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An augmented reality (AR) system is a technology which combines computer-generated representations or information and reality in real-time. Instead of substituting the real situation, as it is possible with dynamic geometry systems (DGS), AR adds virtual objects or information to reality to make the situation experiential. The project MalAR aims at investigating the impact of an augmented reality (AR) learning environment in the subject area of analytic geometry. The focus of the AR learning environment is an AR-App, which supports learners understanding of mathematics situations usually given through textbook tasks. Mathematics situations are implemented in an AR-App such that the situation gets visually and enactively explorable by changing perspectives using the own body movement. The added value of integrating AR in mathematics classes is worked out and based on different learning theories like embodied cognition. The AR-App and first results of the pilot study will be demonstrated and presented. With the findings and results of the study evidence-based didactical insights in the teaching and learning with AR in mathematics instruction may be identified and needs for future AR-supported learning scenarios can be revealed.

It remains a challenge for teachers to integrate modeling tasks in everyday mathematics classes. Many studies have been conducted that show the difficulties faced by teachers.  One of the challenging aspects in this regard is that of assessment. In the present study, a connection between structures of learners’ solution strategies and cognitive considerations is established to develop a practice-oriented instrument to determine and assess the complexity of solution strategies of modeling tasks. In this paper, the selected learners’ strategies’ structure was analyzed in-depth to identify the underlying cognitive structure. The results show that thought operations carried out in parallel complicated a solution strategy.  However, the results also support a purely sequential thought operation approach without weighting parallel thought operations, which corresponds to an intuitive assessment procedure by mathematics teachers. As assessment is a great challenge for many teachers in the context of modeling tasks, this study provides a promising frame of reference for further research in this important domain of assessment and modeling.