PowerPoint Presentation - Curriculum and Evaluation Standards for School Mathematics

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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
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
• F. Joe Crosswhite
• John A. Dossey
• James D. Gates
• Shirley M. Frye
• Shirley A. Hill

Christian R. Hirsch Glenda Lappan Dale
Seymour Lynn A. Steen Paul R. Trafton 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 ones 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 Communication
• Standard 3 Mathematics as Reasoning
• Standard 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 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 Estimation
• Standard 6 Number Sense and Numeration
• Standard 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

• 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
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 Relationships
• Standard 6 Number Systems and Number Theory
• Standard 7 Computation and Estimation
• Standard 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

• 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 Algebra
• Standard 6 Functions
• Standard 7 Geometry from a Synthetic
  Perspective
• Standard 8 Geometry from an Algebraic
  Perspective
• Standard 9 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 Statistics
• Standard 11 Probability
• Standard 12 Discrete Mathematics
• Standard 13 Conceptual Underpinning of Calculus
• Standard 14 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 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 Standards 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 NCTMs 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.