Empirical arguments rely on examples without necessarily addressing all cases. Students should be skeptical of empirical evidence and should seek more secure arguments for generalizations, such as those that explain why a generalization is true for all cases. Generalizing on the basis of patterns in data is an important mathematical practice;…

Thus far, it is unclear how students can learn most effectively from their own errors. In this study, reflections on the rationale behind self-made errors are assumed to enhance knowledge acquisition. In a field experiment with pre/post/follow-up design, the authors practiced fractions with 174 seventh- and eighth-grade students who were randomly…

In recent years, an increasing number of analyses in Learning Analytics and Educational Data Mining (EDM) have adopted a "Discovery with Models" approach, where an existing model is used as a key component in a new EDM/analytics analysis. This article presents a theoretical discussion on the emergence of discovery with models, its…

Although teachers in principle are prepared to make use of science centers, such excursions often fail to facilitate learning processes. Therefore, it is necessary to improve the link between science centers and schools. The design and evaluation of valuable outreach projects may enhance students' out-of-school science learning. In our study, we…

The authors used the 5E learning cycle (engage, explore, explain, extend, and evaluate) and a pulmonary carbon dioxide mystery to introduce eighth grade students to the study of chemistry. The activity engages students in measurement, data collection, data analysis, media and internet research, research design, and report writing as they search…

This document contains the second volume of the proceedings of the 30th Annual Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 60 research reports by presenters with last names beginning between Abr…