This article shows that the recognition of the dualities in equality (operator-equivalent) of the minus sign (unary-binary) and the zero (nullity-totality) during the transitional process from arithmetic to algebra by 12-13 year-old students constitutes a possible way to achieve the extension of the natural number domain to the integers. (Contains…

In a longitudinal study of children in grades 0-4, gender differences are developing very early in some number domains, but there do not appear to be similar differences showing in the measurement and geometry domains studied. The Early Numeracy Research Project collected data at the beginning and end of each year from over 11,000 children in…

In a real sense, PISA 2003 has touched the mathematics education community by stealth rather than by storm. Although PISA brings "baggage" commonly associated with international assessments, it takes some refreshing perspectives especially in the way that it envisions and assesses mathematical literacy. In this panel discussion we focus…

Numeracy can be defined as having the competence and disposition to use mathematics to meet the general demands of life at home, in paid work, and for participation in community and civic life (Willis 1992). An important aspect of developing the capacity to use mathematics in everyday life is, for students at school, to use mathematics to meet the…

Efforts to develop a mathematics curriculum that meets the needs of a modern society are reflected in reform recommendations across the developed world. A common requirement is for students to understand the calculation procedures they are taught and to develop "number sense". This paper will analyse students' strategies for calculating…

The project's focus was to learn more about the ways to best assess and support the development of numeracy in the early grades. Project goals include involving teachers and researchers in: (1) the creation and use of performance-based tasks most appropriate for assessing numeracy in young learners; (2) the development and refinement of…

This paper presents a summary of the first two years of a large research project investigating the numeracy practices of young people across a range of industries. Drawing on both quantitative and qualitative data, the project aims to identify the ways in which numeracy practices are perceived and enacted by young people (students in part-time…

The engineering profession still is a male domain. Many attempts to change this isolation and to call women into the profession failed. Neither the study conditions nor the social recognition were experienced as adequate for women. The focus on the development of deeper understanding, explicit connectedness, comprehension and social concern are…

This paper reports on teachers' views of the effects of compulsory numeracy testing in Years 3, 5, and 7 in Queensland schools. Teachers were surveyed on (i) the validity and worth of the tests, (ii) the impact the tests had on their teaching of mathematics, and (iii) how they were using the results of the tests. Although the results reveal a…

The purpose of the present study was to investigate the effects of forum discussion embedded within metacognitive guidance on mathematical literacy. In particular the study compares two learning environments: (a) Forum discussion with metacognitive guidance (FORUM+META); and (b) Forum discussion without metacognitive guidance (FORUM). Participants…

In this study, we examined 139 prospective elementary teachers' solution processes to additive word problems for which the solution is 1 more or 1 less than the answer produced by the straightforward application of the addition or subtraction of the two given numbers. For each problem, five aspects of their solution processes were examined: (a)…

This research report summarises the results of an exploratory teaching program in a primary and secondary school in rural New South Wales, Australia, focused on improving basic mathematics skills. Pupils, aged 11 to 13 years, identified as consistently low-achieving in Mathematics were targeted. The program ran for approximately twenty-five weeks…

Secondary school students' use of multiplicative strategies in an exploratory New Zealand Numeracy Project was examined. This Numeracy Project enabled teachers to interview each of their students concerning their mathematical knowledge and strategies. The percentage of students who used multiplicative strategies increased from initial to final…

Within a major numeracy project, there were marked differences in achievement between classes, which, as reported in Sullivan and McDonough (2002), we attribute to the teachers. To gain insights into the practices of effective teachers, six case studies of highly effective teachers at the Prep (first year of school) to Grade 2 level were…

Nathan entered third grade having already constructed a Generalized Number Sequence (GNS) for whole numbers that enabled him to coordinate sequences of multiples to find a common multiple of two whole numbers. Nathan was able to apply the operations of his GNS to his understanding of part-whole relations and his emerging use of fractional…