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Conceptual Graphs and Storyboarding for Problem Solving Strategies in Mathematics

Abstract

The major challenge for eLearning courses on undergraduate mathematics is the broadness of the audience they are targeted at. Our proposal how to deal with this challenge is to deploy intelligent assistants using Bayesian learning which, given some initial knowledge on the audience, explore user behavior to build up a model of the learner within the system. This allows us to leave the choice of the most suitable learning material to the learner. Thus, it enables an adaption of the system to individual learning styles while avoiding the risk of overwhelming the user by the plethora of choices of available material.

Starting with models for learner and course, we present a prototypical implementation of such a system within the virtual laboratory V IDEO E ASEL developed at the TU Berlin.

1. Introduction

Scientists’ and engineers’ workplaces are about to change: numerical software and computer algebra systems remove the burden of routine calculation, but demand the ability to familiarize yourself with new concepts and methods quickly. Traditional “learning on supply” might be able to provide some basic knowledge, but this learning model becomes more and more unable to deal with the rapid growth of knowledge in today’s sciences. Instead, learning and teaching methods have to be established that drive learners towards efficient self-controlled learning. New Media and New Technologies present a turning point in the educational system since they provide the basis to support the necessary chances.1

In our understanding, mathematics is the most attractive field for developing and deploying this New Technology:2 first of all, it is the key technology of the 21st century. Studies in engineering sciences, physics, computer science and many other fields depend on a well-funded mathematical education. Teaching mathematics then, however, means that diverse backgrounds and varying interests of the audience have to be taken into account. Traditionally, the choice of the proper learning material for a course is to the lecturer and the teaching staff, but the broader the audience gets the harder it becomes to select exercises that are not only suitable for all students but also still within their field of interest. Our proposed solution for this apparent conflict is to leave the choice of the learning material to the student: an intelligent agent system aids her/him finding the right decision by providing exercises that proved best for previous generations of students.

To make this technology applicable, the learning material must be well-structured — as for example to ensure that all prerequisites to master an exercise are given. Luckily, mathematics as a scientific field already provides a perfectly worked-out internal structure we can exploit here. It is

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Jeschke, M., & Jeschke, S., & Pfeiffer, O., & Reinhard, R., & Richter, T. (2006, June), Conceptual Graphs And Storyboarding For Problem Solving Strategies In Mathematics Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. 10.18260/1-2--773