No abstract

The authors present three studies (two randomized controlled experiments and one embedded quasi-experiment) designed to evaluate the impact of replacement units targeting student learning of advanced middle school mathematics. The studies evaluated the SimCalc approach, which integrates an interactive representational technology, paper curriculum, and teacher professional development. Each study addressed both replicability of findings and robustness across Texas settings, with varied teacher characteristics (backgrounds, knowledge, attitudes) and student characteristics (demographics, levels of prior mathematics knowledge). Analyses revealed statistically significant main effects, with student-level effect sizes of .63, .50, and .56. These consistent gains support the conclusion that SimCalc is effective in enabling a wide variety of teachers in a diversity of settings to extend student learning to more advanced mathematics.

The nature of mathematical reference fields has substantially evolved with the advent of new types of digital technologies enabling students greater access to understanding the use and application of mathematical ideas and procedures. We analyze the evolution of symbolic thinking over time, from static notations to dynamic inscriptions in new technologies. We conclude with new perspectives on Kaput's theory of notations and representations as mediators of constructive processes.

No abstract

We analyze the intersection of new forms of representation infrastructures in a particular dynamic mathematics software (SimCalc MathWorlds Ò ) with the affordances of available communication infrastructures (both hardware and software). We describe the fundamental design principles from a software and curriculum perspective of why these two infrastructures can be overlapped in educational environments for important and meaningful learning outcomes. The products of this intersection result in new modes of expression (in terms of gesture, deixis and informal/formal registers), classroom identity formation in mathematically-meaningful ways, and pedagogy in terms of activity structure and intentionality. We exemplify the results of such intersection on classroom learning, participation and motivation. OverviewFor the past two decades, educational technology has been evolving in various ways along various research and development trajectories. Software has become more visual, interactive and (as is the focus of this special issue) more dynamic. Hardware has evolved to allow more complex programs to be executed for work to be done at a distance (both proximally and longitudinally) through the advances of networks (in particular wireless), and to be more portable in terms of its hand-heldability. These affordances 1 impact two types of infrastructure: (1) representational infrastructures and (2) communication infrastructures. We posit that these infrastructures have at times evolved independently but when they co-evolve or intersect each other's growth pathways, then new forms of activities occur.We begin by describing what this evolving dynamic looks like from the perspective of a mathematics classroom, or mathematics education community, and contextualize our work within a program of research of almost 10 years that has investigated the impact of the integration of dynamic software environments, such as SimCalc MathWorlds Ò and wireless networks (e.g., TI-Navigator TM Learning System) on learning, participation and motivation. This work resulted in highlighting three products from the intersection of representation and communication infrastructures, which we present in this paper. Representational infrastructures and communication infrastructuresTechnology has offered and afforded representations and interactions between representations for a long time. These have been in terms of symbolic manipulators, where computational duties are offloaded to the microprocessor and new actions are linked to traditional notation systems. But in addition, there is now support for new interactive notation systems, such as programming languages underlying 1 By affordance we mean a quality of an object, or an environment, that allows an individual to perform an action. We thank one of our reviewers for offering us a succinct and meaningful definition. mathematics packages (e.g., Maple) and spreadsheets, enhanced interactivity and expressibility of new phenomena by linking traditional notation systems and representations to new ones (e...