verbal (item 11) and vectorial (item 20). All three items include an identical original FCI question in the verbal form. The questions of bar chart and vectorial items include explanation of notations such as $F_{\text{truck}\to \text{car}}$.

Figure 3

Different ways for analyzing the R-FCI data.

Figure 4

(Color) Students’ progress in representational and scientific consistency between pre- and post-tests. The starting point of an arrow shows pretest results and the head shows post-test results.

Figure 5

(Color) Average normalized gains in representational and scientific consistency of themes.

Figure 6

(Color) The percentages of correct answers in the themes with statistically significant differences between representations.

Figure 7

Alternatives for item 2.

Figure 8

Alternatives for item 11.

Figure 9

Alternatives for item 20.