The purpose of this qualitative case study was to describe the strategies teachers chose to successfully differentiate for high achieving upper elementary mathematics students. The context of the study was mixed ability classes in international schools. The study used Vygotsky's sociocultural learning theory as a theoretical framework to investigate teachers' actions and decisions when planning and delivering instruction. The research questions that guided this study were: What strategies are teachers using to differentiate for high achieving mathematicians in mixed ability classes? Why do they choose these strategies? The use of the term high achieving is explored and defined within the context of the study and within the literature. In addition, characteristics of high achieving mathematics students are further explored. Studies have shown it is difficult to adjust instruction to challenge high achieving students in mixed ability classes. This study suggests that establishing a class environment based on sociocultural learning such as frequent teacher-student dialogue and questioning, collaborative learning, and frequent and varied formative assessment, allows for successful use of strategies to differentiate successfully for higher ability mathematics students. In addition, the study's findings highlighted that characteristics such as efficacy, enjoyment, and subject confidence were common to teachers who differentiated instruction for high achieving mathematics students in the elementary school. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]