To achieve adaptive learning, a dynamic assessment system equipped with a cognitive diagnosis was developed for this study, which adopts a three-stage model of diagnosis-intervention-assessment. To examine how this system influenced spatial geometry learning, the study used a quasi-experimental method to investigate student learning outcomes…

The aim of this study is to examine how middle school mathematics teachers diagnose and attempt to eliminate students' misconceptions in algebra. The study employed a case study method and embedded single-case design. The research was conducted with three mathematics teachers working in different state schools and having different professional…

This study compared students' learning in troubleshooting and problem solving activities. The troubleshooting activities provided students with solutions to conceptual problems in the form of refutation texts; namely, solutions that portray common misconceptions, refute them, and then present the accepted scientific ideas. They required students…

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…

This study examines the mediating role of homework in the daily practice of a middle-school mathematics teacher and her colleagues in Shanghai. It aims to explore how a system of homework activities mediates and engenders a cultural pedagogy characterized by transforming errors into resources for teaching and learning. The transformation itself…

The handling of mistakes in the mathematics classroom is an area in which only little research is done so far. In mathematics education there are, in fact, several investigations about students' mistakes from a diagnostic perspective, but hardly any studies on the question how teachers react in concrete mathematics lessons. In this article…