Original Research-Special Collection: Teaching and learning: mathematics, science, design, technology in the Early Years

Rational number understanding: The big picture, not the essence

Bruce Brown
South African Journal of Childhood Education | Vol 9, No 1 | a561 | DOI: https://doi.org/10.4102/sajce.v9i1.561 | © 2019 Bruce Brown | This work is licensed under CC Attribution 4.0
Submitted: 28 July 2017 | Published: 09 September 2019

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Bruce Brown, Department Education, Rhodes University, Grahamstown, South Africa

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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.


Fraction Learning; Rational Number Learning; Sense-Making; Conceptual Development; Relational Understanding.


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