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In2Math
Interactive basic education in mathematics and informatics
The project supports fundamental parts of undergraduate courses in mathematics and theoretical computer science for students in university classes, including calculus, logic, algebra, and statistics. Contents rely on approved materials of previous courses and lectures and are combined with interactive elements and various learning tools that are commonly used at the universities involved.
Teaching materials have been developed which optimally combine features of print media, CD-ROMs and the Internet.
For didactical reasons, interactive exercises provided by our learning systems rely on powerful back-engines such as computer algebra systems and theorem provers. Interactive components facilitate feedback for each problem solving step as well as input for updating the student model.
Based on modern pedagogic concepts, our systems dynamically generate learning materials adapted to students´ knowledge, capabilities, and preferences, thus transcending traditional, predefined learning paths. Presentations can be adapted as well, e.g. to an on-screen or printed version. Moreover, they indicate to students to what extent a specific concept should be mastered.
In addition, students can assemble their own learning materials and attach private and public notes to them. The students´ actions are monitored and diagnosed in order to facilitate dynamically generated learning and navigation suggestions. A dictionary permits searching for mathematical concepts and visualizes related learning units. It can be used as a stand-alone tool or referenced from the learning units shown in the browser.
Knowledge management relies on standardized formats for representing learning materials. These materials are segmented into semantic units that can be combined into learning documents with interactive and multimedia components.
The segmentation of the learning materials makes for reuseability of contents within different teaching contexts and scenarios. The description of the units with meta-data allows to account for didactic principles and the individual student´s knowlegde, thus combining these units into personalized learning documents. The semantic representation of mathematical objects in OpenMath/OMDoc captures the meaning of formulas. On the one hand, this permits to handle mathematical meaning, e.g. by copy&paste, and on the other hand it facilitates the interoperability of different mathematical services on those formulas. In addition, XML-formatting of data and meta-data facilitates exchange between web-based systems.
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