Rational number understanding: The big picture, not the essence

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.