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.