Inversion in Mathematical Thinking and Learning

Autor/in	Greer, Brian
Titel	Inversion in Mathematical Thinking and Learning
Quelle	In: Educational Studies in Mathematics, 79 (2012) 3, S.429-438 (10 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-011-9317-2
Schlagwörter	Psychologists; Educational Research; Arithmetic; Mathematics Instruction; Mathematical Logic; Teaching Methods; Mathematical Concepts; Mathematics Teachers + Suchen Sie Ihr Suchwort? Psychologist; Psychologe; Psychologin; Bildungsforschung; Pädagogische Forschung; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Mathematics lessons; Mathematikunterricht; Mathematical logics; Mathematische Logik; Teaching method; Lehrmethode; Unterrichtsmethode; Mathematics; Teacher; Teachers; Mathematik; Lehrer; Lehrerin; Lehrende
Abstract	Inversion is a fundamental relational building block both within mathematics as the study of structures and within people's physical and social experience, linked to many other key elements such as equilibrium, invariance, reversal, compensation, symmetry, and balance. Within purely formal arithmetic, the inverse relationships between addition and subtraction, and multiplication and division, have important implications in relation to flexible and efficient computation, and for the assessment of students' conceptual understanding. It is suggested that the extensive research on arithmetic should be extended to take account of numerical domains beyond the natural numbers and of the difficulties students have in extending the meanings of operations to those of more general domains. When the range of situations modelled by the arithmetical operations is considered, the complexity of inverse relationships between operations, and the variability in the forms that these relationships take, become much greater. Finally, some comments are offered on the divergent goals and preoccupations of cognitive psychologists and mathematics educators as illuminated by research in this area. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10