Total internal reflection-based biochip utilizing a polymer-filled cavity with a micromirror sidewall

A total internal reflection (TIR)-based biochip utilizing a polymer-filled cavity with a micromirror sidewall has been designed and fabricated. The implementation of the micromirror sidewall cavity facilitates precise alignment of the excitation light beam into the system. The incident angle of illumination can be easily modified by selecting polymers of different indices of refraction while optical losses are minimized. The design enables the hybrid, vertical integration of a laser diode and a CCD camera, resulting in a compact optical system. Brownian motion of fluorescent microspheres and real-time photobleaching of rhodamine 6G molecules is demonstrated. The proposed TIR-based chip simplifies current TIR optical configurations and could potentially be used as an optical-microfluidic platform for an integrated lab-on-a-chip microsystem.     

Using half-baked microworlds to challenge teacher educators’ knowing

This article illustrates how four teacher educators in training were challenged with respect to their epistemology and perceptions of teaching and learning mathematics through their interactions with expressive digital media during a professional development course. The research focused on their experience of communally constructing artifacts and their reflections on the nature of mathematics and mathematics teaching and learning with digital media. I discussed three different ways in which this media was used by the teachers; first, as a means to engage in technical-applied mathematics to engineer mathematical models; second, as a means to construct models for students to engage in experimental-constructivist activity; thirdly, as a means to engage in a discussion of a challenging mathematical problem.

Boundary crossing through in-service online mathematics teacher education: the case of scenarios and half-baked microworlds

We address online mathematics teacher education as a means of immersing teachers into new kinds of collectives where professional development may be enhanced by crossing the boundaries of their habitual communities and the norms within these. We analyse the ways in which newly trained teacher educators interacted around their designs and productions for in-service courses they were giving to colleagues. We focus on their uses of scenarios and half-baked microworlds as two kinds of artefacts we had designed to play the role of improvable boundary objects. We consider these interactions as a forum for challenge and for professional development through frequent and relevant boundary crossing.     

Investigating the Role of Context in Experimental Research Involving the Use of Digital Media for the Learning of Mathematics: Boundary Objects as Vehicles for Integration

The paper describes a study of the contexts of six teams, expert in research and development of digital media for learning mathematics, who cross-experimented in classrooms with the use of each other’s artefacts. Contextual issues regarding the designed tasks and technologies, the socio-systemic milieu and the ways in which the researchers worked with the teachers were in focus. We analysed the ways in which a set of mutually constructed and negotiated questions aiming to illuminate otherwise tacit contextual issues operated as boundary objects amongst the teams. We discuss the need to develop special tools such as these boundary objects in order to elicit issues of context and the ways they may affect the production of theory.     

Mathematics Education & Digital Technologies: Facing the Challenge of Networking European Research Teams

This paper introduces the IJCML Special Issue dedicated to digital technologies and mathematics education and, in particular, to the work performed by the European Research Team TELMA (Technology Enhanced Learning in Mathematics). TELMA was one of the initiatives of the Kaleidoscope Network of Excellence established by the European Community (IST-507838—2003–2007) to promote the joint elaboration of concepts and methods for exploring the future of learning with digital technologies. TELMA addressed the problem of fragmentation of theoretical frameworks in the research field of mathematics education with digital technologies and developed a methodology based on the in field cross-experimentation of educational digital environments for maths. Six European research teams engaged in cross-experimentation in classrooms as a means to begin to develop a common language and to analyse the intertwined influence played, both explicitly and implicitly, by different contextual characteristics and theoretical frames assumed as reference by the diverse teams participating in the initiative.     

Normalising geometrical figures: dynamic manipulation and construction of meanings for ratio and proportion

Enlarging-shrinking geometrical figures by 13 year-olds is studied during the implementation of proportional geometric tasks in the classroom. Students worked in groups of two using ‘Turtleworlds’, a piece of geometrical construction software which combines symbolic notation, through a programming language, with dynamic manipulation of geometrical objects by dragging on sliders representing variable values. In this paper we study the students’ normalising activity, as they use this kind of dynamic manipulation to modify ‘buggy’ geometrical figures while developing meanings for ratio and proportion. We describe students’ normative actions in terms of four distinct Dynamic Manipulation Schemes (Reconnaissance, Correlation, Testing, Verification). We discuss the potential of dragging for mathematical insight in this particular computational environment, as well as the purposeful nature of the task which sets up possibilities for students to appreciate the utility of proportional relationships.     

Charting the microworld territory over time: design and construction in mathematics education

The study discusses the development of theoretical ideas and constructs related to digital microworlds within the mathematics education community and their implications for interpretations of mathematics learning. Starting from Papert’s introduction of the concept during ICME 2 in 1972, we trace the evolution of theoretical approaches concerning the essence of the idea in an attempt to situate the notion of constructionism in the light of contemporary frameworks. We argue that microworlds, and the search for a learnable mathematics, have a continued relevance to mathematics education, but that the lens research attention has shifted over time, with the current foci on communal design, situated and embodied approaches and artefacts whose use crosses boundaries between different practices. To illustrate these shifts and the challenges that still remain, we present examples from our current work involving the use of microworlds for learning and teaching through communication, design and construction.     

Mathematics with Component-Oriented Exploratory Software

In this paper we discuss a component-oriented architecture which we are employing to develop programmable exploratory software for mathematics. We argue that the architecture can be used to provide synergy between end-user programming and efficient behavior of components, i.e. Computational objects of a wide range of technical complexity and functionalities. We give examples of components with mathematics in their behavior and components which in themselves embody mathematical relations. Through both formal language and visual means, users can link them to form creative configurations with interesting functionalities and use the resulting environments for exploratory activity. We conclude that this architecture enables a more efficient collaboration between technical and educational expertise in developing exploratory software. This revised version was published online in July 2006 with corrections to the Cover Date.