Active and supportive computer-mediated resources for student-to-student conversations

Communication is a central aspect of human learning. Using the Probability Inquiry Environment (PIE) as an example, we examine how external representations (both textual and iconic) mediate face-to-face conversations among students, and support productive mathematical discourse. We provide quantitative data that suggests that seventh grade students who used PIE learned some of the basic principles of probability. Two cases studies are that illustrate how communication supported by computer-mediated representations contributed to this success. The first case study demonstrates how the computer can actively prompt student conversations that lead to learning. The second case study examines how an animated graphical representation supported these productive conversations

Cornerstone Mathematics: Designing Digital Technology for Teacher Adaptation and Scaling

We report the results of a design-based research project in England that embeds digital technology. The research followed from two phases in the USA: (1) a design phase that used dynamic representations to foster conceptual understanding of hard-to-teach mathematical ideas, and (2) a research phase that measured the efficacy of the resulting technology-based curriculum units as implemented in Texas schools. The goal of the third phase in England was initially to “scale up” the US approach. We determined, however, that the materials had to be re-designed for adaptability by English teachers. We report how the features of the innovation—particularly its technological infrastructure—could be leveraged, not only to achieve positive learning outcomes, but also to lay the foundations for change in pedagogy and learning at scale. We identify an emergent framework of design affordances for teacher adaptability that are particularly salient when technology is a critical element

Scaling a technology-based innovation: windows on the evolution of mathematics teachers' practices

This paper reports research on effects on teachers’ classroom practices resulting from their engagement in sustained professional development and classroom teaching of a resource that embeds carefully designed dynamic technology within middle school mathematics (11–14 years). The research investigated the self-reported evolution of teachers’ classroom and departmental practices as they sought to integrate the materials and the technology into their teaching. The sample comprised 203 English middle school mathematics teachers who participated in the professional development and taught the materials during 2013–2014. The methodology used questionnaires, administered to match individual teachers’ teaching schedules, and the resulting data were analyzed quantitatively to give summative statistics, and qualitatively to elicit more nuanced contextualised information. The questionnaire data were thus supplemented by two case studies to illustrate how the trajectory of development of teacher practices was shaped, first by their initial motivations to participate in the innovation, but later more strongly by the ways they chose to align their practices to the institutional goals of their schools in order for the innovation to be sustained