Why is it important to have a diverse repertoire of instructional practices?

“Mathematics is a subject that allows for precise thinking, but when that precise thinking is combined with creativity, flexibility, and multiplicity of ideas, the mathematics comes alive for people. Teachers can create such mathematical excitement in classrooms, with any task, by asking students for the different ways they see and can solve tasks and by encouraging discussion of different ways of seeing problems.” (Boaler, Mathematical Mindsets, 2015, p 59)

"As teachers from multiple grades levels plan and consistently implement common routines, students will experience a more coherent and better-articulated mathematical experience. In addition, the use of common models such as number lines and Venn diagrams within the routines will improve students' ability to accurately and strategically use these models. (Barnett, Combs, McCoy, High-Yield Routines Grades K-8, p 3)