Mathematical Proficiency for All Students: Toward a Strategic Research and Development Program in Mathematics Education

By Deborah Loewenberg Ball | Go to book overview

Chapter Three
TEACHING AND LEARNING MATHEMATICAL PRACTICES

Because expertise in mathematics, like expertise in any field, involves more than just possessing certain kinds of knowledge, we recommend that the second strand of the proposed research and development program focus explicitly on mathematical know-how—what successful mathematicians and mathematics users do. We refer to the things that they do as mathematical practices. Being able to justify mathematical claims, use symbolic notation efficiently, and make mathematical generalizations are examples of mathematical practices. Such practices are important in both learning and doing mathematics, and the lack of them can hamper the development of mathematics proficiency.

Our rationale for this focus is grounded in our fundamental concerns for mathematical proficiency and its equitable attainment. While some students develop mathematical knowledge and skill, many do not, and those who do acquire mathematical knowledge are often unable to use that knowledge proficiently.1Further, debates over the improvement of students’ mathematics achievement are often intertwined with questions about what we mean by “proficiency.” The work related to mathematical practices that the RAND Mathematics Study Panel proposes should contribute to a better understanding of proficiency and hence to greater clarity and consensus about goals for the improvement of mathematical education.

It is important to note that this focus is the most speculative of the three we propose in this report. After much deliberation, we chose it because we hypothesize that a focus on understanding these practices and how they are learned could greatly enhance our capacity to create significant gains in student achievement, especially among currently low-achieving students who may have had fewer opportunities to develop these practices. Our belief that this focus would contribute to greater precision about what is meant by mathematical proficiency reinforced our decision to make it a priority.

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1
1Boaler, 2002, and Whitehead, 1962.

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