Supporting students of all levels to move beyond empirical arguments, which employ example based reasoning to endorse universal truths and are thus mathematically invalid, remains a challenging goal in mathematics education. Arguments that make use of generic examples are both mathematically valid and accessible for even young learners. However,…

The importance of understanding the various uses of the literal symbol in algebra, and in particular the idea of generalised number, is well documented in the literature. Many research findings have also reported student difficulties with this vital and central concept. This research study examines the use of a combination of historical and…

This paper focuses on selected findings from a study that explored the use of multiplication and division with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. The focus of instructional tasks was on working with groups of ten to support the understanding of place value. Findings from relevant assessment tasks…

This paper builds from a prior study into the teaching and learning of basic number facts in New Zealand. It reports the changes in practice of one teacher that were brought about by her reflection on the effectiveness of her teaching and learning programme. It details how this teacher created a process which helped make the learning of basic…

The value of a consideration of large numbers and exponentiation in primary and early secondary school should not be underrated. In Indian history of mathematics, consistent naming of, and working with large numbers, including powers of ten, appears to have provided the impetus for the development of a place value system. While today's students do…

This document contains the fifth volume of the proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 59 research reports by presenters with last names beginning between Sac and Zaz:…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) The Affective Views of Primary School Children (Peter Grootenboer); (2) Theoretical Model of Analysis of Rate Problems in Algebra (Jose Guzman, Nadine Bednarz and Fernando Hitt); (3) Locating Fractions on…

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…