ActiveMath is a complex web-based adaptive learning environment with a number of components and interactive learning tools. The basis for handling semantics of learning content is provided by its semantic (mathematics) content markup, which is additionally annotated with educational metadata. Several components, tools and external services can make use of that content markup, eg, a course generator, a semantic search engine and user input evaluation services. The components and services have to communicate, pass content and state changes, actions, etc including mathematical semantics and educational markup. The novel event infrastructure supports this communication. This paper focuses on the usage of the content's semantics by selected novel components and sketches the communication. IntroductionThe broad accessibility and interaction of web resources and web services requires the reuse and interoperability of content resources and services. Our research in several ActiveMath-related projects contributes to these general goals of the Semantic Web in various ways. Some of the results are described in this paper.

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Education and learning take place in a situation that is heavily influenced by the culture. The learners’ cultural context affects cognitive processes in learning. Hence, to improve the conditions for learning, e-learning environments and their contents have to interact with the learner in a culturally appropriate way. Therefore, an e-learning system intended for cross-cultural usage has to adapt to the students’ diverse cultural background. For the enculturation of the European platform for mathematics learning, ActiveMath, a number of dimensions are adapted culturally. These are: presentation of system and learning material, terminology, selection and sequencing of learning objects, interaction, and learning scenarios. This chapter describes ActiveMath’ enculturation: computational model, computational techniques, and the empirical basis for the cultural adaptation.

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