Teaching Children How to Include the Inversion Principle in Their Reasoning about Quantitative Relations

Autor/inn/en	Nunes, Terezinha; Bryant, Peter; Evans, Deborah; Bell, Daniel; Barros, Rossana
Titel	Teaching Children How to Include the Inversion Principle in Their Reasoning about Quantitative Relations
Quelle	In: Educational Studies in Mathematics, 79 (2012) 3, S.371-388 (18 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-011-9314-5
Schlagwörter	Intervention; Word Problems (Mathematics); Calculus; Subtraction; Mathematics Instruction; Mathematical Concepts; Number Concepts; Arithmetic; Teaching Methods; Problem Solving; Calculators + Suchen Sie Ihr Suchwort? Textaufgabe; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Subtraktion; Mathematics lessons; Mathematikunterricht; Number concept; Zahlbegriff; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Teaching method; Lehrmethode; Unterrichtsmethode; Problemlösen; Calculator; Rechner; Rechenmaschine
Abstract	The basis of this intervention study is a distinction between numerical calculus and relational calculus. The former refers to numerical calculations and the latter to the analysis of the quantitative relations in mathematical problems. The inverse relation between addition and subtraction is relevant to both kinds of calculus, but so far research on improving children's understanding and use of the principle of inversion through interventions has only been applied to the solving of a + b - b = ? sums. The main aim of the intervention described in this article was to study the effects of teaching children about the explicit use of inversion as part of the relational calculus needed to solve inverse addition and subtraction problems using a calculator. The study showed that children taught about relational calculus differed significantly from those who were taught numerical procedures, and also that effects of the intervention were stronger when children were taught about relational calculus with mixtures of indirect and direct word problems than when these two types of problem were given to them in separate blocks. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10