Relations between representational consistency, conceptual understanding of the force concept, and scientific reasoning

Previous physics education research has raised the question of “hidden variables” behind students’ success in learning certain concepts. In the context of the force concept, it has been suggested that students’ reasoning ability is one such variable. Strong positive correlations between students’ preinstruction scores for reasoning ability (measured by Lawson’s Classroom Test of Scientific Reasoning) and their learning of forces [measured by the Force Concept Inventory (FCI)] have been reported in high school and university introductory courses. However, there is no published research concerning the relation between students’ ability to interpret multiple representations consistently (i.e., representational consistency) and their learning of forces. To investigate this, we collected 131 high school students’ pre- and post-test data of the Representational Variant of the Force Concept Inventory (for representational consistency) and the FCI. The students’ Lawson pretest data were also collected. We found that the preinstruction level of students’ representational consistency correlated strongly with student learning gain of forces. The correlation (0.51) was almost equal to the correlation between Lawson prescore and learning gain of forces (0.52). Our results support earlier findings which suggest that scientific reasoning ability is a hidden variable behind the learning of forces. In addition, we suggest that students’ representational consistency may also be such a factor, and that this should be recognized in physics teaching.

Figure 1

The correlations between single student normalized FCI gain ($G_{\mathrm{FCI}}$) and the three pretest variables: representational consistency on the R-FCI pretest ($R{C}_{\mathrm{pre}}$), the FCI prescore ($FC{I}_{\mathrm{pre}}$), and the Lawson prescore ($L_{\mathrm{pre}}$).

Figure 2

Corresponding multiple-choice alternatives of a theme. 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 verbal form. The questions with the bar chart and vectorial items include explanations of the notations such as $F_{\mathrm{truck}\to \mathrm{car}}$.

Figure 3

Spearman’s rank correlation between single student normalized FCI gain ($G_{\mathrm{FCI}}$) and the three pretest variables for all the students ($n=131$): representational consistency on the R-FCI ($R{C}_{\mathrm{pre}}$), the FCI score ($FC{I}_{\mathrm{pre}}$), and the Lawson test score ($L_{\mathrm{pre}}$). All correlations are statistically significant ($p<0.001$).

Figure 4

Scatter plot for the students’ ($n=131$) representational consistency on the R-FCI pretest ($R{C}_{\mathrm{pre}}$) and the single student normalized FCI gain ($G_{\mathrm{FCI}}$). Spearman’s rank correlation is 0.51 ($p<0.001$).

Figure 5

Scatter plot for the students’ ($n=131$) Lawson prescore ($L_{\mathrm{pre}}$) and the single student normalized FCI gain ($G_{\mathrm{FCI}}$). Spearman’s rank correlation is 0.52 ($p<0.001$).

Figure 6

Scatter plot for the students’ ($n=131$) FCI prescores ($FC{I}_{\mathrm{pre}}$) and the single student normalized FCI gain ($G_{\mathrm{FCI}}$). Spearman’s rank correlation is 0.33 ($p<0.001$).

Figure 7

Average of single student normalized FCI gain ($G_{\mathrm{FCI}}$) in quartiles of representational consistency on the R-FCI pretest, Lawson prescores, and FCI prescores.

Figure 8

Spearman’s rank correlation between single student normalized FCI gain ($G_{\mathrm{FCI}}$) and the three pretest variables: representational consistency on the R-FCI ($R{C}_{\mathrm{pre}}$), the FCI score ($FC{I}_{\mathrm{pre}}$), and the Lawson score ($L_{\mathrm{pre}}$). Students were placed into the top ($T$, $n=71$) or bottom ($B$, $n=60$) half according to their $L_{\mathrm{pre}}$. ${}^{*}p<0.05$, ${}^{**}p<0.01$, ${}^{***}p<0.001$.

Figure 9

Spearman’s rank correlation between single student normalized FCI gain ($G_{\mathrm{FCI}}$) and the three pretest variables: representational consistency on the R-FCI ($R{C}_{\mathrm{pre}}$), the FCI score ($FC{I}_{\mathrm{pre}}$), and the Lawson score ($L_{\mathrm{pre}}$). Students were placed into the top ($T$, $n=69$) or bottom ($B$, $n=62$) half according to their $R{C}_{\mathrm{pre}}$. ${}^{*}p<0.05$, ${}^{**}p<0.01$, ${}^{***}p<0.001$.