Towards a narrative-oriented framework for designing mathematical learning

This paper proposes a narrative-oriented approach to the design of educational activities, as well as a CSCL system to support them, in the context of learning mathematics. Both Mathematics and interface design seem unrelated to narrative. Mathematical language, as we know it, is devoid of time and person. Computer interfaces are static and non-linear. Yet, as Bruner (1986; 1990) and others show, narrative is a powerful cognitive and epistemological tool. The questions we wish to explore are - - If, and how, can mathematical meaning be expressed in narrative forms - without compromising rigour? - What are the narrative aspects of user interface? How can interface design be guided by notions of narrative? - How can we harness the power of narrative in teaching mathematics, in a CSCL environment? We begin by giving a brief account of the use of narrative in educational theory. We will describe the environment and tools used by the WebLabs project, and report on one of our experiments. We will then describe our narrative-oriented framework, by using it to analyze both the environment and the experiment described

Cooperative WebLab in chemical engineering between France and Brazil: Validation of the methodology

A WebLab is an experiment operated remotely via Internet. Besides the strictly technical aspects of such an experiment, which may contribute to the learning of Chemical Engineering fundamentals, there is also important feedback when teams of students of two different countries are working together: the WebLab becomes an intercultural experience, enhancing the communication skills of the students. A WebLab between Universidade Federal de São Carlos (DEQ/UFSCar) and the Ecole Nationale Supérieure d’Ingénieurs en Arts Chimiques et Technologiques (ENSIACET) is presented in this work. A mass transfer experiment in a bench scale reactor (stirred and aerated) had to be studied by mixed teams, thus emulating challenges that will be common in future working environments. In order to perform the experiment, students in Brazil and in France were put into groups. The students had to make decisions about the procedure for executing the experiments. All the students were able to control the equipment, no matter where they were physically. Students communicated using video conference software. The students' and teachers' opinions of this experience were very positive. This methodology is an important contribution to the education of engineers in a world integrated by modern communication technologies

Sustaining interaction in a mathematical community of practice

This paper focuses on an activity in which students explore sequences through a game, using ToonTalk programming and a web-based collaboration system. Our analytical framework combines theory of communities of practice with domain epistemology. We note three factors which influence the length and quality of interactions: facilitation, reciprocation and audience-awareness

Exploring the mathematics of motion through construction and collaboration

In this paper we give a detailed account of the design principles and construction of activities designed for learning about the relationships between position, velocity and acceleration, and corresponding kinematics graphs. Our approach is model-based, that is, it focuses attention on the idea that students constructed their own models – in the form of programs – to formalise and thus extend their existing knowledge. In these activities, students controlled the movement of objects in a programming environment, recording the motion data and plotting corresponding position-time and velocity-time graphs. They shared their findings on a specially-designed web-based collaboration system, and posted cross-site challenges to which others could react. We present learning episodes that provide evidence of students making discoveries about the relationships between different representations of motion. We conjecture that these discoveries arose from their activity in building models of motion and their participation in classroom and online communities

WebLabs: Virtual collaborative learning experience for researchers, teachers and students

The paper presents experiences from a 3 year international project, WebLabs: New representational infrastructure for e-learning, in which researchers, teachers and young students from UK, Bulgaria, Cyprus, Sweden, Portugal and Italy participated. The project explored innovative pedagogy based on the integration of constructionist learning approach and virtual co-learning. For the purposes of the project a visual programming environment, Toon Talk, and a virtual collaborative system, Wplone, were adopted, and special instruments - webreports - were designed and developed. The experience proved that mathematical and science concepts, usually considered as difficult and unattainable for young children, can be made accessible and meaningful to them, by using different representations as well as group co-learning and reflection

weSPOT: A personal and social approach to inquiry-based learning

weSPOT is a new European initiative proposing a novel approach for personal and social inquiry-based learning in secondary and higher education. weSPOT aims at enabling students to create their mash-ups out of cloud based tools and services in order to perform scientific investigations. Students will also be able to share their inquiry accomplishments in social networks and receive feedback from the learning environment and their peers. This paper presents the research framework of the weSPOT project, as well as the initial inquiry-based learning scenarios that will be piloted by the project in real-life educational settings

Designing a programming-based approach for modelling scientific phenomena

We describe an iteratively designed sequence of activities involving the modelling of 1- dimensional collisions between moving objects based on programming in ToonTalk. Students aged 13-14 in two settings (London and Cyprus) investigated a number of collision situations, classified into six classes based on the relative velocities and masses of the colliding objects. We describe iterations of the system in which students engaged in a repeating cycle of activity for each collision class: prediction of object behaviour from given collision conditions, observation of a relevant video clip, building a model to represent the phenomena, testing, validating and refining their model, and publishing it – together with comments – on our web-based collaboration system, WebReports. Students were encouraged to consider the limitations of their current model, with the aim that they would eventually appreciate the benefit of constructing a general model that would work for all collision classes, rather than a different model for each class. We describe how our intention to engage students with the underlying concepts of conservation, closed systems and system states was instantiated in the activity design, and how the modelling activities afforded an alternative representational framework to traditional algebraic description

Dealing with abstraction: Case study generalisation as a method for eliciting design patterns

Developing a pattern language is a non-trivial problem. A critical requirement is a method to support pattern writers with abstraction, so as they can produce generalised patterns. In this paper, we address this issue by developing a structured process of generalisation. It is important that this process is initiated through engaging participants in identifying initial patterns, i.e. directly dealing with the 'cold-start' problem. We have found that short case study descriptions provide a productive 'way into' the process for participants. We reflect on a 1-year interdisciplinary pan-European research project involving the development of almost 30 cases and over 150 patterns. We provide example cases, detailing the process by which their associated patterns emerged. This was based on a foundation for generalisation from cases with common attributes. We discuss the merits of this approach and its implications for pattern development

Next steps in implementing Kaput's research programme

We explore some key constructs and research themes initiated by Jim Kaput, and attempt to illuminate them further with reference to our own research. These 'design principles' focus on the evolution of digital representations since the early nineties, and we attempt to take forward our collective understanding of the cognitive and cultural affordances they offer. There are two main organising ideas for the paper. The first centres around Kaput's notion of outsourcing of processing power, and explores the implications of this for mathematical learning. We argue that a key component for design is to create visible, transparent views of outsourcing, a transparency without which there may be as many pitfalls as opportunities for mathematical learning. The second organising idea is that of communication, a key notion for Kaput, and the importance of designing for communication in ways that recognise the mutual influence of tools for communication and for mathematical expression

The technological mediation of mathematics and its learning

This paper examines the extent to which mathematical knowledge, and its related pedagogy, is inextricably linked to the tools – physical, virtual, cultural – in which it is expressed. Our goal is to focus on a few exemplars of computational tools, and to describe with some illustrative examples, how mathematical meanings are shaped by their use. We begin with an appraisal of the role of digital technologies, and our rationale for focusing on them. We present four categories of digital tool-use that distinguish their differing potential to shape mathematical cognition. The four categories are: i. dynamic and graphical tools, ii. tools that outsource processing power, iii. new representational infrastructures, and iv. the implications of highbandwidth connectivity on the nature of mathematics activity. In conclusion, we draw out the implications of this analysis for mathematical epistemology and the mathematical meanings students develop. We also underline the central importance of design, both of the tools themselves and the activities in which they are embedded