From intrinsic to non-intrinsic geometry : a study of childrens understandings in logo-based microworlds.

The aim of the present study was to investigate the potential for children to\ud use the turtle methaphor to develop understandings of intrinsic, euclidean\ud and cartesian geometrical ideas. Four aspects of the problem were\ud investigated.\ud a) the nature of the schema children form when they identify with the turtle in\ud order to change its state on the screen;\ud b) whether it is possible for them to use the schema to gain insights into\ud certain basic geometrical principles of the cartesian geometrical system;\ud c) how they might use the schema to form understandings of euclidean\ud geometry developed inductively from specific experiences;\ud d) the criteria they develop for choosing between intrinsic and euclidean\ud ideas.\ud Ten 11 to 12 year - old children participated in the research, previously\ud having had 40 to 50 hours of experience with Turtle geometry. The research\ud involved three case - studies of pairs of children engaging in cooperative\ud activities, each case - study within a geometrical Logo microworld. The data\ud included hard copies of everything that was said, typed and written.\ud Issues a) and b) were investigated by means of the first case - study which\ud involved three pairs of children and a microworld embedding intrinsic and\ud coordinate ideas. A model of the children's intrinsic schema and a model of\ud the coordinate schema which they formed during the study were devised. The\ud analysis shows that the two schemas remained separate in the children's\ud minds with the exception of a limited number of occasions of context specific\ud links between the two.\ud Issue c) was investigated in the second case - study involving one pair of\ud children and a microworld where the turtle was equipped with distance and\ud turn measuring instruments and a facility to mark positions. The analysis\ud illustrates how a turtle geometric environment of a dynamic mathematical\ud nature was generated by the children, who used their intrinsic schema and\ud predominantly engaged in inductive thinking. The geometrical content\ud available to the children within this environment was extended from intrinsic\ud to both intrinsic and euclidean geometry.\ud Issue d) was investigated by means of the third case - study involving a pair of\ud children and a microworld where the children could choose among circle\ud procedures embedding intrinsic and/or euclidean notions in order to construct\ud figures of circle compositions. The analysis shows that the children employed\ud their turtle schema in using both kinds of notions and did not seem to\ud perceive qualitative differences between them. Their decisions on which type\ud of notion to use were influenced by certain broader aspects of the\ud mathematical situations generated in the study

Children challenging the design of half-baked games: Expressing values through the process of game modding

In this paper we look at the potential educational value of placing children in a dual role of identifying and changing rules and values embedded in digital games by hacking them. Children’s participation in the design of learning technologies is a difficult challenge to address, due to limitations in children’s domain-knowledge around which these technologies are developed. Their role in the design process is thus usually limited to that of a user or tester. In this paper we discuss the role of children as “hackers” of what we call ‘half-baked’ games. By hacking a pedagogically engineered half-baked game in order to improve or change it, children are expected to challenge the values, the mechanics and the rules of a fully functioning, but faulty, or inappropriate game originally designed to provoke students to modify it. This discussion uses an example of children modding such a game provocatively called ‘PerfectVille’, which was specially designed to raise problems around the issue of urban sustainability. The game itself was designed with the use of a GIS rule-based authoring tool for game design called ‘sus-x’. The children grappled with both value-laden issues and concepts embedded in the tool they used. The issue of taking children’s values into account but also of helping them to build understandings of wider contested societal values can be addressed by studying the process by which children design and change games affording such experiences. It also illuminated their own perspective and values, which they embedded in the games

Participatory design to lower the threshold for intelligent support authoring

One of the fundamental aims of authoring tools is to provide teachers with opportunities to configure, modify and generally appropriate the content and pedagogical strategies of intelligent systems. Despite some progress in the field, there is still a need for tools that have low thresholds in terms of the users’ technical expertise. Here, we demonstrate that designing systems with lower entry barrier can potentially be achieved through co-design activities with non-programmers and carefully observing novices. Following an iterative participatory co-design cycle with teachers who have little or no programming expertise, we reflect on their proposed enhancements. Our investigations focus on Authelo, an authoring tool that has been designed primarily for Exploratory Learning Objects, but we conclude the paper by providing transferable lessons, particularly the strong preference for visual interfaces and high-level pedagogical predicates for authoring analysis and feedback rules

Metafora: A Web-based Platform for Learning to Learn Together in Science and Mathematics

This paper presents Metafora, both a platform for integrated tools as well as an emerging pedagogy for supporting Learning to Learn Together in science and mathematics education. Our goal is to design technology that brings education to a higher level; a level where students not only learn a subject matter, but also gain a set of critical skills needed to engage in and self-regulate collaborative learning experiences in science and math education. We first discuss the core skills we hope students will gain as they learn to learn together. We then present our design and implementation that can achieve this goal; a platform and pedagogy we have developed to support the learning of these skills. Finally, we present an example use of our system based on results from pilot studies that demonstrates interaction with the platform, and potential benefits and limitations of the tools in promoting the associated skills

Kaleidoscope JEIRP on Learning Patterns for the Design and Deployment of Mathematical Games: Final Report

Project deliverable (D40.05.01-F)Over the last few years have witnessed a growing recognition of the educational potential of computer games. However, it is generally agreed that the process of designing and deploying TEL resources generally and games for mathematical learning specifically is a difficult task. The Kaleidoscope project, "Learning patterns for the design and deployment of mathematical games", aims to investigate this problem. We work from the premise that designing and deploying games for mathematical learning requires the assimilation and integration of deep knowledge from diverse domains of expertise including mathematics, games development, software engineering, learning and teaching. We promote the use of a design patterns approach to address this problem. This deliverable reports on the project by presenting both a connected account of the prior deliverables and also a detailed description of the methodology involved in producing those deliverables. In terms of conducting the future work which this report envisages, the setting out of our methodology is seen by us as very significant. The central deliverable includes reference to a large set of learning patterns for use by educators, researchers, practitioners, designers and software developers when designing and deploying TEL-based mathematical games. Our pattern language is suggested as an enabling tool for good practice, by facilitating pattern-specific communication and knowledge sharing between participants. We provide a set of trails as a "way-in" to using the learning pattern language. We report in this methodology how the project has enabled the synergistic collaboration of what started out as two distinct strands: design and deployment, even to the extent that it is now difficult to identify those strands within the processes and deliverables of the project. The tools and outcomes from the project can be found at: http://lp.noe-kaleidoscope.org

Activity Plan Template: A Mediating Tool for Supporting Learning Design with Robotics

Although Robotics have been designed for education for several decades now, only recently they started being broadly used in education, formal and non formal. In this context many different technologies have emerged accompanied by relevant learning material and resources. Our observation is that the vast number of learning activities is driven by multiple “personal pedagogies” and thus it results in the fragmentation of the domain. To address this problem we discuss in the paper the construct of “activity plan template”, a generic design tool that will facilitate different stakeholders (teachers, instructors, researchers) to design learning activities for different robotic toolkits. In the paper we discuss the characteristics of the activity plan template and the research process of generating such a template. Since we report work in progress, we present here the first version of the activity plan template, the construction of which is based on a set of best practices identified