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Interactive exercising is one of the major ingredients of technology-enhanced learning. It reaches its full potential only, when appropriate feedback is given to the learner. This paper describes a prin-cipled approach for representing and processing interactive exercises in ActiveMath. This approach relies (1) on a modular architecture of the exercise… (More)

Although it may seem that mathematics education material does not need any enculturation, the opposite is true. We report the results of a case study in several European countries and describe the different dimensions in which mathematics educational material has to be adapted to the cultural context of the learner. We describe the knowledge representation… (More)

ActiveMath is an open web-based learning environment for mathematics. It dynamically generates interactive mathematical courses adapted to the student's goals, preferences, capabilities, and knowledge. The content authored for ActiveMath is represented in an extended OMDoc which in turn is an extension of the OpenMath xml-language. ActiveMath is the first… (More)

We investigate whether erroneous examples in the domain of fractions can help students learn from common errors of other students presented in a computer-based system. Presenting the errors of others could spare students the embarrassment and demotivation of confronting their own errors. We conducted lab and school studies with students of different grade… (More)

In this work, we investigate the effect of presenting students with common errors of other students and explore whether such erroneous examples can help students learn without the embarrassment and demotivation of working with one's own errors. The erroneous examples are presented to students by a technology enhanced learning (TEL) system. We discuss the… (More)

This paper reports some deficiencies of the current status of the markup for mathematical documents, OMDoc, and proposes extensions. The observations described arose from trying to represent mathematical knowledge with the goal to present it according to several well-established teaching strategies for mathematics through the learning environment… (More)