Chronis Kynigos

A "Black-and-White Box" Approach to User Empowerment with Component Computing

The paper discusses three aspects central to the 10 year-old process of design, development and use of E-slate, a construction kit for educational software. These are: (1) the design of computational media for user empowerment, (2) the socially-grounded approach to the building of user communities and (3) the issue of long-term sustainability as crucial for the component movement to progress, but also as constituting its real strength in relation to standalone technologies for computational media. An analysis of E-slates features, the process and products of user community constructions with E-slate and the organizational aspects of maintaining on-going development and research is provided. We conclude that the design, development and user-support of empowering computational media should be viewed as a continuing effort to build social change architectures, rather than single R&D projects. We suggest that this can only be done through the development and preservation of hybrid communities across organizations.

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.

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.

Generating Cultures for Mathematical Microworld Development in a Multi-Organizational Context

This article discusses methodological issues of mathematical microworld development integrated with generating innovation in the school setting. This is done by means of vignettes of key episodes in our eight-year-long experience of developing a component architecture for educational software based on Logo as a scripting language. The vignettes touch on the problems of collaboration between organizations and people of different expertise. They also address issues to do with the school and the classroom as social systems, with the method for implementing innovation and with curriculum design, teaching, and learning. A set of issues that emerged as problematic are outlined and discussed; the different priority systems involved, the amount of investment in collaboration, the differing discourses and epistemologies, the notion of a product, the interdependencies, and the contrast between reform and innovation versus instant fit. It is suggested that awareness needs to be raised as well as methods for dealing with these factors in order to generate cultures developing and using exploratory software.

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.

Working with Teachers: Context and Culture

This chapter concerns collaborations between teacher educators and teachers in activities involving digital technologies in the teaching and learning of mathematics. In light of the complexity involved in introducing new artefacts into existing cultures of practices, we focus on our attempts to develop ways of working with teachers so that they can become active participants in designing practices and routines appropriate for the particularities of their own classrooms. Three case studies are presented, from three different countries, Norway, Greece and Brazil, each of which describes the participation of teachers in a process of communal design of mathematical tools and activities. Two theoretical notions, boundary objects and instrumental genesis, are employed in order interpret the case studies and to illuminate the challenges associated with involving teachers in considering when, how and why digital technologies might be used fruitfully in the teaching of mathematics.

Constructionism: Theory of Learning or Theory of Design?

Constructionism has established itself as an epistemological paradigm, a learning theory and a design framework, harnessing digital technologies as expressive media for students’ generation of mathematical meanings individually and collaboratively. It was firstly elaborated in conjunction with the advent of digital media designed to be used for engagement with mathematics. Constructionist theory has since then been continually evolving dynamically and has extended its functionality from a structural set of lens to explanation and guidance for action. As a learning theory, the constructionist paradigm is unique in its attention to the ways in which meanings are generated during individual and collective bricolage with digital artefacts, influenced by negotiated changes students make to these artefacts and giving emphasis to ownership and production. The artefacts themselves constitute expressions of mathematical meanings and at the same time students continually express meanings by modulating them. As a design theory it has lent itself to a range of contexts such as the design of constructionist-minded interventions in schooling, the design of new constructionist media involving different kinds of expertise and the design of artifacts and activity plans by teachers as a means of professional development individually and in collective reflection contexts. It has also been used as a lens to study learning as a process of design. This paper will discuss some of the constructs which have or are emerging from the evolution of the theory and others which were seen as particularly useful in this process. Amongst them are the constructs of meaning generation through situated abstractions, re-structurations, half-baked microworlds, and the design and use of artifacts as boundary objects designed to facilitate crossings across community norms. It will provide examples from research in which I have been involved where the operationalization of these constructs enabled design and analysis of the data. It will further attempt to forge some connections with constructs which emerged from other theoretical frameworks in mathematics education and have not been used extensively in constructionist research, such as didactical design and guidance as seen through the lens of Anthropological Theory from the French school and the Theory of Instrumental Genesis.

Children's inductive thinking during intrinsic and Euclidean Geometrical activities in a computer programming environment

This paper presents a case study investigating the knowledge constructed by two 12 year-old children working with a geometrical Logo microworld allowing the Logo turtle to measure distances, and turns relative to previously constructed points on the plane. A qualitative analysis of data consisting of everything that the children said, typed and wrote on paper during the 15 hours of the research, provided evidence of the childrens developing use of concepts belonging to Plane Geometry. The measuring of angular and length quantities, enabled them to conjecture, reflect on and manipulate triangle properties and relations traditionally associated with Euclidean Geometry. Their developing awareness of the existence of geometrical relations in their work, encouraged an increase in their readiness to use and reflect on them. The paper concludes that the generation of learning environments such as the above may well enhance the opportunity for children to form inductive geometrical understandings.

Perspectives in analysing classroom interaction data on collaborative computer-based mathematical projects

In view of the potential of CSCL for educational innovation, this paper illuminates some aspects resisting the development of quality social interaction in pupil collaboration. A study is reported where pupils worked in small groups in computer-based classroom activity within the framework of a six year-old innovation program in a primary school. A combined ethnographic and discourse analytic model is used to describe group dynamics in four groups of pupils (aged 8-11) involved in tasks of exploratory learning. We analyzed the data taking three distinct perspectives, a personal or insideris perspective, an interactionist perspective and a social norms perspective. The former revealed the pupil to be a person who seemed to perceive the society within which he/she was called upon to act, as a forum in which to claim and defend his/her social role. The interactionist perspective brought forward the issue of role negotiation and its overbearing presence in social exchange in the form of groupthink, role confusion and vagueness. Finally, the group and classroom social norms, which seemed to have emerged as functional within these societies, had a judgmental character.

Programming as a Means of Expressing and Exploring Ideas: Three Case Studies Situated in a Directive Educational System

This chapter discusses programmability as an important property of exploratory software for education within a framework of progressive discrimination of which of its aspects are good agents for infusing pupil control over technology and their own learning, the enjoyment of personal construction and the ability to express ideas and generalizations. The ones discussed are programming a) as an agent for developing an alternative teaching and learning paradigm within a directive educational culture, b) enabling pupils to construct objects consisting of a set of ideas, understood in varying depth, but concurrently explorable, and c) providing the potential for exploring ideas from content domains other than mathematics, such as physics. The arguments are based on a description of three Logo learning environments situated in the Greek educational system.