Modeling the developmental trajectories of rational number concept(s) |
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| Institution: | 1. Centre for Learning Research, University of Turku, Finland;2. Department of Teacher Education, University of Turku, Finland;3. Turku Institute for Advanced Studies, University of Turku, Finland;1. Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213, USA;2. National Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing 100875, China;3. Department of Special Education, Peabody College, Vanderbilt University, Nashville, TN 37203, USA;4. School of Education, University of Delaware, Newark, DE 19716, USA;5. Instructional Research Group, Los Alamitos, CA 90720, USA;1. Education Research Unit, Faculty of Psychology and Educational Sciences, KU Leuven, Belgium;2. Department of Teacher Training, Vives, Belgium;3. Department of Mathematics, KU Leuven, Belgium |
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| Abstract: | The present study focuses on the development of two sub-concepts necessary for a complete mathematical understanding of rational numbers, a) representations of the magnitudes of rational numbers and b) the density of rational numbers. While difficulties with rational number concepts have been seen in students' of all ages, including educated adults, little is known about the developmental trajectories of the separate sub-concepts. We measured 10- to 12-year-old students' conceptual knowledge of rational numbers at three time points over a one-year period and estimated models of their conceptual knowledge using latent variable mixture models. Knowledge of magnitude representations is necessary, but not sufficient, for knowledge of density concepts. A Latent Transition Analysis indicated that few students displayed sustained understanding of rational numbers, particularly concepts of density. Results confirm difficulties with rational number conceptual change and suggest that latent variable mixture models can be useful in documenting these processes. |
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| Keywords: | Conceptual change Rational numbers Latent Profile Analysis Latent Transition Analysis |
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