This randomized controlled trial examined a fraction intervention enhanced with worked examples (presolved problems) to develop verbal conceptual explanations in grade 5 students with mathematics difficulties. Students analyzed worked examples depicting correct and incorrect solutions-both individually and in pairs for comparison-to explain key fraction concepts and common misconceptions. Ninety-nine students were randomly assigned to the intervention (n = 48) or a business-as-usual comparison group (n = 51). The intervention consisted of 36 lessons delivered over 12 weeks. Results favored intervention students significantly on fractions proficiency (g = 0.39-1.11) and both verbal and written explanations (g = 0.89-1.11). Findings suggest that incorporating worked examples to develop students' verbal explanations is effective when embedded in multicomponent fractions interventions for students with mathematics difficulties.
The factors that influence the construction of a teacher’s sense of self-efficacy are complex. The authors used a qualitative research design to explore the reflections of a sample of 25 K-12 early career teachers as they made sense of their own abilities. The results show that theorized sources of self-efficacy—mastery experiences, vicarious experiences, and verbal persuasion—all remain important but are interpreted through each participant’s unique background and conception of identity. Teacher Self-Efficacy emerged as a construct that both influenced and was influenced by this collection of individual factors. This study provides insight into how each teacher’s unique experiences interact dynamically with school environments and personal stories to shape their sense of self-efficacy. The findings can influence how new teachers are supported by coaches and teacher educators to build the confidence and motivation necessary to persist through the challenges of teaching.
