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,…

Specialised Content Knowledge (SCK) is defined by Ball, Hoover-Thames, and Phelps (2008) as mathematical knowledge essential for effective teaching. It is knowledge of mathematics that is beyond knowledge which would be required outside of teaching; for instance, the capacity to determine what misconception(s) may lie behind an error in…

In this paper we report on two assessment tasks extracted from a larger study. The tasks involved number-line placements on two different number lines (0-to-10 and 0-to-20) and place-value understanding. Participants were 119 children from four different classes (Years 1-3). Children's placements were more accurate on the 0-to-20 than the 0-to-10…

Research in both the New Zealand and international contexts identifies the need for New Zealand classrooms to foster culturally responsive and mathematical practices that align with Påsifika students' cultural values, backgrounds, interests and experiences. The aim of this study was to investigate how the use of culturally responsive tasks along…

This paper outlines a framework to explain the early development of place-value understanding based on an analysis of data from 84 five- to seven-year-old children from diverse cultural and linguistic backgrounds. The children were assessed individually on number knowledge tasks (recalled facts, subitizing, counting, place-value understanding) and…

This paper focuses on children's number fact knowledge from a study that explored the impact of using multiplication and division contexts for developing number understanding with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. After a series of focused lessons, children's knowledge of number facts, including…

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…

Derived initially from a strategic analysis of children's methods of counting, the New Zealand Numeracy Projects used, as a starting point for the professional development of teachers, a strategy framework that traces children's development in number reasoning. A pilot study indicated the usefulness of professional development where teachers use…

This article explores how a focus on understanding divisibility rules can be used to help deepen students' understanding of multiplication and division with whole numbers. It is based on research with seven Year 7-8 teachers who were observed teaching a group of students a rule for divisibility by nine. As part of the lesson, students were shown a…

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…

In this paper we review and compare language policy in relation to adult numeracy education in Wales and New Zealand with respect to the Maori and Welsh languages in the latest stage of our international comparative study of adult numeracy education. While much has been written about the relationship between language and literacy, the relationship…

Lexical variation abounds in New Zealand Sign Language (NZSL) and is commonly associated with the introduction of the Australasian Signed English lexicon into Deaf education in 1979, before NZSL was acknowledged as a language. Evidence from dictionaries of NZSL collated between 1986 and 1997 reveal many coexisting variants for the numbers from one…

Here is the only reference book you will ever need for teaching primary school mathematics and statistics. It is full of exciting and engaging snapshots of excellent classroom practice relevant to "The New Zealand Curriculum" and national mathematics standards. There are many fascinating examples of investigative learning experiences,…

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:…