Dynamic geometry constructions are commonly embedded into hypertext documents to create interactive exercises. In practice, this approach often constrains the possibilities of creating complex learning environments due to technical limitations. A Java-based framework for the development of interactive learning environments based on exploration laboratories containing dynamic geometry applets is presented. Dynamic geometry software (DGS) applets of different types can be integrated into the same laboratory and interact with each other. Within our framework, interactive exercises based on DGS constructions can be enriched with automated and semiautomated assessment algorithms. Students' learning processes can be recorded using capture-and-replay software. Two sample learning environments based on the framework are presented.
Combinatorial optimization is a substantial pool for teaching authentic mathematics. Studying topics in combinatorial optimization practice different mathematical skills, and because of this have been integrated into the new Berlin curriculum for secondary schools. In addition, teachers are encouraged to use adequate teaching software. The presented software package "Visage" is a visualization tool for graph algorithms. Using the intuitive user interface of an interactive geometry system (Cinderella), graphs and networks can be drawn very easily and different textbook algorithms can be visualized on the graphs. An authoring tool for interactive worksheets and the usage of the build-in programming interface offer new ways for teaching graphs and algorithms in a classroom.
During a one-year-subproject, student teachers develop and pilot learning scenarios and materials in mathematics classrooms for third and fourth graders fostering 'Computational Thinking'. To evaluate these interventions regarding the impact on the student teachers as well as the schoolchildren 'impact models' are used. These models based on program impact theory will be continuously refined to converge to a 'proof of the success' of the project.
In Lernumgebungen zum entdeckenden Mathematiklernen spielen die Werkzeuge, anhand derer die Untersuchungen durchgeführt werden, eine sehr wichtige Rolle. Eine mögliche Werkzeuggruppe für Entdeckungen in verschiedenen Kontexten der Arithmetik und der Geometrie sind altersgerechte Programmierumgebungen wie z. B. Scratch oder die Nutzung von Bildungs- bzw. Lern-Robotern wie Bee Bots, mBots, Lego Mindstorms und anderen. Direkt steuerbare Roboter können in verschiedenen Szenarien eingesetzt werden: In der „Unplugged-Phase“ können sie beim Einstieg in das Programmieren beim Aufbau erster Vorstellungen zu den notwendigen Bewegungsschritten und einem passenden Programmcode unterstützen. Weiter lassen sich die Roboter auch bei arithmetischen Entdeckungen im Hunderterfeld nutzen. The available tools in learning environments for inquiry-based learning of mathematics play a very important role. An interesting category constitute coding environments for children like Scratch or educational robots like Bee Bots, mBots, Lego Mindstorms and others are appropriate tools to explore topics in arithmetic or geometry. Directly controllable robots can be used in different scenarios: In an unplugged phase with programming beginners, they can support the mental models needed for the movements and the control codes. Further, these robots can support arithmetical explorations in the hundreds chart.
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