Teaching children how to include the inversion principle in their reasoning about quantitative relations |
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| Authors: | Terezinha Nunes Peter Bryant Deborah Evans Daniel Bell and Rossana Barros |
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| Institution: | (1) University of Oxford, Oxford, UK |
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| 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. |
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