Learning mathematics in a classroom community of inquiry

This article considers the question of what specific actions a teacher might take to create a culture of inquiry in a secondary school mathematics classroom. Sociocultural theories of learning provide the framework for examining teaching and learning practices in a single classroom over a two-year period. The notion of the zone of proximal development (ZPD) is invoked as a fundamental framework for explaining learning as increasing participation in a community of practice characterized by mathematical inquiry. The analysis draws on classroom observation and interviews with students and the teacher to show how the teacher established norms and practices that emphasized mathematical sense-making and justification of ideas and arguments and to illustrate the learning practices that students developed in response to these expectations.

An examination of learning processes during critical incident training: Implications for the development of adaptable trainees

Three experiments are reported that examined the process by which trainees learn decision-making skills during a critical incident training program. Formal theories of category learning were used to identify two processes that may be responsible for the acquisition of decision-making skills: rule learning and exemplar learning. Experiments I and 2 used the process dissociation procedure (L. L. Jacoby, 1998) to evaluate the contribution of these processes to performance. The results suggest that trainees used a mixture of rule and exemplar learning. Furthermore, these learning processes were influenced by different aspects of training structure and design. The goal of Experiment 3 was to develop training techniques that enable trainees to use a rule adaptively. Trainees were tested on cases that represented exceptions to the rule. Unexpectedly, the results suggest that providing general instruction regarding the kinds of conditions in which a decision rule does not apply caused them to fixate on the specific conditions mentioned and impaired their ability to identify other conditions in which the rule might not apply. The theoretical, methodological, and practical implications of the results are discussed.

Using Developmental Theories to Inform the Design of Technology for Children

Electronic Blocks are a new programming environment, designed specifically for children aged between three and eight years. As such, the design of the Electronic Block environment is firmly based on principles of developmentally appropriate practices in early childhood education. The Electronic Blocks are physical, stackable blocks that include sensor blocks, action blocks and logic blocks. Evaluation of the Electronic Blocks with both preschool and primary school children shows that the blocks' ease of use and power of engagement have created a compelling tool for the introduction of meaningful technology education in an early childhood setting. The key to the effectiveness of the Electronic Blocks lies in an adherence to theories of development and learning throughout the Electronic Blocks design process.

Building learning communities to support beginning teachers use of technology

This paper reports on the early stages of a three year study that is investigating the impact of a technology-enriched teacher education program on beginning teachers' integration of computers, graphics calculators, and the internet into secondary school mathematics classrooms. Whereas much of the existing research on the role of technology in mathematics learning has been concerned with effects on curriculum content or student learning, less attention has been given to the relationship between technology use and issues of pedagogy, in particular the impact on teachers' professional learning in the context of specific classroom and school environments. Our research applies sociocultural theories of learning to consider how beginning teachers are initiated into a collaborative professional community featuring both web-based and face to face interaction, and how participation in such a community shapes their pedagogical beliefs and practices. The aim of this paper is to analyse processes through which the emerging community was established and sustained during the first year of the study. We examine features of this community in terms of identity formation, shifts in values and beliefs, and interaction patterns revealed in bulletin board discussion between students and lecturers.