The purpose of this dissertation was to study how teachers and school leaders perceived a specific set of classroom math innovations, and how those innovations impacted instruction in relation to the Georgia Vision Project (GVP) standards and recommendations. This was a qualitative study conducted in two GVP districts. The participants in the study were five elementary teachers, two school administrators, and two district leaders. The participants were interviewed to gain an understanding of their perceptions of recent math innovations. The innovations included (a) math instruction using manipulatives (such as counting objects and puzzles) that utilize the Concrete Representational Abstract (CRA) model, which engages students to conceive from the concrete to the abstract; (b) differentiation through flexible student grouping; (c) information about how different subgroups of students learn mathematics; and (d) math professional learning. Previous research had focused on these innovations separately. However, no research study had grouped these innovations together to see how teachers perceived them within the context of a math classroom, and how teachers implemented them in their classrooms in order to increase student achievement. This qualitative case study included schoolteacher and educational leader interviews, observations, and artifacts. The two districts in the study were high performing in the area of mathematics. The results indicated that schoolteachers and educational leaders could not directly relate the math innovations to student success and, moreover, to the GVP standards and recommendations. During the study all GVP standards were analyzed at varying levels. The study primarily focused on the teaching and learning standard, which was a significant initiative for both districts. Both districts had varying levels of implementation concerning the innovations in the study: (a) use of manipulatives, (b) differentiation in classrooms, and (c) professional learning. All participants referenced the innovations as a part of their instruction, but could not directly relate the innovations beneficial to the success of the students.