Summary of Reference
Pitkethly, A. & Hunting, R.
A review of recent research in the area of initial fraction concepts
Educational Studies in Mathematics, 30, 5-38, 1996.
This article begins with the consensus of recent research that the rational number construct includes five subconstructs: part-whole, quotient, ratio, operator and measure. Of these the part-whole subconstruct is fundamental to the development of rational number knowledge. The identification of the unit, partitioning, and the notion of quantity underlie each subconstruct but play a paramount role in the part-whole subconstruct.
It is suggested that the basis of rational number building is initial fraction concepts. Key to this is a flexible concept of the unit as in “the equidivision of a unit into parts; the recursive division of a part into subparts; and the reconstruction of the unit”. These initial fraction concepts are comprised of a number of aspects including the language and symbols of fractions; intuitive fraction knowledge; various mechanisms such as whole number partitioning, measuring, equivalencing, relational schemes by which more advanced reasoning evolves; partitioning; and continuous and discrete contexts. Some mechanisms may inhibit the development of rational number knowledge.
Two sets of research are reviewed for this article; one set of studies investigates children’s intuitive knowledge of fractions and how this might be developed through formal instruction; and a second set of studies focuses on ideas of ratio and proportion in children’s early ideas about fractions. The article concludes with an overall analysis of all the studies described. The authors identify links between the findings. In particular they discuss partitioning, discrete and continuous contexts, whole number schemes, and ratio and proportion relationships. They emphasise the role of students’ informal knowledge in the development of fraction concepts. They discuss the implications of these findings for the way in which we teach fractions. They reiterate the complexity of rational number thinking and the challenges that this brings to classroom instruction.