In this article, we report on a study examining those factors which contribute to the mathematics performance of a sample of children aged between 8 and 13 years. The study was designed specifically to consider the potency of a number of mathematical affective factors, as well as background characteristics (viz., gender, ethnicity, and…

This study investigated teachers' attitudes towards proofs in the secondary school mathematics curriculum. The study was motivated by a desire to fill a gap existing in the literature in relation to teachers' attitudes towards proofs. Thirty-four secondary school mathematics teachers' responses to a Likert type questionnaire and interviews were…

The TIMSS 1995, 1999, and 2003 data have been gathered from Hong Kong before and after its sovereignty switch from the United Kingdom to China in 1997. Built on a reciprocal relation theory from the research literature, this investigation is designed to examine models of student self-concept and mathematics achievement during the political…

The notion of quality in undergraduate mathematics lectures is examined by using theoretical notions and research results from the literature and empirical data from a case study on lecturing on limits of functions. A systemic triangular model is found to catch critical quality aspects of a mathematics lecture, consisting of mathematical…

This paper examines the conflict in interest between teaching experiments and professional learning when they are combined in a research project. The study reported in this paper is the fourth year of a five year longitudinal study on the introduction of early algebraic concepts. The ten teacher participants are from five state primary schools in…

This paper considers mathematical abstraction as arising through a natural mechanism of the biological brain in which complicated phenomena are compressed into thinkable concepts. The neurons in the brain continually fire in parallel and the brain copes with the saturation of information by the simple expedient of suppressing irrelevant data and…

One of the missions of education is to prepare children for complex tasks that occur in their cultural environment. By means of abstracting, the effects of this complexity can be reduced. Recent research and theoretical development show us that young children already seem to be able to think abstractly. The acknowledgement of this potential in…

A model for processes of abstraction, based on epistemic actions, has been proposed elsewhere. Here we apply this model to processes in which groups of individual students construct shared knowledge and consolidate it. The data emphasizes the interactive flow of knowledge from one student to the others in the group, until they reach a shared…

This paper is structured in two sections. The first examines views of mathematical abstraction in two broad categories: empiricist and dialectical accounts. It documents the difficulties involved in and explores the potentialities of both accounts. Then it outlines a recent model which takes a dialectical materialist approach to abstraction in…

There is evidence that spontaneous learning leads to relational understanding and high positive affect. To study spontaneous abstracting, a model was constructed by combining the RBC model of abstraction with Krutetskii's mental activities. Using video-stimulated interviews, the model was then used to analyze the behavior of two Year 8 students…

Mathematics games are widely employed in school classrooms for such reasons as a reward for early finishers or to enhance students' attitude towards mathematics. During a four week period, a total of 222 Grade 5 and 6 (9 to 12 years old) children from Melbourne, Australia, were taught multiplication and division of decimal numbers using calculator…

This study focuses on a group of practitioners from a school district that adopted reform-oriented curriculum materials but later rejected them, partially due to the inclusion of alternative algorithms in the materials. Metaphors implicit in a conversation among the group were analysed to illuminate their perspectives on instructional issues…

This paper focuses on the construction, development, and use of mathematical models by prospective science and mathematics teachers enrolled in a university physics course. By studying their involvement in an inquiry-based, experimental approach to learning kinematics, we address a fundamental question about the meaning and role of abstraction in…

This study implemented a multiplication program based on systematic practice, aimed at improving children's recall of basic multiplication facts. Four Year 5 classes were recruited to participate in the study. Two classes practised multiplication facts using pencil and paper worksheets and another two classes practised on computers. Eleven…

The mathematical performance of Chinese students, from mainland China, Hong Kong and Taiwan, is widely acclaimed in international comparisons of mathematics achievement. However, in the eyes of the Western educators, the environments established in Chinese schools are deemed relatively unfavourable for mathematics learning. This paper reports on a…