Abstract
Background: The learning of rational numbers is a complex and difficult process that begins in the early grades. This teaching often focuses on the mastery of essential knowledge, including particular skills (e.g. using fractions to describe part–whole diagrams) and interpretations (e.g. sharing), which often results in an incomplete and inflexible understanding of these numbers.Aim: This article proposes a holistic and relational perspective on rational number knowing and sense-making.Setting: This possibility emerged through research into the learning of rational number concepts by Foundation Phase and Grade 4 children.Methods: This research forms part of an ongoing, in-depth, exploratory research programme into the processes of learning rational numbers. Clinical interviews and classroom observations were the primary methods of data collection and an in-depth, constant comparative method of analysis was performed on the data.Results: Thinking relevant to rational numbers was identified within four different perspectives through which children make sense of their interactions with the world, namely, social, instrumental, personal and symbolic sense-making.Conclusion: The learning of rational numbers may be usefully seen as arising from the interrelation of multiple aspects of knowing and doing that develop as children balance these different ways of sense-making.
Highlights
The complexity of rational numbers and the difficulty of learning this number system in school are widely acknowledged (Kilpatrick, Swafford & Swindell 2001)
A number of organising principles for rational number learning have been proposed. These include viewing rational number learning as a process of conceptual change (Vanvakoussi & Vosniadou 2004); building on the idea of ‘magnitude’ as a concept that unifies the whole, rational and real number systems (Siegler, Thompson & Schneider 2011); the prime importance of relational understanding for rational numbers (Brown 2015; McMullen et al 2015); and the rational number sub-constructs that constitute this conceptual field (Wright 2014)
Understanding as synthesis, not analysis. These investigations suggest that a number of different elements contribute to the manner in which children make sense of rational numbers and draw on this sense-making to inform and regulate their interaction with the world
Summary
The complexity of rational numbers and the difficulty of learning this number system in school are widely acknowledged (Kilpatrick, Swafford & Swindell 2001). Research in this field has generated a great deal of results, spanning a wide range of issues. The learning of rational numbers is a complex and difficult process that begins in the early grades. This teaching often focuses on the mastery of essential knowledge, including particular skills (e.g. using fractions to describe part–whole diagrams) and interpretations (e.g. sharing), which often results in an incomplete and inflexible understanding of these numbers
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