Thomas J. Cooper

Students’ perspectives of workplace learning and training in vocational education

Reports on the evaluation of a programme which was designed to enable students to complete a traineeship or apprenticeship, and their senior certificate in accordance with a variety of combined school and work programmes, including the New Apprenticeship Scheme. A multimethod approach was adopted which includes interviews with students, vocational educators and employers regarding their perceptions of: competencies, learning outcomes and training acquired during the programme. The results of the interviews with the students illustrated some similar and different perceptions between teachers and students, and showed that students’ main reason for undertaking the vocational education programme were the opportunity to gain “hands on” experience, and a “headstart” to employment. Implications for further research included: an investigation into the perceived status barrier between vocational and general education, the development of work attitudes; and the implementation of a strategic business and marketing plan.

Flexibility and inflexibility in accurate mental addition and subtraction: two case studies

This paper reports on a study of two children’s mental computation in addition and subtraction, and compares their mental architecture. Both students were identified as being accurate, however, one student used a variety of mental strategies (was flexible) while the other student used only one strategy that reflected the written procedure for each of the addition and subtraction algorithms taught in the classroom. Interviews were used to identify both children’s knowledge and ability with respect to number sense (including numeration, number and operations, basic facts, estimation), metacognition and affects. Frameworks were developed to show how these factors interacted to explain the two types of accuracy in mental addition and subtraction. Flexible accuracy was related to the presence of strong number sense knowledge integrated with metacognitive strategies and beliefs and beliefs about self and teaching; while inflexible accuracy was a result of compensation of inadequate knowledge supported by beliefs about self and teaching.

Developing Mathematics Understanding and Abstraction: The case of Equivalence in the Elementary Years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data was gathered from multiple sources including interviews, videos of classroom teaching, and pre- and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

Young Children's Ability to Use the Balance Strategy to Solve for Unknowns.

This article examines students’ ability to use the balance model to solve for unknowns. A teaching experiment was conducted in four Year 3 classrooms. This experiment focused on exploring the application of the balance model as an analogue for representing equations and solving for unknowns. The teaching experiment promoted a shift by students towards viewing addition and subtraction equations in terms of equivalence, where the situation is viewed in a multi-directional way (i.e., balance). Initially the lessons were trialed by the researchers in two classrooms. The lessons were then implemented in a further two classrooms by two classroom teachers in conjunction with the researchers. Two weeks after the conclusion of the teaching experiment, a one-on-one interview was conducted with a random sample comprising twenty students with an average age of eight years. The interviews indicated that while the balance model did assist students reach solutions for finding unknowns, for some students further explicit teaching was required.

The place of personal writing in a PhD thesis: Epistemological and methodological considerations

This paper reports on a particular approach to doing a doctorate in which the first author has used personal writing to increase the relevance, autonomy and quality of her learning and to allow her to present her study, her personal reactions to the study and the experiences that have led her to the study in one thesis. The personal writing consisted of reflective and critical journal and letter writing through which Mary dealt with the affective, social and moral factors she believed to be an integral part of deep learning in a social science. The paper describes how, as well as having consequences for her research on improving autonomy, motivation and learning in Year 8 science students, this has led her to present her PhD thesis on two levels: science education and narrative.

Teachers’ responses to an investigative mathematics syllabus: Their goals and practices

Despite attempts to encourage teachers to adopt investigative teaching behaviours, there is strong evidence of the resilience of teacher-centred school mathematics teaching. This study uses interpretive research methods to explore teachers’ practices and relate these to their goals. Analysis of case studies indicates that syllabus documents have influenced teachers’ choices of teaching strategies. Most teachers had calculation-based goals for less able students and conceptual goals for more able students. Three distinct teaching strategies were identified and described. The relationships between teachers’ goals, beliefs, and practices can guide the construction of teacher programmes that focus on student construction of knowledge.

Introducing Functional Thinking in Year 2: a case study of early algebra teaching

Sixty-five Year 2 children with ages ranging from six to seven years participated in a teaching experiment to introduce functional thinking. The results show that young children are capable of generalising, can provide examples of relations and functions, can describe the inverse of such relationships and give valid reasons for how they found the inverse relationships. They also indicate that specific features of instruction assist this process, particularly abstracting underlying mathematical relationships, notably the materials used by the teacher and the children, the types of activities and the questions asked by the teacher. This leads to specific implications for the teaching of arithmetic in the early years.

Combining teaching experiments and professional learning : conflicts between research and teacher outcomes

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 middle class areas in Brisbane, Queensland. The findings from this investigation suggest that potentially many conflicts exist between the interest of a teaching experiment and that of professional learning. Some of these conflicts can be overcome, others can be minimised by restructuring, but some are fundamentally inherent when the methodologies are combined.

Bridging the educational gap : Indigenous and non-Indigenous beliefs, attitudes and practices in a remote Australian school

Indigenous education remains of grave concern within Australian society (Fitzgerald, 2002). Systems are currently making limited educational impact in Aboriginal and Torres Strait Islander communities (Department of Education, Training and Employment, 1999). In particular, Indigenous students’ beliefs about the relevance of education, attitudes towards school, behaviour in school and attendance at school are affecting their educational performance (Bourke et al., 2000; Cataldi and Partington, 1998; Ministerial Council on Education, Employment, Training and Youth Affairs, 2002). This chapter reports on the success of a 3-year longitudinal professional learning project in a remote Australian school. Using mathematics as the vehicle, this project set out to improve Indigenous students’ learning outcomes by enhancing their beliefs, attitudes and practices and thus to begin to bridge the current educational gap between them and non-Indigenous students. The chapter reviews the literature relevant to the relationship between beliefs, attitudes, practices and performance, outlines the project generally and, for the particular school Albertown (pseudonym), describes findings with regard to beliefs and attitudes, and discusses the implications for future intervention projects.

“Training the Trainer” in Australia’s Adult and Community Education Sector

Reports on the results of a survey with training officers addressing education training needs of Australia’s Adult and Community Education sector. The responses show that training officers believe that this sector is rapidly growing, is important to the economic wellbeing of Australia and will benefit from course provision at both undergraduate and postgraduate levels. Discusses issues of course content and delivery, stressing the need for maximum flexibility in modes of study, etc.