Fraction Competence and Algebra Competence: Measuring, Modelling, and Explaining Their Predictive Inter-Relations

• Applicants: Professor Dr. Andreas Obersteiner; Professor Dr. Michael Schneider
• Subject Area: Developmental and Educational Psychology ; General and Domain-Specific Teaching and Learning
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 460233476

Algebra competence, in particular equation solving competence, is a gatekeeper for higher mathematical competence. Recent studies found that fraction competence predicts school students’ algebra competence over years even after controlling for confounding variables. This suggests that fraction competence, mediated through algebra competence, affects livelong trajectories of mathematical competence. However, empirical evidence on the relations between fraction competence and algebra competence is sparse and the underlying causal mechanisms are ill-understood. Fraction competence is an example of numerical cognition, whereas algebra largely requires non-numerical mathematical reasoning. Explaining their inter-relations helps to better understand how numerical and non-numerical components of mathematical competence support each other in learners. Investigations of the relations need to account for the fact that fraction competence and algebra competence are not homogeneous. For example, conceptual and procedural knowledge are partly independent facets of competence in both domains. The main goals of this project are (a) providing more differentiated empirical evidence on which conceptual and procedural facets of fraction competence and algebra competence predict each other, (b) testing competing hypotheses about processes mediating the predictive relations, (c) examining the directionality of the predictive relations, and (d) testing causal hypotheses about interventions activating and linking prior knowledge about fractions to algebra. To reach these goals we conduct four empirical studies with school students from Grades 5 to 9. Study 1 is a factor-analytic investigation of partly independent facets of fraction and algebra competence. In Study 2, we use longitudinal path analyses to compare competing hypotheses about the mediating processes linking these facets. Study 3 comprises tests of whether the longitudinal relations are bi-directional so that prior knowledge about early algebra predicts learning gains from school instruction on fractions. Study 4 is a field experiment testing whether two instructional interventions that aim at linking knowledge about fractions and algebra via one of two mediators are more effective than regular school instruction on algebra. The anticipated results contribute to (a) understanding how numerical cognition supports more abstract higher-order mathematical competence, (b) predicting trajectories of mathematical competence acquisition in school students, (c) explaining how students’ widespread problems with fraction learning contribute to deficiencies in algebra competence, and (d) improving the effectivity of instruction on algebra.

• DFG Programme: Research Grants
• International Connection: USA
• Cooperation Partner: Professorin Dr. Bethany Rittle-Johnson