In this study, teachers are giving an opportunity to design and develop their own educational games. The following three questions guide the research: (1) What are the characteristics of teacher designed and developed games? (2) What theories do teachers use when they make games for educational purposes? (3) What are the design considerations when teachers engage in game authoring experiences? Framed in a qualitative, naturalistic case study perspective, this paper explores 83 teachers’ experience and thinking grounded in enactivism. Participating teachers are enrolled in a graduate course focusing on game based learning. Data sources include: teacher written assignments, teacher created digital artifacts, instructor’s reflective journal, and learner feedback after class. The analysis of the data show that teachers tend to create quiz games using the software they are familiar with, prefer collaborative design process, and math is a popular subject for games. They like to author games that are customized, with detailed storylines, and are appropriate for the local contexts. Implication and recommendations are also discussed.

Abstract In this article, we present a re-framing of tea- cher development that derives from our convictions regarding the enactive approach to cognition and the bio- logical basis of being. We firstly set out our enactivist stance and then distinguish our approach to teacher development from others in the mathematics education literature. We show how a way of working that develops expertise runs through all mathematics education courses at the University of Bristol, and distil key principles for running collaborative groups of teachers. We exemplify these principles further through analysis of one group that met over 2 years as part of a research project focused on the work of Gattegno. We provide evidence for the effec- tiveness of the group in terms of teacher development. We conclude by arguing that the way of working in this group cannot be separated from the history of interaction of participants.

Key words: mathematics teacher development, awareness, purposes, collaborative group, enactivism, expertise.

I report on a characterisation of algebraic learning which was guided by an enactivist theoretical framework. Ideas emerged within a longitudinal study investigating the learning of algebra in two schools through the observation of effective behaviours in different classrooms. Six themes, which supported ways of acting algebraically in different ways, were identified in the patterns of students’ behaviours. Through the enactivist analysis of these themes, algebraic learning was found to be promoted in classrooms where the embodied, rational, emotional and social aspects of learning were taken into account. In these environments, where students found a need for the use of algebra, and where acting algebraically became part of their behaviour, procedures were substantiated with explanations and justifications and were carried out within the exploration of mathematical structure.

Excerpt: A number of intentions triggered this research forum on enactivism and mathematics education research, and those are significant to highlight as they have in return structured the content and form that this forum takes. First, there has been and continues to be a substantial amount of research and writing on issues of enactivism undertaken by mathematics education researchers; thus we wanted to highlight and synthesize this body of research. At the same time, although much research has been conducted within the enactivist perspective, many of those contributions, and their authors, are not always well known and have often been seen merely as “interesting” orientations or “alternative” perspectives – but clearly not mainstream. Because we believe enactivism offers an insightful orientation which shows promise for enhancing our understanding of mathematics teaching and learning, we wanted to bring forth the nature and wide spectrum of enactivist contributions in order to share and create dialogue with the PME community about significant issues raised through this orientation. A third intention is in reaction to what might be thought of as a hegemony of constructivism in the mathematics education literature. We believe that enactivism, as a theory of cognition, offers a more encompassing and enlightening perspective on learning, teaching, and epistemology. Therefore, the following concerns will orient and be continuously present in the research forum unfoldings: retrospectives (as well as perspectives and prospectives) on research studies and writing done on enactivism in mathematics education will be shared; contributors will focus on insightful features that enactivism offers us; particularities of enactivism as a theory of cognition will permeate all discussions and presentations; and finally, but not least, interactions and discussions will take place about the ideas put forward.

This paper seeks to establish a research framework for an investigation into the extent to which pupils are able to visualise figural cues in multiple ways within the context of pattern generalisation. Enactivism, along with the constructs of knowledge objectification and figural apprehension, are identified as forming an ideal theoretical framework for such a study. Although largely theoretically driven, this paper also presents results from an initial pilot study in order to contextualise the theoretical milieu.

Excerpt: Radical changes have been advocated in recent reports on mathematics education, such as NCTM’s Curricu- lum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics 1989) and Everybody Counts (MSEB and National Research Council 1989). Unfortunately, many educators are fo- cusing on alterations in content rather than the reports’ recommendations for fundamental changes in instruc- tional practices. Many of these instructional changes can best be understood from a constructivist perspec- tive. Although references to constructivist approaches are pervasive, practical descriptions of such approaches have not been readily accessible. Therefore, to promote dialogue about instructional change, each “Research into Practice” column this year will illustrate how a constructivist approach to teaching might be taken for a specific topic in mathematics.

This chapter deals with the problems of operationalizing Radical Constructivism (hereafter referred to as RC) in teaching. In that context we call it ‘didactic constructivism’.

Excerpt: To conclude, the interpretation of science I have advanced entails neither a subjectivist position nor a relativist position in the common sense of the word. It requires the working out of an empirical, constructivist epistemology which conceives of the order generated by science as a (material) process of embodiment and incorporation of objects in our language and practices. Needless to say, the effort to develop such an interpretation of science has only just begun. Quite obviously, I think that the programme will profit from (but need not be bounded by) the microscopic investigation of scientific practice.

In the last two decades, one can clearly observe a boom of interest for e-learning and web-supported programs. However, one can also notice that many of these programs focus on the accumulation and delivery of content generally as a business industry with no much concern for theoretical underpinnings. The existing research, at least in online English language teaching (ELT), has demonstrated a lack of an effective online teaching pedagogy anchored in a well-defined theoretical framework. Hence, this paper comes as an attempt to present constructivism as one of the theoretical bases for the design of an effective online language teaching pedagogy which is at the same time technologically intelligent and theoretically informed to help envision how education can best take advantage of the information and communication technology (ICT) tools. The present paper discusses the key principles underlying constructivism, its implications for online language teaching design, as well as its limitations that should be avoided in the e-learning instructional design. Although the paper is theoretical in nature, essentially based on an extensive literature survey on constructivism, it does have practical illustrations from an action research conducted by the author both as an e-tutor of English using Moodle online educational platform at the Virtual University of Tunis (VUT) from 2007 up to 2010 and as a face-to-face (F2F) English teaching practitioner in the Professional Certificate of English Language Teaching Training (PCELT) at AMIDEAST, Tunisia (April-May, 2013).

Constructivism, or more precisely, a constructivist metatheory, presently prevails throughout professional education circles. Most educators easily accept constructivism’s central premise that learners approach tasks with prior knowledge and expectations based on their knowledge of the world around them. Naturally, then, constructivist educational technologists have been guided by the implicit (and increasingly explicit) desire to create “authentic” environments for learning: environments that correspond to the real world. In this paper, I argue that technologists have tended to paper over the critical epistemological dimension of constructivism by “preauthenticating” learning environments: creating environments that are predetermined to reflect the real world even though constructivist theory contrindicates precisely this. I suggest that a rhetorical perspective on constructivism offers a way out of this bind and I propose some guidelines to assist developers of educational technologies in accommodating the essentially dialogic nature of teaching and learning.