This study explores the self-efficacy and problem-solving skills of middle school mathematics students. The students -- 111 9th graders who were studying a unit for the analysis of function -- were given mathematics instruction that was based on either dynamic or static visualization. Findings revealed a positive impact of instruction that was based on dynamic visualization that involved the use of the technological GeoGebra application, compared to instruction that was based on static visualization. The students who were exposed to dynamic visualization instruction displayed high levels of mathematics self-efficacy in real time. Improvement in the mathematics problem-solving skills of these students was shown both immediately after the intervention and three months later, demonstrating better conceptual and procedural understanding. The findings imply that exposure to instruction-based dynamic visualization contributed to closing both the affective and cognitive gaps between high and low achievers. The study offers a significant contribution to theoretical and methodological aspects, and provides practical understanding of instruction-based dynamic visualization about performance of mathematics students in both the affective and cognitive domains.