The process of actively building a model for a randomization test – insights into learners’ modeling activities based on a case study

ABSTRACT

Inferential reasoning is an integral part of science and civic society, but research shows that it is a problematic domain for many people. One possibility for a more accessible approach to inferential reasoning is to use randomization tests via computer simulations. A case study was conducted with primary preservice teachers after they had passed a course module that introduced inferential reasoning with randomization tests. The study examines how three pairs of primary preservice teachers construct models in a randomization test task with both hands-on and computer-supported components. Our findings suggest that there is a common sequence in the model building process: planning, modeling the random assignment, setting sample size and replacement, and running the simulation. Our findings show in depth how TinkerPlots can be a supportive and constraining medium in the modeling process, building on experiences with physical simulations of a randomization test. These insights can be used for redesigning technology-supported learning trajectories for randomization tests. Together with other case studies our findings provide a good sense of university students’ modeling processes.

KEYWORDS:

• Inferential reasoning
• randomization tests
• simulation and modeling
• digital tools for learning
• preservice teacher education
• statistics education

Acknowledgments

We thank the anonymous reviewers and the editors of the special issue in Mathematical Thinking and Learning for their very detailed and helpful comments on earlier versions of this manuscript. Further thanks go to Tim Erickson for valuable comments and suggestions on an earlier version of the paper and for providing suggestions for language improvements.

Additional information

Notes on contributors

Susanne Podworny

Susanne Podworny, PhD, works at Paderborn University, Germany, as a senior researcher and teacher educator in mathematics education. Her main research interest is teaching and learning statistics and probability with technology.

Rolf Biehleris Professsor of Mathematics Education at Paderborn University, Germany. His research interests include teaching and learning probability and statistics with technology, professional development of mathematics teachers and tertiary mathematics education.