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This resource was developed by CSMC faculty and doctoral students with support from the National Science Foundation under Grant No. ESI-0333879. The opinions and information provided do not necessarily reflect the views of the National Science Foundation. 12-19-05

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Committees and Reports that Have Influenced the Changing Mathematics

Curriculum This set of PowerPoint slides is one of a series of resources produced by the Center for the Study of Mathematics Curriculum. These materials are provided to facilitate greater understanding of mathematics curriculum change and permission is granted for their educational use.Curriculum and Evaluation

Standards for School Mathematics

National Council of Teachers of Mathematics

Commission on Standards for School Mathematics • 1989

http://www.mathcurriculumcenter.org

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Curriculum and Evaluation Standards for School

MathematicsNational Council of Teachers of

Mathematics

Commission on Standards for School Mathematics

1989

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Prominent Issues and Forces

• Poor student performance on national and international assessments

• Too many students, including a disproportionate number from minority groups, leaving school without the mathematical proficiency necessary for productive lives

• Increasing use of quantitative methods in business, economics, linguistics, biology, medicine, and sociology

• Advances in technology and broadening of areas in which mathematics is applied resulted in growth and changes in mathematics itself

• Emerging research and changing perspectives on how students learn mathematics

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NCTM Commission on Standards for School Mathematics, est. 1986

Thomas A. Romberg, ChairmanIris M. CarlF. Joe CrosswhiteJohn A. DosseyJames D. GatesShirley M. FryeShirley A. Hill

Christian R. HirschGlenda LappanDale SeymourLynn A. SteenPaul R. TraftonNorman Webb

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1.Create a coherent vision of what it means to be mathematically literate both in a world that relies on calculators and computers to carry out mathematical procedures and in a world where mathematics is rapidly growing and is extensively being applied in diverse fields.

2.Create a set of standards to guide the revision of the school mathematics curriculum and its associated evaluation toward this vision. (NCTM, p. 1)

• To ensure quality• To indicate goals• To promote change

Purpose

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New Societal Goals for Education

• Mathematically literate workers

• Lifelong learning

• Opportunity for all

• Informed electorate

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New Goals for Students

• Learn to value mathematics

• Become confident in one’s ability to do mathematics

• Become a mathematical problem solver

• Learn to communicate mathematically

• Learn to reason mathematically

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Grades K-12 Process Standards

Standard 1: Mathematics as Problem Solving

Standard 2: Mathematics as CommunicationStandard 3: Mathematics as ReasoningStandard 4: Mathematical Connections

Across the grade bands K-4, 5-8, 9-12, each of these standards appear and increase in level of sophistication and expectation in developmentally-appropriate ways. Habits of mind are developed so that students become mathematically powerful and mathematically literate as they learn to value mathematics.

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Members of the Grades K-4 Working Group

Paul R. Trafton, Chair

Hilde HowdenMary M. LindquistEdward C. RathmellThomas E. RowanCharles S. Thompson

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The Grades K-4 Standards were premised on the assumptions that mathematics curriculum and instruction should:

• be conceptually oriented emphasizing mathematical concepts and understanding;

• actively involve students in doing mathematics by exploring and discussing mathematical ideas;

• emphasize the development of students’ thinking and reasoning abilities;

• emphasize the application of mathematics;

• include a broad range of content beyond arithmetic: measurement, geometry, statistics, probability, and algebra;

• make appropriate use of calculators and computers.

Assumptions Underlying the Grades K-4 Standards

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Grades K-4 Content Standards

Standard 5: EstimationStandard 6: Number Sense and NumerationStandard 7: Concepts of Whole Number Operations

Standard 8: Whole Number Computation

Implementation of these standards should increase attention to place-value concepts, meaning of operations, mental computation and estimation, thinking strategies for basic facts, and use of technology; and

decrease attention to complex and isolated treatment of pencil-and-paper computation, standard algorithm for division, and use of rounding to estimate.

