Astrid Wichmann

Computational Modelling and Simulation Fostering New Approaches in Learning Probability

Discovery learning in mathematics in the domain of probability based on hands‐on experiments is normally limited because of the difficulty in providing sufficient materials and data volume in terms of repetitions of the experiments. Our cooperative, computational modelling and simulation environment engages students and teachers in composing and simulating stochastic experiments, e.g. throwing dice or drawing balls, playing lottery games. It also facilitates validation and presentation. Engaging teachers in the design process led to the complementary development and evaluation of several learning activities in German secondary schools. Evaluating the results of our action research work indicated the potential of our approach for expanding traditional mathematics instruction when assisting students to develop a sustainable conceptual basis of probability principles, offering them a higher degree of responsibility for their learning.

Group Formation for Small-Group Learning: Are Heterogeneous Groups More Productive?

There is an underexploited potential in enhancing massive online learning courses through small-group learning activities. Size and diversity allow for optimizing group composition in small-group tasks. The purpose of this paper was to investigate how groups formed based on learner behavior affect productivity of students in a small-group task. Students classified as high, average and low were randomly assigned to homogeneous or heterogeneous groups. Results indicate that overall, heterogeneous groups were either similarly or a bit more productive than homogeneous groups. Yet, we found that homogeneous groups classified as high-level were as or more than heterogeneous groups. However, heterogeneous groups were still more productive than homogeneous-average and homogeneous-low groups suggesting heterogeneous groups are the best choice for the entire community. Students classified as low-level were more productive in homogeneous groups, suggesting that grouping less active students together, makes social loafing more difficult and students participate more.