• Summary
  • Contents
  • Subject index

The Standards for Mathematical Practice, according to the CCSS document describe the mathematical “habits of mind” that teachers, at all levels, should develop in their students, and without which the content standards cannot be successfully implemented. Attention to the Mathematical Practices connected with content must be enacted in teaching, which will require professional development. Though the CCSS Mathematical Content Standards differ in detail from other content standards, their form is familiar to teachers: a list of things to know. The Mathematical Practices are not so easily condensed into a lesson or unit, not so easily tested and, generally, not so familiar. Content standards are specified grade by grade and build on each other rather than repeating year after year. The Mathematical Practices are different. Though they can be enacted in an appropriate way at any level, they evolve and mature over years rather than days, along with children's cognitive development and the nature and sophistication of the Mathematical Content. It can be expected that the developers of the CCSS, and the states that collaborated in calling for the development of the CCSS, will work with the developers of assessments to ensure that the Mathematical Practices are taken seriously in testing. Hull, Miles, and Balka are writing this book as PD resource to help school and math leaders grapple with the changes that must be addressed, in order to move their teachers toward implementation of the practices required by the CCSS.

Introduction
Introduction

There is one predominant theme that is carefully threaded throughout this book: the CCSS for Mathematical Practice. When the K–12 standards development teams established the common mathematics content, they also created a list of standards for mathematical practice. These eight practices are based on research and delineate how students should learn mathematics with meaning. While common mathematics content across state borders is a remarkable achievement with tremendous possibilities, the mathematical practice standards provide the real potential for changing mathematics teaching and learning. These standards are:

  • Make sense of problems and persevere in solving them
  • Reason abstractly and quantitatively
  • Construct viable arguments and critique the reasoning of others
  • Model with mathematics
  • Use appropriate tools strategically
  • Attend to precision
  • Look for and make use of structure
  • Look for and express regularity in repeated reasoning

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