John Malone

A Typology of Mathematics Teachers' Beliefs About Teaching and Learning Mathematics and Instructional Practices

The primary purposes of the study reported here were to investigate Greek mathematics teachers’ beliefs regarding the nature of mathematics and mathematics teaching and learning, and to explore the various links between these beliefs and instructional practice. Two orientations that are characteristic of secondary mathematics teachers’ beliefs were identified: A contemporary — constructivist orientation, and a traditional — transmission — information processing orientation. A case study of a veteran teacher demonstrated that classrooms can be complex sites of political, historical, social and cultural influences, and that the teacher’s beliefs about mathematics learning and teaching were less traditional than her actual teaching practice.

Bridging the Boundaries of Compartmentalised Knowledge: Student learning in an integrated environment

The integration of content from the science, mathematics and technology learning areas is well grounded in the philosophy of middle schooling. However, there is a notable absence of recent empirical research to show if and/or how students learn science and mathematics concepts in integrated settings. This paper presents a case study of a Year 9 class that participated in a technology project constructing a solar boat involving science and mathematics components on electric circuits, statistical analysis, critical pathways and the reading of sun charts. The case study focuses on three pairs of students in the class and the results consists of three learning episodes that made up part of the students’ learning experience. The discussion explores the nature of the students’ learning and concludes that learning was enhanced as a result of the students’ involvement in the solar boat project.

Assessment of Classroom Environments in Reformed Calculus Education

Research was conducted to determine if current reforms in calculus education are more inclusive of students of different genders, personalities, attributional beliefs, mathematical abilities, and computer attitudes. Two types of calculus reform are examined: a computer-assisted, student-centred and inductive reform based on the Calculus and Maple (C&M) package; and a teacher-only, teacher-centred and deductive reform. Both methods emphasise student participation in the learning and employ collaborative-learning groups mixed by ability and the assessed sociometric measures, but not mixed by gender. The classroom environments of the reform classes were assessed qualitatively using free-form surveys, interviews and classroom observations, and assessed quantitatively using the College and University Classroom Environment Inventory (CUCEI). The classroom environment of reform classes was compared qualitatively to the normal lecture environment. Students assessed the classroom environment as being significantly less favourable than preferred, confirming general dissatisfaction with socio-emotional aspects of university classes, even when adopting modern educational reforms. Differences in the actual and preferred classroom environments were observed in all class sub-divisions (i.e. gender, personality) and across all environment scales of the CUCEI. The research illustrates the psychosocial diversity of reforms for university classrooms and the desirability of evaluating such reforms using a learning environment inventory as well as conventional qualitative measures.

Negotiation of meaning in mathematics classrooms: A study of two year 5 classes

This study investigated the relationship between students’ classroom experiences and the manner in which they construct mathematical meanings. There were two intertwined research foci: (a) how students make sense of and utilise mathematics concepts and operations, and (b) the social context within which teachers’ and students’ individual contributions play a role in the sense-making and utilisation of mathematics concepts and skills. Data was collected from classroom observations and video-taping sessions and from subsequent video-stimulated interviews with 6 students in each of two Year 5 classes. Analysis revealed the existence of four primary sources by which students determined the meaning or correctness of mathematical activity: the teacher, intuition, familiarity and procedural knowledge. In relation to the social level, the teacher emerged as playing the most valued role in the sense making and ratifying of procedures or answers.

The influence of students’ cognitive preferences on the selection of science and mathematics subjects

This study examined the subject‐choice process engaged in by a sample of Western Australian school students. The theoretical background was provided by career education models in which aspects of cognitive preferences are related to the choice of particular science and mathematics subjects. CareerMate, a computerised career counselling instrument, was used to identify cognitive preferences in the four dimensions of energy projection, experience preference, helping and closure. Aspects of the students’ preferences were correlated with their subject choices and gender and subject specific relationships emerged. There were significant differences in cognitive preferences between the academically capable females who chose matriculation physical science and mathematics subjects and those who did not. These differences need to be considered when encouraging females to select such subjects. If these subjects are to attract capable females currently choosing alternatives, then changes to the curriculum content an...

Differential Participation in Whole-Class Activities.

Target students are defined as those who dominate interactions with the teacher, usually in whole-class interactions by asking and responding to questions. In this study of five Year 8 mathematics classes, approximately five target students were evident in three of five participant classes. The majority of the target students were high ability males. Target student involvement was facilitated by the behaviours of teachers and students and management problems which prevailed in each of the three classes. The two other classes provided a marked contrast to those which contained target students. In one class, the teacher systematically involved a larger number of students in whole-class interactions and, in the other, there were few whole-class interactions. The disproportionate involvement of target students is regarded as problematic because of the relatively high proportion of time allocated to whole-class activities.

Exemplary Grade 1 Mathematics Teaching: A Case Study.

Abstract Because much of past educational research paints a gloomy picture and highlights the problems and negative aspects of education, a series of case studies of exemplary practice in science and mathematics education was initiated to provide a focus upon the successful and positive facets of schooling. It was assumed that much could be learned from case studies of exemplary practice that would stimulate and guide improvements in science and mathematics education. In this article, a report is given of that part of the overall project which involved a case study of exemplary mathematics teaching in an Australian first grade. The main sources of qualitative information were interviews and intensive classroom observations. The case study highlights a teachers ability to integrate the different subject areas, her flair in communication skills, her genuine concern for children and her skills in capitalizing on unexpected situations as some of the ingredients that made her mathematics teaching exceptional.

Double Degree Courses: A Viable Proposition for the CAE Sector

ABSTRACT Double‐degree courses (studies in which two disciplines are taught in conscious relationship to one another) are almost exclusively a phenomenon of the university sector in Australian tertiary education. This article examines the double‐degree program from the college perspective. It describes a rationale for the approach and suggests why colleges should pursue this type of study program; it describes several organisational models which have been initiated in various institutions both in Australia and overseas; it considers the areas in which such development might take place in a college; it discusses the advantages and limitations of these courses and it highlights some of the difficulties and issues in their implementation.