NCTM%20Curriculum%20Focal%20Points%20and%20State%20Standards

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NCTM Curriculum Focal Points and State Standards
Barbara Reys, University of Missouri
Center for the Study of Mathematics Curriculum
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Overview

• Review the influence of NCTMs curriculum
  recommendations on state standards.
• Examine the alignment of topics designated as
  CFPs with current state standards.

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Influence of NCTM standards

• NCTMs entry into articulating mathematics
  standards (1989) coincided with an increased role
  by states in providing leadership for standards
  (Long, 2003)
• During this period the role, authority, and
  specification of state standards varied (CCSSO,
  1995 and 1997).
• Curriculum and Evaluation Standards for School
  Mathematics (1989) and Principles and Standards
  for School Mathematics (2000) had a significant
  impact on the content of state standards (Martin,
  Stein, Ferrini-Mundy, 2002)

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No Child Left Behind (2001)

• Each state is required to
• adopt challenging academic content standards that
  will be used by the State, its local educational
  agencies, and its schools.
• measure the achievement of students in
  mathematics against the standards in each of
  grades 3 through 8.

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Grade-Level Learning Expectations (GLEs)

• Prior to NCLB, many states did not have content
  standards that specified the mathematics that
  students should learn at each grade level.
• As of 2006, 42 states published GLEs.
• - Most common K-8 (37 states)
• - Others K-7, 3-8 or 3-10 (5 states)

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Increased Specificity, Authority, and Influence

• For many states, GLEs represented increased
  specificity compared to previous standards.
• GLEs carry additional weight or influence since
  they are tied to NCLB-mandated annual
  assessments.
• Teachers and state department leaders acknowledge
  increased influence of GLEs at the classroom
  level.

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Influence of NCTM Standards

• In a 2005 survey of ASSM members (47 states
  responding), PSSM was noted as the most
  influential reference document in the development
  of the state standards - 80 of respondents
  indicated PSSM was a strong influence (NAEP
  framework cited as the next most influential
  document by 40 of respondents).
• In the same survey 85 of respondents indicated
  that national leadership for mathematics
  curriculum articulation is needed.

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• To what extent is the grade placement of NCTMs
  Curriculum Focal Points consistent with state
  GLEs?

To what extent is the grade placement of K-8 GLEs
similar across states?
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• Selected topics within the number and operation
  strand
• Fluency with basic number combinations
• Fluency with whole number computation
• Fluency with fraction computation
• Reviewed GLEs from 42 state documents.
• Compiled and compared grade placement of specific
  GLEs.
• When are particular topics introduced and when is
  proficiency expected?

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Differences in GLE Documents

• Language
• Level of specificity or grain size
• Grade placement of key topics
• Trajectory of development of topics

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Example of Variation of GLEs (Basic Number
Combinations)

• Know the addition facts (sums to 20) and the
  corresponding subtraction facts and commit them
  to memory. (CA, gr. 1)
• States and uses with efficiency and accuracy
  basic addition facts with sums from 0 to 20 and
  corresponding subtraction facts. (KS, gr. 2)
• Recall basic addition and subtraction facts
  through 18. (ID, gr. 3)

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Level of Specificity

• Demonstrate computational fluency for basic
  addition and subtraction facts with sums through
  18 and differences with minuends through 18,
  using horizontal and vertical forms. (AL, gr. 2)
• vs.
• State addition and subtraction facts.
• (AZ, gr. 2)

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Fluency with Fraction Computation
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Progression of GLEs (FL)(addition/subtraction of
fractions)

• Explains and demonstrates the addition and
  subtraction of common fractions using concrete
  materials, drawings, story problems, and
  algorithms. (Gr. 4)
• Solves real-world problems involving the addition
  or subtraction of decimals (to hundredths) or
  common fractions with like and unlike
  denominators. (Gr. 4)
• Solves real-world problems involving addition,
  subtraction, multiplication, and division of
  whole numbers, and addition, subtraction, and
  multiplication of decimals, fractions, and mixed
  numbers using an appropriate method (for example,
  mental math, pencil and paper, calculator). (Gr.
  5)

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Progression of GLEs (AZ) (addition/subtraction
of fractions)

