NCTM Standards: Building the Foundations for Reform, 1989-2009
In 1989, NCTM’s Curriculum and Evaluation Standards for School Mathematics recommended that we teach and assess students in very nontraditional ways. It called for a shift in curriculum, moving towards less attention to procedural manipulation without understanding and more towards a focus on conceptual understanding and connecting mathematics across its content areas and to other disciplines. Noting that mathematics education needs to continually address societal needs, it listed content currently taught that should be deleted, along with others to be added, such as probability, statistics, and technology. In addition to curriculum reform, NCTM published other major documents that called for major shifts in learning, teaching, and assessment.
The NCTM’s Professional Standards for Teaching Mathematics document (1991) recommended principles for the professional development of mathematics teachers and for the evaluation of mathematics teaching. It provided guidelines for helping teachers create a rich mathematical environment in which students are engaged in challenging mathematics to make them mathematically powerful. Students with such power can demonstrate the application of the standards by their ability to explore, conjecture, reason logically, and successfully apply a number of different strategies to solve nonroutine problems.
Assessment Standards (1995) addressed the principles to build assessments that support the development of mathematical power for all students. It recommended that teachers derive information from multiple sources during instruction and that, in addition to pencil-and-paper tests, evidence to support student learning be collected from sources that included close observation, one-on-one discussions, projects, homework, and classroom discourse. A key difference in the document from traditional methods is in the use of assessment tools as a process for stimulating growth and interest in mathematics rather than as a way for separating and ranking students.
Principles and Standards for School Mathematics (2000) integrated and updated the recommendations from the other documents on curriculum, teaching, and assessment into one document. It consists of six principles, five processes, and ten standards that describe the characteristics of quality instructional programs and goals for students’ mathematical knowledge. The six principles address the question: What are the characteristics of mathematics instructional programs that will provide all students with high-quality mathematics education experiences across the grades? Its principles—based on equity, curriculum, teaching, learning, assessment, and technology—were revised in 2014, and details are provided later in this chapter. The ten standards address the question: What mathematical content and processes should students know and be able to do as they progress through school? Of the ten, five are mathematical content standards that describe what students should know and be able to do within the areas of number and operations, algebra, geometry, measurement, data analysis, probability, and statistics. Five process standards address students’ acquisition, growth in, and use of mathematical knowledge in the areas of problem solving, reasoning, connections, communication, and representation. Together, the Principles and Standards form the basis for developing effective mathematics instruction within four grade-band chapters: Prekindergarten through grade 2, grades 3-5, grades 6-8, and grades 9-12.