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Our research aimed to investigate the potential learning benefits to young children of implementing digital interactive multimodal technologies that provide both visual and haptic experiences in elementary mathematics classrooms. We studied the ways in which fourth-grade students collaboratively create collective strategies for solving mathematical problems utilizing dynamic geometry software with multi-touch interfaces, a combination we call a multi-touch Dynamic Geometry Environment. We examine in-depth two case studies each illustrating how mathematical strategies, collaboration, and socially mediated metacognition emerge in the small groups of children while working on an activity using the Geometer's Sketchpad® on the iPad to make sense of an intuitive idea of covariation. We found that children's interactions with their peers, the interviewer, and the mDGE favored the emergence of varied collaborative behaviors and socially mediated metacognitive processes that fostered the co-construction and development of mathematical strategies over a short period of time. [ABSTRACT FROM AUTHOR]

Variance and invariance are two powerful mathematical ideas to support geometrical and spatial thinking, yet there is limited research about teachers' knowledge of variance and invariance. In this paper, we examined how high school teachers deal with the task of looking for invariant properties in a dynamic geometry environment (DGE) setting. Specifically, we investigated if they even attend to invariant properties; what invariant properties they discern and discuss; and how DGE can support such discernment. Our analysis found that teachers tend to discern and discuss invariant properties mainly when they were probed to consider invariance. We also found four categories of invariant properties that seem to be important for a robust and rich understanding of geometric objects in the context of invariance and DGE. The use of DGE allowed teachers to see and interact with invariant properties, thus suggesting that accessing geometry dynamically may have structural affordances especially when exploring invariance. Teachers were able to enact different DGE movements to discern and discuss invariant properties, as well as to reason with and about them. We also saw that teachers' backgrounds and past experiences can play an important role in their descriptions of invariant properties. Possible future research directions and implications to teacher education are discussed. [ABSTRACT FROM AUTHOR]

We report on two large studies conducted in advanced algebra classrooms in the US, which evaluated the effect of replacing traditional algebra 2 curriculum with an integrated suite of dynamic interactive software, wireless networks and technology-enhanced curriculum on student learning. The first study was a cluster randomized trial and the second was a quasi-experimental replication study using a subset of the original treatment teachers. Both studies demonstrated significant impact on student learning of core algebra concepts including both procedural and conceptual problems. Various variables were modeled to understand the impact of such an intervention including demographic factors and class level. We found that being in an honors class significantly predicts learning gains but being in a non-honors SimCalc class significantly predicts learning gains versus all other groups. We also found significant effects of treatment on difference scores for problems which demanded simple procedural approaches and those that demanded complex conceptual understanding. [ABSTRACT FROM AUTHOR]

We investigated prospects for reported sustainable adoption and sharing of an educational innovation through survey research including online questionnaires and telephone interviews. This investigation is part of the Scaling-Up SimCalc experimental program, which combines dynamic representational algebra software (SimCalc MathWorlds) with integrated curriculum and small professional development workshops focused on how to use the software and how to integrate this intervention into the larger year-long curriculum. Teachers who (1) perceived the usefulness of the SimCalc professional development as being consistent with personal aims and (2) perceived specific affordances of the software/curriculum to be valuable were more likely to report continued use of the innovation after the research had ended and that they had shared it with colleagues over time. [ABSTRACT FROM PUBLISHER]

We describe the application of Hierarchical Linear Modelling (HLM) in a cluster-randomised study to examine learning algebraic concepts and procedures in an innovative, technology-rich environment in the US. HLM is applied to measure the impact of such treatment on learning and on contextual variables. We provide a detailed description of such methods, methodically analysing nested classroom data with respect to various outcome measures through HLM. [ABSTRACT FROM AUTHOR]

The article discusses how haptic technologies can be utilized by young children in investigating mathematical concepts and ideas , such as geometric shapes and surfaces. It describes why and how young learners must work in learning environments with new technology. It also highlights how young children must be doing mathematical problem-solving in the future as well as the Omni force-feedback device.

We present epistemological ruptures that have occurred in mathematical history and in the transformation of using technology in mathematics education in the twenty-first century. We describe how such changes establish a new form of digital semiotics that challenges learning paradigms and mathematical inquiry for learners today. We focus on drawing analogies between the emergence of non-Euclidean geometry with recent advances in technological environments that are dynamic and interactive both visually and haptically. This analysis yields a new digital semiotic theory. [ABSTRACT FROM AUTHOR]

Wireless networks are fast becoming ubiquitous in all aspects of society and the world economy. We describe a method for studying the impacts of combining such technology with dynamic, representationally-rich mathematics software, particularly on participation, expression and projection of identity from a local to a public, shared workspace. We describe the types of mathematical activities that can utilize such unique combinations of technologies. We outline specific discourse analytic methods for measuring participation and methodologies for incorporating measures of identity and participation into impact studies. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The article discusses various reports published within the April 2008 issue of the journal "Educational Studies in Mathematics," including one on the contribution of professor Jim Kaput to the teaching of mathematics, and another on various ways to strengthen the theory and curriculum of schools.

Background: Executive dysfunction has been reported at different ages in autism. It is not clear however, when this impairment emerges or how its expression is affected by development. Methods: 61 non-mentally retarded autism participants (AUT) and 61 age, gender, and IQ matched typically developing participants (CON) were assessed with two oculomotor executive function tasks, the oculomotor delayed response task (ODR) and the antisaccade task (AS), as well as a visually-guided saccade sensorimotor task (VGS). Results: The AUT group demonstrated impairments in response inhibition and spatial working memory at all ages tested. Developmental improvements in speed of sensorimotor processing and voluntary response inhibition were similar in both groups indicating sparing of some attentional control of behavior. Developmental progression in the speed of initiating a cognitive plan and maintaining information on line over time, however, was impaired in the AUT group indicating abnormal development of working memory. Conclusions: These results indicate that while executive dysfunction is present throughout development, there is evidence for both typical and atypical developmental progression of executive functions in autism. The plasticity suggested by the developmental improvements may have implications regarding appropriate developmental epochs and types of interventions aimed at enhancing cognitive capacities in individuals with autism. [Copyright &y& Elsevier]

We describe a four-level spectrum of pedagogical awareness (SPA) that emerged from the analysis of six undergraduate mathematics tutors' (1) conceptualizations of their first-year students' difficulties; (2) descriptive accounts of their strategies for facilitating the overcoming of these difficulties; and (3) self-reflective accounts regarding their teaching practices. These were recorded in 45 semistructured interviews conducted during the 8-week Oxford University term and following minimally participant observation of their tutorials. We exemplify the four levels of SPA, across these three strands, in 12 characteristic examples where tutors discuss episodes from the observed tutorials. The design and analysis of the study reflect three underlying theoretical perspectives: constructivist, sociocultural, and enactivist. Finally, we draw on participants' comments to suggest that our methodology encouraged reflection, raised awareness, and demonstrated the pedagogical potential of collaboration between mathematicians and mathematics educators. We see such awareness and collaborative goodwill as prerequisites to conceptualizing and implementing reform of pedagogical practice. [ABSTRACT FROM AUTHOR]