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Grades K-4 Content Standards

Implementation of these standards should increase attention to geometric properties and relationships, spatial sense, measuring and the concepts of measurement, collecting and organizing data, recognizing and describing patterns, using variables to express relationships, engaging in real-world problems and developing problem solving strategies; and

decrease attention to naming geometric figures, memorizing unit of measurement equivalencies, and using clue words to determine operations to use in problem solving.

Standard 9: Geometry and Spatial SenseStandard 10: MeasurementStandard 11: Statistics and ProbabilityStandard 12: Fractions and DecimalsStandard 13: Patterns and Relationships

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Members of the Grades 5-8 Working Group

Glenda Lappan, ChairDaniel T. DolanJoan F. HallThomas E. KierenJudith E. MummeJames E. Schultz

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Assumptions Underlying the Grades 5-8 Standards

The Grades 5-8 Standards were premised on the assumptions that mathematics curriculum and instruction should: • focus on basic topics in algebra, geometry, probability and statistics, rather than computational skills. • be available to everyone, not simply those who have demonstrated proficiency with calculation and pencil-and-paper computation. • provide students with new problem solving opportunities that renew motivation for learning and provide context for the mathematical skills they are learning. • include allowing students to wrestle with problems that are not well- defined. • include hands-on activities in tactile, auditory, and visual instruction modes. • incorporate the cultural background and unique characteristics of each student into the learning environment.

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Grades 5-8 Content Standards

Standard 5: Number and Number RelationshipsStandard 6: Number Systems and Number TheoryStandard 7: Computation and EstimationStandard 8: Patterns and Functions

Implementation of these standards should increase attention to exploring whole numbers, integers, and rational numbers, developing number sense, identifying and using functional relationships, and creating and using tables, graphs and rules; and

decrease attention to memorizing procedures, rules and algorithms, finding exact forms of answers, and tedious paper-and-pencil computations.

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Grades 5-8 Content Standards

Implementation of these standards should increase attention to developing an understanding of variables, expressions and equations, using statistical methods to analyze and make decisions, creating experimental models, using geometry in solving problems and estimating and using measurement; and

decrease attention to manipulating symbols, memorizing procedures, formulas, facts and relationships and converting within and between measurement systems.

Standard 9: AlgebraStandard 10: StatisticsStandard 11: ProbabilityStandard 12: GeometryStandard 13: Measurement

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Members of the Grades 9-12 Working Group

Christian R. Hirsch, ChairSue Ann McGrawGerald R. RisingHarold L. SchoenCathy L. SeeleyBert K. Waits

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Assumptions Underlying the Grades 9-12 Standards

• Students entering 9th grade will bring experience with the broad integrated curriculum described in the grades K-8 standards.

• Students will not be denied access to the broad, rich curriculum proposed for high school because of lack of paper-and-pencil computational facility.

• Graphing calculators will be available for students at all times and at least one computer will be available in every classroom.

• A three-year core curriculum will be studied by all students with differentiation in terms of depth and breadth of topics.

• College-intending students will be expected to study mathematics each year of high school with calculus no longer viewed as the capstone of high school mathematics.

• All students will study appropriate mathematics during their senior year.

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Grades 9-12 Content Standards

Standard 5: AlgebraStandard 6: FunctionsStandard 7: Geometry from a Synthetic Perspective

Standard 8: Geometry from an Algebraic Perspective

Standard 9: TrigonometryImplementation of these standards should involve increased attention to technology, communication, real-world applications, mathematical modeling, multiple representations, and connections between strands; and

decreased attention to symbolic manipulation, by-hand graphing of functions, development of synthetic geometry as a complete axiomatic system, and two-column proofs.

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Grades 9-12 Content Standards

Standard 10: StatisticsStandard 11: ProbabilityStandard 12: Discrete MathematicsStandard 13: Conceptual Underpinning of Calculus

Standard 14: Mathematical StructureImplementation of these standards should involve increased opportunities to study contemporary mathematics largely influenced by the explosion of technology and to develop a deeper understanding of change and the broad underlying themes and logical consistency of mathematics; and

decreased attention to topics and skills only needed as preparation of some for calculus.

