Design and Validation of a Test for Representational Fluency of 9th Grade Students in Physics and Mathematics: The Case of Linear Functions

• Published in: Physical review. Physics education research Vol. 14; no. 2; pp. 020105 - 20123
• Main Authors: Ceuppens, Stijn, Deprez, Johan, Dehaene, Wim, De Cock, Mieke
• Format: Journal Article
• Language: English
• Published: College Park American Physical Society 10-08-2018
• Subjects: Accuracy; Context; Design factors; Difficulty Level; Error Patterns; Foreign Countries; Formulas (mathematics); Gender Differences; Grade 9; Graphical representations; Graphs; High School Students; Kinematics; Linear functions; Mathematical analysis; Mathematical Formulas; Mathematics; Mathematics Tests; Multiple Choice Tests; Physics; Secondary School Students; Students; Switching; Tables (Data); Test Construction; Test Items; Test Validity; Testing; Belgium
• ISSN: 2469-9896; 2469-9896
• DOI: 10.1103/PhysRevPhysEducRes.14.020105

This study reports on the development, validation, and administration of a 48-item multiple-choice test to assess students' representational fluency of linear functions in a physics context (1D kinematics) and a mathematics context. The test includes three external representations: graphs, tables, and formulas, which result in six possible representational transitions between them. Moreover, four linear function types are included: negative "y" intercept and positive slope, zero "y" intercept and positive slope, positive "y" intercept and negative slope, and positive "y" intercept and positive slope. The test is administered to 385 students aged 14-15 in the 9th grade from 13 schools in Flanders (Belgium) and--after validation--is analyzed by means of generalized estimating equations (GEE). The results show a significant main effect for all design factors and a significant interaction effect between representational transition and function type, as well as additional interaction effects with the gender of the respondents. Furthermore, representational transitions which include a formula prove to be significantly more difficult; in particular for the directly proportional function type, the transition to a formula stands out from the analysis. Mean accuracies in physics are significantly lower compared to mathematics. Function types with negative values for either "y" intercept or slope also result in significantly lower mean accuracies indicating the difficulty students have with negative numbers in linear functions. A distractor analysis of the incorrect answers chosen by the students reveals three distinct dominant errors: concept switching, sign switching, and switching of the directly proportional function type and the function type with positive "y" intercept and positive slope.