Comparing common mathematical errors to correct examples may facilitate learning, even for students with limited prior domain knowledge. We examined whether studying incorrect and correct examples was more effective than studying two correct examples across prior knowledge levels. Fourth- and fifth-grade students (N = 74) learned about decimal…

It is widely documented that the density property of rational numbers is challenging for students. The framework theory approach to conceptual change places this observation in the more general frame of problems faced by learners in the transition from natural to rational numbers. As students enrich, but do not restructure, their natural number…

This study examined whether cooperative learning and feedback facilitate situated, example-based e-learning in the field of statistics. The factors "social context" (individual vs. cooperative) and "feedback intervention" (available vs. not available) were varied; participants were 137 university students. Results showed that…

In this study, we use children's prior knowledge to support their development of cardinality understanding, based on Bermejo's (1996) model of cardinality understanding and on the distinction between cardinality (the number of items in a set is represented by a number-word) and the cardinality principle (the last number-word used in counting…

In the present article, we argue that the conceptual change approach to learning can apply in the case of mathematics, taking into consideration the particular nature of mathematical knowledge and the neurobiological bases of mathematical cognition. In the empirical study that is reported in this article, we investigated ninth graders'…