• Demonstrate addition and subtraction of fractions
  with like denominators (halves) using models.
  (gr. 1)
• Demonstrate addition and subtraction of fractions
  with like denominators (halves and fourths) using
  models. (gr. 2)
• Add or subtract fractions with like denominators
  (halves, thirds, fourths, eighths, and tenths)
  appropriate to grade level. (gr. 3)
• Add or subtract fractions with like denominators,
  no regrouping. (gr. 4)
• Add or subtract proper fractions and mixed
  numbers with like denominators with regrouping.
  (gr. 5)
• Add or subtract proper fractions and mixed
  numbers with unlike denominators with regrouping.
  (gr. 6)

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Addition and Subtraction of Fractions
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Curriculum Focal Point

• Developing an understanding of and fluency with
  addition and subtraction of fractions and
  decimals. (Grade 5)

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Addition and Subtraction of Fractions
CFP
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Addition and Multiplication of Basic Number
Combinations
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Addition of Basic Number Combinations
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Curriculum Focal Point

• Developing understandings of addition and
  subtraction and strategies for basic addition
  facts and related subtraction facts. (Grade 1)
• Developing quick recall of addition facts and
  related subtraction facts and fluency with
  multidigit addition and subtraction. (Grade 2)

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Addition of Basic Number Combinations
CFP
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Fluency with Multiplication of Basic Number
Combinations
CFP
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Curriculum Focal Point

• Developing understandings of multiplication and
  division and strategies for basic multiplication
  facts and related division facts. (Grade 3)
• Developing quick recall of multiplication facts
  and related division facts and fluency with whole
  number multiplication (Grade 4)

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Fluency with Multiplication of Basic Number
Combinations
CFP
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Multi-digit Computation Addition and Subtraction
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Progression of GLEs (CA)(Multi-digit Whole
Number Addition)

• Solve addition and subtraction problems with one-
  and two-digit numbers (Grade 1)
• Find the sum or difference of two whole numbers
  up to three digits long (Grade 2)
• Use mental arithmetic to find the sum or
  difference of two two-digit numbers (Grade 2)
• Find the sum or difference of two whole numbers
  between 0 and 10,000 (Grade 3)
• Demonstrate an understanding of, and the ability
  to use, standard algorithms for the addition and
  subtraction of multidigit numbers (Grade 4)

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Fluency with Addition of Multi-Digit Whole
Numbers
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Curriculum Focal Point

• Developing quick recall of addition facts and
  related subtraction facts and fluency with
  multidigit addition and subtraction. (Grade 2)

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Fluency with Addition of Multi-Digit Whole
Numbers
CFP
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Multi-digit Computation Multiplication
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Fluency with Multiplication of Multi-Digit Whole
Numbers
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Curriculum Focal Point

• Developing quick recall of multiplication facts
  and related division facts and fluency with whole
  number multiplication (Grade 4)

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Multiplication of Multi-Digit Whole Numbers
CFP
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• Across state GLEs, for most topics, there is
  considerable variation with regard to the grade
  placement (introduction, development,
  proficiency/fluency).
• Within state GLEs, development of topics such as
  computational fluency are spread across several
  grades rather than serving as a focal point in
  any one grade.

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• The idea of organizing learning goals according
  to focal points is not a common concept in the
  U.S., and not represented in most state
  standards.
• There is considerable work to be done to realize
  the vision of curriculum focal points
• Not just about matching the grade level to CFP.
• Major shift in how curriculum is organized.
• Look to standards and curriculum from other
  countries for some models.

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For more details . . . .

• Executive Summary of the report
• http//mathcurriculumcenter.org/reports_publicatio
  ns.php
• Full report
• Information Age Publishing Company
• http//www.infoagepub.com/
• ISBN 1-930608-52-70

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• PSSM (Grades 3-5)
• develop and use strategies to estimate
  computations involving fractions and decimals in
  situations relevant to students experience.
• use visual models, benchmarks, and equivalent
  forms to add and subtract commonly used fractions
  and decimals.
• PSSM (Grades 6-8)
• develop and analyze algorithms for computing with
  fractions, decimals, and integers and develop
  fluency in their use.
• develop and use strategies to estimate the
  results of rational-number computations and judge
  the reasonableness of the results.