Design, implementation and application of a reusable component framework for interactive mathematical eLearning sites

摘要

This thesis presents an eLearning framework that allows to interactively work and experiment with mathematics; applications using this framework therefore open an intuitive perspective on mathematics and its practical use. The thesis is mainly organised in four chapters, each of which documents a step in the development process of the framework. The first chapter discusses the technical and practical foundations of web based learning and analyses existing solutions in the field of mathematics. The second chapter then takes a look at didactical concepts that are helpful for designing the framework and presents a didactical design process. The third chapter in turn describes the implementation of a component framework which meets the requirements stated in the first two chapters, and the last chapter describes the application and evaluation of the framework in a wide range of learning scenarios. Technical Concepts and Existing Solutions Taking a look at the constraints of web based learning reveals the sharp distinction between micro (client-based) and macro (server-based) level applications that leads to the specific structure of existing technical solutions in this field of eLearning software. Additionally, it can be seen that the content of an eLearning site is strongly determined by the underlying role model. This is illustrated by the analysis of two exemplary eLearning sites, which vary not only in terms of interactivity but also by the stakeholders (student, author, tutor, etc.) they address. It is shown that an increase of interactivity and reusability may be achieved on the one hand by extending the role model and on the other hand by adding further levels of development on the micro-level. Didactical Model After discussing the differences of learning models and their relation to the concept of interactivity, we use Bruner's Theory of Representations to design a suitable content model in mathematical eLearning. This content model is complemented on the methodic level by the taxonomy of Bloom. Combined with the discussion of some aspects of learner orientation, this leads to a comprehensive didactic design process for mathematical eLearning media. The Component Framework Based on the technical and didactical requirements, the resulting implementation is described, consisting primarily of two frameworks: The MathletFactory, a framework for mathematical applets, and the TestletFactory a framework for interactive tests. While both of these offer a high amount of flexibility and reusability to students and authors, the MathletFactory additionally has a specific interface, allowing application programmers to rapidly develop new mathlets by simply adding mathematical entities to an applet and by specifying their displayed representation and update behaviour. Applications and Outlook A focus of this work is put on the evaluation of the framework in several courses and training activities, leading to further didactical insights and to substantial technical improvements of the framework. For example, in response to discovered misconceptions, further user information like the domain of mathematical expressions are added. Also, the teacher's and author's perspective on the framework is illuminated, leading to a higher degree of flexibility and reusability of the framework and eventually even to its transferability to extra-mathematical contexts. The outlook finally provides a view on possible integration paths leading towards a mathematical eLearning/-Teaching/-Research (eLTR) infrastructure as well as to an improved integration into the university's local eLearning network.