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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Notes
Lai, Baroody and Johnson (2008) report an intervention study in which they taught the children about the inverse relation; however, it was taught as an aim in itself, not as a tool to solve computations. For this reason, it is not reviewed here.
The characters in the story were common cartoon characters at the time. Permission was obtained for use of these in the research. For copyright reasons, a different illustration is used in Fig. 1.
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Acknowledgment
The authors are grateful to the Economic and Social Research Centre, Teaching and Learning Research Programme for grant #L139251015 which made this research possible. We are very thankful to the schools, teachers, and children without whose generous participation, no research would be possible.
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Nunes, T., Bryant, P., Evans, D. et al. Teaching children how to include the inversion principle in their reasoning about quantitative relations. Educ Stud Math 79, 371–388 (2012). https://doi.org/10.1007/s10649-011-9314-5
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DOI: https://doi.org/10.1007/s10649-011-9314-5