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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
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http://www.mathcurriculumcenter.org
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Curriculum and Evaluation
Standards for School
Mathematics
National 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, Chairman
Iris M. Carl
Christian R. Hirsch
F. Joe Crosswhite
Glenda Lappan
John A. Dossey
Dale Seymour
James D. Gates
Lynn A. Steen
Shirley M. Frye
Paul R. Trafton
Shirley A. Hill
Norman Webb
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Purpose
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
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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:
Standard 2:
Standard 3:
Standard 4:
Mathematics as Problem Solving
Mathematics as Communication
Mathematics as Reasoning
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 Howden
Mary M. Lindquist
Edward C. Rathmell
Thomas E. Rowan
Charles S. Thompson
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Assumptions Underlying
the Grades K-4 Standards
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.
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Grades K-4 Content Standards
Standard 5:
Standard 6:
Standard 7:
Standard 8:
Estimation
Number Sense and Numeration
Concepts of Whole Number Operations
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 penciland-paper computation, standard algorithm for division, and use
of rounding to estimate.
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Grades K-4 Content Standards
Standard 9: Geometry and Spatial Sense
Standard 10: Measurement
Standard 11: Statistics and Probability
Standard 12: Fractions and Decimals
Standard 13: Patterns and Relationships
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.
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Members of the Grades 5-8
Working Group
Glenda Lappan, Chair
Daniel T. Dolan
Joan F. Hall
Thomas E. Kieren
Judith E. Mumme
James 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 welldefined.
• 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:
Standard 6:
Standard 7:
Standard 8:
Number and Number Relationships
Number Systems and Number Theory
Computation and Estimation
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 paperand-pencil computations.
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Grades 5-8 Content Standards
Standard 9: Algebra
Standard 10: Statistics
Standard 11: Probability
Standard 12: Geometry
Standard 13: Measurement
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.
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Members of the Grades 9-12
Working Group
Christian R. Hirsch, Chair
Sue Ann McGraw
Gerald R. Rising
Harold L. Schoen
Cathy L. Seeley
Bert 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:
Standard 6:
Standard 7:
Standard 8:
Standard 9:
Algebra
Functions
Geometry from a Synthetic Perspective
Geometry from an Algebraic Perspective
Trigonometry
Implementation 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:
Standard 11:
Standard 12:
Standard 13:
Standard 14:
Statistics
Probability
Discrete Mathematics
Conceptual Underpinning of Calculus
Mathematical Structure
Implementation 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, Chair
Elizabeth Badger
Diane J.Briars
Thomas J. Cooney
Tej N. Pandey
Alba 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 Standards
Organized in three sections:
General Assessment Standards: Recommends principles relevant to
any form of assessment and program evaluation.
Standard 1: Alignment
Standard 2: Multiple Sources of Information
Standard 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 Power
Standard 5: Problem Solving
Standard 6: Communication
Standard 7: Reasoning
Standard 8: Mathematical Concepts
Standard 9: Mathematical Procedures
Standard 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 Evaluation
Standard 12: Curriculum and Instructional Resources
Standard 13: Instruction
Standard 14: Evaluation Team
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Significance: Curriculum and Instruction
• Stimulated major school mathematics curriculum development projects
funded by NSF
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)
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Significance: Curriculum and Instruction
•
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 studentcentered 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.
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Significance: Evaluation
•
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.
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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.
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