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While the report focuses on curriculum and learning, some of the discussion relates to instruction and to issues of professional development. A key message is that the report endorses no single instructional approach but contends that “instruction needs to configure the relations among teachers, students, and mathematics in ways that promote the development of mathematical proficiency. Under this view, significant instructional time is devoted to developing concepts and methods; carefully directed practice, with feedback, supports learning. Discussions build students' thinking, attend to relationships between problems and solutions and to the nature of justification and mathematical argument as the strands of proficiency grow in a coordinated, interactive fashion” (p. 11).

Finally, explaining why so much of the report focuses on the domain of number, it notes that “most of the controversy over how and what mathematics should be taught in elementary and middle school revolves around number” (p. 20), including questions such as the following:

  • Should children learn computational methods before they understand the concepts involved?

  • Should they be introduced to standard algorithms for arithmetic computation, or should they be encouraged to develop their own algorithms first?

  • How proficient do children need to be at paper-and-pencil arithmetic before they are taught algebra and geometry?

Thoughtful discussion about these and similar controversial questions is provided in this report, which considers the mathematical knowledge children bring to school and how students develop proficiency with numbers and in other mathematical areas. The report also discusses teaching for mathematical proficiency, describes instruction as “interactions among teachers and students around content” (p. 313), and outlines what it takes to be proficient at mathematics teaching.

Adding It Up emphasizes two points:

  • “Our experiences, discussions, and review of the literature have convinced us that school mathematics demands substantial change” (p. 407); and

  • “…[T]hroughout the grades from pre-K through 8 all students can and should be mathematically proficient” (p. 409).

Adding It Up comes to the following conclusion:

School mathematics in the United States does not now enable most students to develop the strands of mathematical proficiency in a sound fashion. Proficiency for all demands fundamental changes be made concurrently in curriculum,



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