Theory and its role in mathematics education

The increased recognition of the theory in mathematics education is evident in numerous handbooks, journal articles, and other publications. For example, Silver and Herbst (2007) examined ―Theory in Mathematics Education Scholarship‖ in the Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007) while Cobb (2007) addressed ―Putting Philosophy to Work: Coping with Multiple Theoretical Perspectives‖ in the same handbook. And a central component of both the first and second editions of the Handbook of International Research in Mathematics Education (English, 2002; 2008) was ―advances in theory development.‖ Needless to say, the comprehensive second edition of the Handbook of Educational Psychology (Alexander & Winne, 2006) abounds with analyses of theoretical developments across a variety of disciplines and contexts. Numerous definitions of ―theory‖ appear in the literature (e.g., see Silver & Herbst, in Lester, 2007). It is not our intention to provide a ―one-size-fits-all‖ definition of theory per se as applied to our discipline; rather we consider multiple perspectives on theory and its many roles in improving the teaching and learning of mathematics in varied contexts.

Teacher change and professional development in mathematics education

It is generally agreed that if authentic teacher change is to occur then the tacit knowledge about how and why they act in certain ways in the classroom be accessed and reflected upon. While critical reflection can and often is an individual experience there is evidence to suggest that teachers are more likely to engage in the process when it is approached in a collegial manner; that is, when other teachers are involved in and engaged with the same process. Teachers do not enact their profession in isolation but rather exist within a wider community of teachers. An outside facilitator can also play an active and important role in achieving lasting teacher change. According to Stein and Brown (1997) “an important ingredient in socially based learning is that graduations of expertise and experience exist when teachers collaborate with each other or outside experts” (p. 155). To assist in the effective professional development of teachers, outside facilitators, when used, need to provide “a dynamic energy producing interactive experience in which participants examine and explore the complex components of teaching” (Bolster, 1995, p. 193). They also need to establish rapport with the participating teachers that is built on trust and competence (Hyde, Ormiston, & Hyde, 1994). For this to occur, professional development involving teachers and outside facilitators or researchers should not be a one-off event but an ongoing process of engagement that enables both the energy and trust required to develop. Successful professional development activities are therefore collaborative, relevant and provide individual, specialised attention to the teachers concerned. The project reported here aimed to provide professional development to two Year 3 teachers to enhance their teaching of a new mathematics content area, mental computation. This was achieved through the teachers collaborating with a researcher to design an instructional program for mental computation that drew on theory and research in the field.

Realigning capital portfolios : international students' educational experiences in higher education

This paper reports on first year experiences of international students who use English as an additional language (EAL) in higher education in Australia. It examines how valued resources can foster a positive educational experience of these students from sociological perspectives. It draws data from an interview study, exploring narrative accounts of 17 EAL international students from nine countries about their educational relations and strategies across their first year of study. Their narratives were analysed through Bourdieu's concepts of field, habitus, capital and legitimation, as well as tools of narrative inquiry. The paper finds that the students took up strategies to realign their capital portfolios with new rules of the game. Their decisions were dependent on their personal trajectories and conditions on offer. This paper suggests that more effort needs to be made to understand international students' differentiated access to valued resources in higher education.

Handbook of International Research in Mathematics Education [3rd Ed.]

"This third edition ofthe Handbook of International Research in Mathematics Education provides a comprehensive overview of the most recent theoretical and practical developments in the field of mathematics education. Authored by an array of internationally recognized scholars and edited by Lyn English and David Kirshner, this collection brings together overviews and advances in mathematics education research spanning established and emerging topics, diverse workplace and school environments, and globally representative research priorities. New perspectives are presented on a range of critical topics including embodied learning, the theory-practice divide, new developments in the early years, educating future mathematics education professors, problem solving in a 21st century curriculum, culture and mathematics learning, complex systems, critical analysis of design-based research, multimodal technologies, and e-textbooks. Comprised of 12 revised and 17 new chapters, this edition extends the Handbook’s original themes for international research in mathematics education and remains in the process a definitive resource for the field."--Publisher website

Changing agendas in international research in mathematics education

Handbooks serve an important function for our research community in providing state-of-the-art summations, critiques, and extensions of existing trends in research. In the intervening years between the second and third editions of the Handbook of International Research in Mathematics Education, there have been stimulating developments in research, as well as new challenges in translating outcomes into practice. This third edition incorporates a number of new chapters representing areas of growth and challenge, in addition to substantially updated chapters from the second edition. As such, the Handbook addresses five core themes, namely, Priorities in International Mathematics Education Research, Democratic Access to Mathematics Learning, Transformations in Learning Contexts, Advances in Research Methodologies, and Influences of Advanced Technologies...

Predictors of attitudes toward inclusion of students with special educational needs in future education professionals

One of the main pillars in the development of inclusive schools is the initial teacher training. Before determining if it is necessary to make changes (and of what type) in training programs or curriculum guides related to the attention to diversity and inclusive education, the attitudes of future education professionals in this area should be analyzed. This includes the identification of the relevant predictors of inclusive attitudes. The research reported in this article pursued this objective, doing so with a quantitative survey methodology based on the use of cross-sectional structured data collection and statistical analyses related to the quality of the attitude questionnaire (factor analysis and Cronbach's alpha), descriptive statistics, correlations, hypothesis tests for difference of means, and regression analysis in order to predict attitudes towards inclusion in education. Firstly, the results show that the participants held very positive attitudes toward the inclusion of students with special educational needs. Particularly, older respondents, those with a longer training and, to a lesser extent, women and those who had been in touch with disabled people stood out within this attitude. Secondly, it is evidenced that self-transcendence values ​and, more weakly, contact, function as robust predictors of attitudes of future practitioners towards the inclusion of students with special needs. Some applications for the initial professionalization of educators are suggested in the discussion.

Mathematical modelling in mathematics education and instruction

This paper aims at giving a concise survey of the present state-of-the-art of mathematical modelling in mathematics education and instruction. It will consist of four parts. In part 1, some basic concepts relevant to the topic will be clarified and, in particular, mathematical modelling will be defined in a broad, comprehensive sense. Part 2 will review arguments for the inclusion of modelling in mathematics teaching at schools and universities, and identify certain schools of thought within mathematics education. Part 3 will describe the role of modelling in present mathematics curricula and in everyday teaching practice. Some obstacles for mathematical modelling in the classroom will be analysed, as well as the opportunities and risks of computer usage. In part 4, selected materials and resources for teaching mathematical modelling, developed in the last few years in America, Australia and Europe, will be presented. The examples will demonstrate many promising directions of development.

Discourses of power in Mathematics Education research : concepts and possibilities for action. 'Discursos sobre el poder en la investigación en Educación Matemática : conceptos y posibilidades para la acción'.

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Digital technology in mathematics education : why it works (or doesn't)

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