Fostering the development of mental number representations and arithmetic competencies in the first school year

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Event Abstract Back to Event Fostering the development of mental number representations and arithmetic competencies in the first school year Andreas Obersteiner1*, Stefan Ufer1 and Kristina Reiss1 1 Technische Universität München, Heinz Nixdorf-Stiftungslehrstuhl für Didaktik der Mathematik, School of Education, Germany The development of arithmetic competencies is a main goal of early mathematics instruction. These competencies comprise exact mental calculation as well as approximate calculation and number estimation [1]. Various manipulative materials are used in primary schools in order to support students’ development of mental number representations. These materials can represent either exact numerosities (e.g., a pegboard with two rows of ten pegs each) or analogue quantities (e.g., empty number line). While theoretical considerations support their use, the empirical foundation of effects on students’ learning is scarce. This is the starting point for our study. We investigate students’ mathematical achievement after a training phase aimed at fostering either exact or approximate mental number representations. It is of particular interest whether the two trainings have different effects on a) the development of the respective mental number representations and b) general arithmetic achievement. Furthermore, it is explored if c) general cognitive abilities, e.g., spatial abilities, are related to these learning processes. According to cognitive psychological and neuropsychological theories, which suggest that exact and approximate number processing rely on distinct mental representations, different learning effects can be expected. For implementing the training sessions, modified versions of the adaptive computer game “The Number Race”[2] are used. One version requires exact and the other one approximate number processing. The present study can be regarded as an example how neuropsychological findings and cognitive theories are used in educational contexts to support students’ learning at school. We will present the theoretical background of the study as well as first results of piloting studies.