Revealing conceptions of rate of change

Rate of change is an important mathematical concept. Research referring to students’ difficulties with this concept spans more than twenty years. Research suggests that problems experienced by some calculus students are likely a result of pre-existing limited or incorrect conceptions of rate of change. This study investigated 23 Victorian Year 10 students’ understanding of rate as revealed by phenomenographic analysis of interviews. Eight conceptions of rate of change emerged. Four important aspects of the concept were identified and gaps in students’ thinking defined. In addition, the employment of phenomenography, to reveal conceptions of rate, is described in detail.

Learning theories and interdisciplinary epistemologies

Interdisciplinary teaching and learning in higher education incorporates multiple ways of knowing. As interdisciplinary pedagogies become increasingly important in a global knowledge economy, which learning theories best inform thinking and practice in these endeavours? This paper explores a range of theories and ideas about learning, including constructivism, situated learning, experiential learning and phenomenography, and their relevance to interdisciplinarity in higher education.

Environmental attitudes of pre-service teachers : a conceptual and methodological dilemma in cross-cultural data collection

Human generated environmental problems are significant issues of global concern. Despite this, varying attitudes towards environments continue to exist across the globe, impacting on environmental decision-making and action at local, national and international levels. This paper probes some of the similarities and differences in environmental attitudes amongst pre-service teachers in Australia, Republic of Maldives and Indonesia. Data were collected using an established environmental attitude questionnaire and individual interviews. The three communities exhibited a similar range of environmental attitudes using the established questionnaire but significant differences emerged when the interview data were analysed phenomenographically. These differences reflect diversity within and across cultural groups that cannot be satisfactorily explained by the theory underpinning the established questionnaire. Consequently, a revised conceptual framework is proposed.

An investigation of middle secondary students' mathematical conceptions of rate

This study identified four educationally critical aspects of ‘rate’ through analysis of phenomenographic, video-recorded interviews with Year 10 students. Further analysis indicated understandings in one representation or context were not necessarily transferable.

A framework for teachers’ knowledge of mathematical reasoning

Exploring and developing primary teachers’ understanding of mathematical reasoning was the focus of the Mathematical Reasoning Professional Learning Research Program. Twenty-four primary teachers were interviewed after engagement in the first stage of the program incorporating demonstration lessons focused on reasoning conducted in their schools. Phenomenographic analysis of interview transcripts exploring variations in primary teachers’ perceptions of mathematical reasoning revealed seven categories of description based on four dimensions of variation, establishing a framework to evaluate development in understanding of reasoning.

Using video to promote pre-service teachers’ thinking about their transition to teaching

This paper reports on research investigating the use of video representations of first-year teachers’ experiences in undergraduate teacher education workshops that focus on the transition to teaching. The use of the video is a responsive act that draws on the notion of looking back, where graduates in their first year of teaching ‘speak to’ current students. Scenes from video footage of the theatre-based research performance The First Time shaped workshop activities and discussions in the unit. Themes ranged from pedagogical to practical, covering topics such as teacher identity discourses; epiphanic and revelatory moments of transition to becoming a teacher; and preparing for job applications and interviews. Data from the researcher’s journal, Student Evaluation of Teaching and Units (SETU) comments, and semi-structured interviews with undergraduate students upon completion of the workshops are framed within a phenomenographic paradigm. The aim in phenomenography is to describe variations of conception that people have of a particular phenomenon (Sin, 2010), in this case the video as a tool to promote critical thinking about the transition to teaching. The researcher explored her own, and participants’ experiences, and identified a range of conceptual meanings of the phenomenon. These were classified into categories according to their similarities and differences concerning the effectiveness of this specific video in assisting undergraduates in their transition to teaching. Early results reveal some similarities and many variations among participants as to the effectiveness of the video as a tool. Their conceptions of the phenomenon are individual and relational, and as such are quite varied. Emergent varied themes include: ‘I know what it is that I need to learn’; ‘Is this theory or practice?’; and ‘I don’t do drama’. Emergent similarities include: ‘Preparing for the unexpected’.

A framework for primary teachers’ perceptions of mathematical reasoning

Mathematical reasoning has been emphasised as one of the key proficiencies for mathematics in the Australian curriculum since 2011 and in the Canadian curriculum since 2007. This study explores primary teachers’ perceptions of mathematical reasoning at a time of further curriculum change. Twenty-four primary teachers from Canada and Australia were interviewed after engagement in the first stage of the Mathematical Reasoning Professional Learning Program incorporating demonstration lessons focused on reasoning conducted in their schools. Phenomenographic analysis of interview transcripts exploring variation in the perceptions of mathematical reasoning held by these teachers revealed seven categories of description based on four dimensions of variation. The categories delineate the different perceptions of mathematical reasoning expressed by the participants of this study. The resulting outcome space establishes a framework that facilitates tracking of growth in primary teachers’ awareness of aspects of mathematical reasoning.

Family physician preceptors' conceptualizations of health advocacy: implications for medical education

PURPOSE: Despite its official acceptance as an important physician responsibility, health advocacy remains difficult to define, teach, role model, and assess. The aim of the current study was to explore physicians' conceptions of health advocacy based on their experience with health-advocacy-related activities. METHOD: In 2012, the authors conducted 11 semistructured interviews with family physician clinical preceptors and analyzed the interviews in the tradition of phenomenography. RESULTS: The authors identified three distinct but related ways of understanding health advocacy: (1) Clinical: Health advocacy as support of individual patients in addressing health care needs related to the immediate clinical problem within the health care system, (2) Paraclinical: Health advocacy as support of individual patients in addressing needs that the physician preceptors viewed as peripheral yet parallel to both the health care system and the immediate clinical problem, and (3) Supraclinical: Health advocacy as population-based activities aimed at practice- and system-level changes that address the social determinants of health. CONCLUSIONS: The qualitatively different understandings of health advocacy shed light on why current approaches to defining, teaching, role modeling, and assessing health advocacy competencies in medical education appear idiosyncratic. The authors suggest the development of an inclusive and extensive conceptual framework that may allow the medical education community to imagine novel ways of understanding and engaging in health advocacy.

Using elicitation interview within a phenomenographic framework : developing the breadth of research designs associated with game based approaches

This paper describes how elicitation interview technique was used within a phenomenographic research design to explore physical education teachers’ experiences of teaching games using a Game Based Approach (GBA). Participants taught in one of two different international contexts, Australia or England, and all had some experience of using a GBA to teach games. The focus of the paper is the presentation and discussion of the unique research design used to generate understanding about GBA teaching experiences as well as extending the examination of GBAs from different philosophical viewpoints. Authors’ reflections on the utilised research design are presented with concluding discussion identifying further research opportunities relating to GBAs in teaching and coaching contexts.