To achieve the goal of mathematical proficiency for all, many components of U.S. school mathematics must be changed. In particular, instruction, instructional materials, assessments, teacher education and professional development, and the broader educational system must work together to ensure that all students become engaged with mathematics throughout their elementary and middle school years. The following sections address each of these five areas of needed change.
Whether students will become proficient in mathematics depends in large part on the instruction they receive. Teaching that builds proficiency can take many forms; although there is no best way to teach, not all ways of teaching are equally effective. The key question to ask about any instance of instruction is: Does it provide opportunities for students to develop all five strands of mathematical proficiency?12
Teaching for proficiency requires thoughtful planning, careful execution, and continual improvement of instruction. Lessons need to be designed with specific mathematical learning goals in mind. Teachers must ask: How will this lesson help students develop and integrate the strands of proficiency? How will students’ learning in this lesson build on past lessons and set the stage for later lessons? What knowledge do students bring with them to this lesson, and how are they likely to respond to the mathematical tasks it contains? What materials and activities can help students achieve the goals for the lesson?