This case study describes how reflection-on-self-efficacy-to-learn-mathematics training combined with skill training enhanced junior-high students’ performance in geometry. Skill training was based on geometric constructions using traditional as well as computational tools. To raise students’ interest, three simple and beautiful theorems presenting the preservation principle were introduced to the students: the Steiner’s theorem for the trapezoid, the Napoleon’s theorem for triangle and the Van Aubel’s theorem for quadrilaterals. These theorems were not part of the regular curriculum. The study participants were eighth graders from a junior-high school in northern Israel  The study was designed to develop a rich perception of the factors that constructed the students’ self-efficacy, self-regulation, the instruction-learning-assessment culture and progress, by describing and analyzing them qualitatively. Research tools were: students’ reflection tasks  non-participant classroom observations  teacher reflection and field notes and a structured feedback questionnaire. The data were analyzed using constant comparative analysis and grounded theory techniques. The analysis produced a refined list of categories that were developed into conceptual abstractions. Qualitative validity of data gathering was found by triangulation. Inter-rater agreement was 86%. The means of the students’ answers in the structured questionnaire were calculated and explained. Results show that these students made outstanding progress, which is rare in the current school system. The theoretical contribution of this study is the successful combination of reflection-on-self-efficacy-to-learn-mathematics training and skill training to empower geometry learning. Enhanced self-efficacy reinforced skill acquisition, which in turn contributed to higher efficacy beliefs and vice-versa.

self-efficacy, reflection, skill training, self-regulation, problem solving, high order thinking, creativity, collaboration, performance task.