Productive failure has shown positive effects on conceptual and transfer measures, but no clear effects on procedural measures. It is therefore an open question whether, and to what extent, productive failure methods may be used to enhance the learning of procedural skills. A typical productive failure study focuses on a single, complex concept;…

The present study examines the effectiveness of incorporating worked examples with prompts for self-explanation into a middle school math textbook. Algebra 1 students (N = 75) completed an equation-solving unit with textbooks either containing the original practice problems or in which a portion of those problems were converted into a combination…

The adaptive use of strategies, that is selecting a strategy which allows an efficient solution for a given problem, can be considered as an important individual ability relevant in various domains. Based on models of subjects' skills of adaptive use of strategies, two idealized instructional approaches are suggested to foster students in their…

Drawing comparisons between students' alternative solution strategies to a single mathematics problem is a powerful yet challenging instructional practice. We examined 80 preservice teachers' when asked to design a short lesson when given a problem and two student solutions--one correct and one incorrect. These micro-teaching events were…

In two studies, we investigated the impact of instructors' different knowledge bases on the quality of their instructional explanations. In Study 1, we asked 20 mathematics teachers (with high pedagogical content knowledge, but lower content knowledge) and 15 mathematicians (with lower pedagogical content knowledge, but high content knowledge) to…

The purposes of this study were to investigate (a) the effects of volition support (VoS) on students' motivation, effort regulation, and performance as well as (b) the perceptions of students about VoS in an online mathematics course offered at a community college. VoS was developed based on the theories of and research on volition (e.g., Corno…