Thomas Kuhn (1962/2012) introduced the term "paradigm shift" to the scientific literature to describe how knowledge in science develops. The aims of this article are to identify paradigm shifts, or revolutions, that have occurred in mathematics, and to discuss their relevance to teaching mathematics in schools. The authors argue that…

Although number sense is difficult to define, it involves having a good intuition about numbers and their relationships, including the ability to have a "feel" for the relative size of numbers and to make reasonable estimations. Students with good number sense typically recognise the relative magnitude of numbers, appreciate the effect…

A solid understanding of equivalent fractions is considered a steppingstone towards a better understanding of operations with fractions. In this article, 55 rural Australian students' conceptions of equivalent fractions are presented. Data collected included students' responses to a short written test and follow-up interviews with three students…

Several researchers have noted how children's whole number schemes can interfere with their efforts to learn fractions. An Australian study found that children who were successful with the solution of rational number tasks exhibited greater whole number knowledge and more flexible solution strategies. Behr and Post (1988) indicated that children…

Interviews with (n=55) children and their teachers in years one, two, and three showed a closer association between knowledge of place value and levels of counting than between levels of counting and the ability to explain the counting sequence. (13 references) (MKR)

Profiled interviews of (n=41) kindergarten and first-grade children's numerical development over a school year. Significant mismatches between children's numerical development and typical curricula are described, and changes to current practice are recommended. Appendix includes sample interview tasks. (Contains 21 references.) (MKR)

Describes research which compared the processing loads of mathematical representations and strategies used by (n=3) teachers and (n=29) children aged 5-8 for interpreting subtraction operations represented in numerical form. Some representations and strategies appeared to impose an extra processing load which can interfere with conceptual…

The first volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains plenary lecture and research forum papers as listed below. Short oral communications papers, poster presentations, brief summaries of discussion groups, and working sessions are also included in the volume. The plenary…

This is a record of the proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia (MERGA). The theme of the conference is "Mathematics: Essential research, essential practice." The theme draws attention to the importance of developing and maintaining links between research and practice and…