ACTIVEMATH is a Web-based learning environment for mathematics. In this article, we discuss ACTIVEMATH from a service and semantics perspective. We describe the service-oriented technologies of ACTIVEMATH and how the services interplay with the domain semantics (mathematics) and the pedagogical semantics used, e. g., for course generation. More specifically, we provide details on the knowledge representation for mathematics we use in ACTIVEMATH and how it is used to represent learning materials. We also elaborate on the representation of learning objects from a pedagogical point-of-view, that is, how we capture the instructional semantics. We then show how learning goals are represented and how a course generator assembles sequences of learning objects to fulfil these goals. Some tools in ACTIVEMATH are client-based and require different techniques. We use our assembly tool as an example to illustrate how ACTIVEMATH integrates client-based tools.
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