Surveying theories and philosophies of mathematics education

Any theory of thinking or teaching or learning rests on an underlying philosophy of knowledge. Mathematics education is situated at the nexus of two fields of inquiry, namely mathematics and education. However, numerous other disciplines interact with these two fields which compound the complexity of developing theories that define mathematics education. We first address the issue of clarifying a philosophy of mathematics education before attempting to answer whether theories of mathematics education are constructible? In doing so we draw on the foundational writings of Lincoln and Guba (1994), in which they clearly posit that any discipline within education, in our case mathematics education, needs to clarify for itself the following questions: (1) What is reality? Or what is the nature of the world around us? (2) How do we go about knowing the world around us? [the methodological question, which presents possibilities to various disciplines to develop methodological paradigms] and, (3) How can we be certain in the “truth” of what we know? [the epistemological question]

Politicizing mathematics education : has politics gone too far? Or not far enough?

In this chapter we tackle increasingly sensitive questions in mathematics education, those that have polarized the community into distinct schools of thought as well as impacted reform efforts.

Mathematical modelling in the early school years

In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the Butter Beans Problem and the Airplane Problem). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data, together with background information containing specific criteria to be considered in the solution process. Four classes of third-graders (8 years of age) and their teachers participated in the 6-month program, which included preparatory modelling activities along with professional development for the teachers. In discussing our findings we address: (a) Ways in which the children applied their informal, personal knowledge to the problems; (b) How the children interpreted the tables of data, including difficulties they experienced; (c) How the children operated on the data, including aggregating and comparing data, and looking for trends and patterns; (c) How the children developed important mathematical ideas; and (d) Ways in which the children represented their mathematical understandings.

Young children's early modelling with data

An educational priority of many nations is to enhance mathematical learning in early childhood. One area in need of special attention is that of statistics. This paper argues for a renewed focus on statistical reasoning in the beginning school years, with opportunities for children to engage in data modelling activities. Such modelling involves investigations of meaningful phenomena, deciding what is worthy of attention (i.e., identifying complex attributes), and then progressing to organising, structuring, visualising, and representing data. Results are reported from the first year of a three-year longitudinal study in which three classes of first-grade children and their teachers engaged in activities that required the creation of data models. The theme of “Looking after our Environment,” a component of the children’s science curriculum at the time, provided the context for the activities. Findings focus on how the children dealt with given complex attributes and how they generated their own attributes in classifying broad data sets, and the nature of the models the children created in organising, structuring, and representing their data.

Teachers and the emotional dimensions of class in resource-affected rural Australia

In recent years, a 'cultural turn' in the study of class has resulted in a rich body of work detailing the ways in which class advantage and disadvantage are emotionally inscribed and embodied in educational settings. To date, however, much of this literature has focused on the urban sphere. In order to address this gap in the literature, this paper focuses on the affective evaluations made by teachers employed in rural and remote Australian schools of students' families, bodies, expectations and practices. The central argument is that moral ascriptions of class by the teachers are powerfully shaped by dominant socio-cultural constructions of rurality that equate 'the rural' with agriculture.

If teams are so good.. : science teachers' conceptions of teams and teamwork

The focus of this study is the phenomenon of teams and teamwork. Currently the Professional Standards of Queensland’s teachers state that teams are critical to teachers’ work. This study uses a phenomenographic approach to investigate science teachers’ conceptions of teams and teamwork in the science departments of fifteen Queensland State secondary schools. The research identifies eight conceptions of teams and teamwork. The research findings suggest that the team represents a collective of science teachers bounded by the Science Department and their current timetabled subject. Collaboration was found in the study to be an activity that occurred between teachers in the same social space. The research recognises a new category of relationship between teachers, designated as ‘ask-and-receive’. The research identifies a lack of teamwork within the science department and the school. There appears to be no teaming with other subject departments. The research findings highlight the non-supportive team and teamwork policies, procedures and structures in the schools and identify the lack of recognition of the specialised skills of science teachers. The implications for the schools and science teachers are considerable, as the current Professional Standards of Education Queensland and the Queensland College of Teachers provide benchmarks of knowledge and practice of teams and teamwork for teachers. The research suggests that the professional standards relating to teams and teamwork cannot be achieved in the present school environment.

Researching Teachers for the Middle Years

The educational landscape around middle schooling reform is a contemporary focus of the Australian school education agenda. The University of Queensland Middle Years of Schooling pre-service teacher education program develops specialist teachers for this crucial phase of schooling. This program has become a national leader for middle school teacher education. This paper reports on aspects of a longitudinal study that began with the first cohort of students in the program in 2003. To date 234 students have been involved as participants in the study. The findings demonstrate that students: can articulate what is meant by the term middle years and can identify with a need for a philosophy of middle schooling; are aware that they are part of a reform movement which has swept the nation and which has implications for teaching in schools in the twenty first century; are confident the program is producing highly skilled professional teachers willing to take on the challenges of teaching in the middle years; can say how their training has helped them understand and account for the educational experiences of students in a time of transition; and hold quiet, yet firm beliefs about teaching in the middle years. Furthermore, using a measure of lexical density to analyze the verbs used by respondents, it seems that this quiet confidence has grown in the period from 2003 – 2006.

Potency in professional development for teachers

There has been significant research into the impact of professional development (PD) on professional organisation and behaviour. PD has emerged in a diversity of forms in schools. Programs range form one hit seminars provided by an external consultant, through to a broad range of programmed development plans that integrate seminars; school based planning groups, action research, collaborative projects across schools, clusters and with critical friends, and mentoring. PD has been delivered to prompt school and teacher professional transformation or to support an ongoing development plan. PD is not uni-lateral and exists to support a very wide range of school and teacher development needs. The relevance and effectiveness of PD design and delivery is tied to the nature of the PD need and the context of provision. This paper reports an investigation into efficacy of various approaches to PD in Queensland schools. The research drew on responses to an online survey tool, focus groups and semi-structured interviews with PD coordinators, teachers, and school and district administrators to develop a model for effective PD planning that considers strategies for addressing current and future PD need and amelioration of barriers to PD effectiveness.

Critical social theory and transformative learning : evidence in pre-service teachers' service-learning reflection logs

This paper reports on the opportunities for transformational learning experienced by a group of pre-service teachers who were engaged in service-learning as a pedagogical process with a focus on reflection. Critical social theory informed the design of the reflection process as it enabled a move away from knowledge transmission toward knowledge transformation. The structured reflection log was designed to illustrate the critical social theory expectations of quality learning that teach students to think critically: ideology critique and utopian critique. Butin's lenses and a reflection framework informed by the work of Bain, Ballantyne, Mills and Lester were used in the design of the service-learning reflection log. Reported data provide evidence of transformational learning and highlight how the students critique their world and imagine how they could contribute to a better world in their work as a beginning teacher.