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Members of the Evaluation Working Group

Norman Webb, ChairElizabeth BadgerDiane J.BriarsThomas J. CooneyTej N. PandeyAlba G. Thompson

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Assumptions Underlying the Evaluation Standards

• Student assessment should be integral to instruction.

• Multiple means of assessment methods should be used.

• All aspects of mathematical knowledge and its connections should be assessed.

• Instruction and curriculum should be considered equally in judging the quality of a program.

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Evaluation StandardsOrganized in three sections:

General Assessment Standards: Recommends principles relevant to any form of assessment and program evaluation.Standard 1: AlignmentStandard 2: Multiple Sources of InformationStandard 3: Appropriate Assessment Methods and Uses

Student Assessment Standards: Identifies aspects of mathematical knowledge that should be assessed, as derived from the Curriculum Standards. Standard 4: Mathematical PowerStandard 5: Problem SolvingStandard 6: CommunicationStandard 7: ReasoningStandard 8: Mathematical ConceptsStandard 9: Mathematical ProceduresStandard 10: Mathematical Disposition

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Evaluation Standards

Program Evaluation Standards: Examine the assessment of the extent to which a mathematics program is consistent with the Standards.

Standard 11: Indicators for Program EvaluationStandard 12: Curriculum and Instructional ResourcesStandard 13: InstructionStandard 14: Evaluation Team

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Significance: Curriculum and Instruction

Three elementary school curriculum projects:– Everyday Mathematics (University of Chicago School Mathematics

Project)– Investigations in Number, Data, and Space (TERC)– Math Trailblazers (Teaching Integrated Mathematics and Science

Project)

Five middle school curriculum projects: – Connected Mathematics (Connected Mathematics Project)– Mathematics in Context (Wisconsin Center for Education Research)– MathScape: Seeing and Thinking Mathematically (Education Development

Center)– MATHThematics (STEM) (University of Montana)– Pathways to Algebra and Geometry (MMAP)

Five high school curriculum projects:– Contemporary Mathematics in Context (Core-Plus Mathematics Project)– Interactive Mathematics Program (IMP)– MATH Connections: A Secondary Mathematics Core Curriculum (CBIA)– Mathematics: Modeling Our World (COMAP)– SIMMS Integrated Mathematics (SIMMS)

• Stimulated major school mathematics curriculum development projects funded by NSF

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• Stimulated development of standards for other school subjects.

• NSF funded numerous professional development projects to support the necessary work with teachers, districts, and communities to successfully implement these Standards and the new Standards-based instructional materials.

• State-level curriculum frameworks and assessments were developed that reflected the content of the Standards.

• General Mathematics, Consumer Mathematics, and other remedial high school courses were replaced by Standards-based courses.

• Changes were made in instructional practices toward more student-centered approaches.

• Use of technology, particularly hand-held calculators, in teaching increased dramatically.

• “Math wars” emerged as implementation of these standards were construed in ways unintended by the Standard’s authors.

Significance: Curriculum and Instruction

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• Alternatives to pencil-and-paper tests, such as writing assignments, projects, portfolios, and classroom dialogue began to be used by teachers to assess student understanding.

• Local and statewide testing moved away from strictly short answer and multiple-choice questions to include constructed response questions to assess student understanding.

• Standardized tests such as the ACT and SAT and AP exams began to allow calculator use, to reflect the trend in high school classrooms.

• Curriculum evaluation began to be viewed as a K-12 initiative, rather than a grade-level or building level issue.

• Many schools and individual teachers evaluated the alignment of their curriculum and instructional methods with the NCTM Standards and later with state frameworks.

Significance: Evaluation

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References

National Council of Teachers of Mathematics Commission on Standards for School Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: The Council. http://www.standards.nctm.org/index.htm

McLeod, D. B., Stake, R. E., Schappelle, B. P., Mellissinos, M., & Gierl, M. J. (1996). Setting the Standards: NCTM’s role in the reform of mathematics education. In S. A. Raizen & E. D. Britton (Eds.), Bold ventures: Case studies of U.S. innovations in mathematics education. (Vol. 3, pp. 13-132). Dordrecht, The Netherlands: Kluwer Academic.