Bright, GW et all (1988) Identifying Fractions on number lines, Journal for Research in Mathematics Education. Vol 19, No 3, p215 – 232
This study investigated the ways students represented fractions on number lines and the effects of instruction on those representations. Two clinical teaching experiments and one large-group teaching experiment were conducted with fourth and fifth graders.
Wong M & Evans D (2007) Students Conceptual Understanding of Equivalent Fractions, Mathematics: Essential Research, Essential Practice, |Volume 2, Proceedings of the 30th annual conference of the Mathematics Education Research group of Australasia. P824 – 833
This paper investigates students’ conceptual understanding of equivalent fractions by examining their responses to questions using symbolic and pictorial representations. Five questions from this fraction assessment instrument were analysed. The different types of knowledge used to answer each question were examined and common misconceptions identified. The responses of students with limited general mathematics achievement were compared to those of their more competent peers. The differences that emerged between the two groups in their conceptual understanding of equivalent fractions, were highlighted.
Davidson S & Askew M (2012) Concept cartoons as a Way to Elicit Understandings and Encourage Reasoning about Decimals in Year 7 in J.Dindyal, L.P. Cheng & S.F.Ng (Eds), Mathematics Education: Expanding horizons (Proceedings of the 35th annual conference of the Maths Education Research Group of Australasia). Singapore: MERGA p218 – 225.
This paper is located within the research into encouraging learners to reason mathematically and become engaged with concepts rather than just procedures. It reports on a research in progress examining two techniques to be used at the beginning of a sequence of lessons in order to elicit students’ prior knowledge and understanding of topics about to be studied. Two techniques will be used to elicit the students’ prior understandings: Concept Maps and Concept Cartoons. This paper reports on the ideas behind Concept Cartoons and the development of Concept Cartoons for eliciting understandings of decimals. The paper briefly outlines the research into difficulties with decimals before discussing the rationale and design of the cartoons.
Nrich Primary team. Teaching Fractions with Understanding: Part-whole Concept. Nrich article, available on their website.
In her studies of children learning about rational numbers, Grace Lopez-Charles has identified some different perspectives through which children see fractions. This article starts looking at some of those perspectives, firstly by considering what happens in situations where learners are trying to create equal shares. From sharing using halves learners move to partitioning using other divisions, such as fifths or sixths. This results in the need to develop understandings of equivalence which is discussed in the second section of this article. Finally, we look at some ways of teaching fractions more effectively that arise from Grace's work.
Bernard Bagnall. Early Fraction Development. Nrich article, available on their website.
In this article, Bernard outlines suggestions for tasks which will help young children develop the concept of fractions.