Making Sense of the Math Revisions

1
Making Sense of the Math Revisions

• George W. Bright, Ph.D.
• Special Assistant to the Superintendent
• OSPI
• George.Bright_at_k12.wa.us

2
Overview of the Session

• National Mathematics Advisory Panel
• Legislative Actions Graduation Requirements
• Revised Mathematics Standards Feb 29 version
• Platter Review and Recommendations
• Digging into the Revised Standards

3
National Mathematics Advisory Panel

• Final Report released on March 13, 2008.
• 45 Recommendations and Findings
• Major Topics of School Algebra
• Critical Foundations of Algebra
• Benchmarks for the Critical Foundations

4
National Mathematics Advisory PanelK-8 Curriculum

• The mathematics curriculum in Grades PreK8
  should be streamlined and should emphasize a
  well-defined set of the most critical topics in
  the early grades.

5
National Mathematics Advisory PanelInstruction

• Instructional practice should be informed by
  high-quality research, when available, and by the
  best professional judgment and experience of
  accomplished classroom teachers. High-quality
  research does not support the contention that
  instruction should be either entirely student
  centered or teacher directed. Research
  indicates that some forms of particular
  instructional practices can have a positive
  impact under specified conditions.

6
National Mathematics Advisory PanelTeachers

• Our citizens and their educational leadership
  should recognize mathematically knowledgeable
  classroom teachers as having a central role in
  mathematics education and should encourage
  rigorously evaluated initiatives for attracting
  and appropriately preparing prospective teachers,
  and for evaluating and retaining effective
  teachers.

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National Mathematics Advisory PanelEffort

• Use should be made of what is clearly known from
  rigorous research about how children learn,
  especially by recognizing a) the advantages for
  children in having a strong start b) the
  mutually reinforcing benefits of conceptual
  understanding, procedural fluency, and automatic
  (i.e., quick and effortless) recall of facts and
  c) that effort, not just inherent talent, counts
  in mathematical achievement.

8
National Mathematics Advisory PanelAssessment

• NAEP and state assessments should be improved in
  quality and should carry increased emphasis on
  the most critical knowledge and skills leading to
  Algebra.

9
National Mathematics Advisory PanelResearch

• The nation must continue to build capacity for
  more rigorous research in education so that it
  can inform policy and practice more effectively.

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Major Topics of School Algebra (1 and 2)

• Symbols and Expressions
• Polynomial expressions, Rational expressions,
  Arithmetic and finite geometric series
• Linear Equations
• Real numbers as points on the number line,
  Linear equations and their graphs, Solving
  problems with linear equations, Linear
  inequalities and their graphs, Graphing and
  solving systems of simultaneous linear equations
• Quadratic Equations
• Factors and factoring of quadratic polynomials
  with integer coefficients, Completing the square
  in quadratic expressions, Quadratic formula and
  factoring of general quadratic polynomials, Using
  the quadratic formula to solve equations

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Major Topics of School Algebra (1 and 2)

• Functions
• Linear functions, Quadratic functionsword
  problems involving quadratic functions, Graphs of
  quadratic functions and completing the square,
  Polynomial functions (including graphs of basic
  functions), Simple nonlinear functions (e.g.,
  square and cube root functions absolute value
  rational functions step functions), Rational
  exponents, radical expressions, and exponential
  functions, Logarithmic functions, Trigonometric
  functions, Fitting simple mathematical models to
  data
• Algebra of Polynomials
• Roots and factorization of polynomials, Complex
  numbers and operations, Fundamental theorem of
  algebra, Binomial coefficients (and Pascals
  Triangle), Mathematical induction and the
  binomial theorem
• Combinatorics and Finite Probability
• Combinations and permutations

12
Critical Foundations of Algebra

• Fluency with Whole Numbers
• Fluency with Fractions
• Particular Aspects of Geometry and Measurement

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13
National Mathematics Advisory PanelBenchmarks
Whole Numbers

• 1) By the end of Grade 3, students should be
  proficient with the addition and subtraction of
  whole numbers.
• 2) By the end of Grade 5, students should be
  proficient with multiplication and division of
  whole numbers.

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National Mathematics Advisory PanelBenchmarks
Fractions

• 1) By the end of Grade 4, students should be able
  to identify and represent fractions and decimals,
  and compare them on a number line or with other
  common representations of fractions and decimals.
• 2) By the end of Grade 5, students should be
  proficient with comparing fractions and decimals
  and common percents, and with addition and
  subtraction of fractions and decimals.
• 3) By the end of Grade 6, students should be
  proficient with multiplication and division of
  fractions and decimals.

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National Mathematics Advisory PanelBenchmarks
Fractions

• 4) By the end of Grade 6, students should be
  proficient with all operations involving positive
  and negative integers.
• 5) By the end of Grade 7, students should be
  proficient with all operations involving positive
  and negative fractions.
• 6) By the end of Grade 7, students should be able
  to solve problems involving percent, ratio, and
  rate and extend this work to proportionality.

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National Mathematics Advisory PanelBenchmarks
Geometry and Measurement

• 1) By the end of Grade 5, students should be able
  to solve problems involving perimeter and area of
  triangles and all quadrilaterals having at least
  one pair of parallel sides (i.e., trapezoids).
• 2) By the end of Grade 6, students should be able
  to analyze the properties of two-dimensional
  shapes and solve problems involving perimeter and
  area, and analyze the properties of
  three-dimensional shapes and solve problems
  involving surface area and volume.
• 3) By the end of Grade 7, students should be
  familiar with the relationship between similar
  triangles and the concept of the slope of a line.

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Reflection on the NMAP Final Report

• Which of the findings and recommendations
  strike you as unusual or particularly important?
• How might the findings and recommendations of
  the National Mathematics Advisory Panel affect
  discussions and decisions about standards,
  curriculum, and testing in WA?

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Legislative Actions in 2008

• Legislative actions were completed prior to the
  release of the Final Report of the National
  Mathematics Advisory Panel.
• Implementation of these actions may be
  influenced by that Final Report.

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Status of Legislation Standards (Bill 6534)

• By May 15
• receive report of national consultants review
  of Feb 29 version of Standards
• consult WA Mathematics Panel about the
  consultants recommendations
• hold public hearing
• direct modifications to consultants report
• forward final report and recommendations to
  OSPI for implementation

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Status of Legislation Standards (Bill 6534)

• By July 01
• OSPI shall revise the mathematics standards
  to conform precisely to and incorporate each of
  the recommendations of the State Board of
  Education
• By July 31
• approve adoption of the standards
• OR
• develop a plan to do this by September

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Probable Schedule Standards

• By April 17
• SBE approves K-8 standards
• By May 15
• SBE approves standards for Algebra 1,
  Geometry, Integrated Mathematics 1, Integrated
  Mathematics 2
• By July 15
• SBE approves standards for Algebra 2,
  Integrated Mathematics 3

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Status of Legislation WASL (Bill 3166)

• shorten the tests for grades 3-8
• create diagnostic tools (NOTE diagnostic is
  not defined)
• by 2010 create end-of-course tests for Algebra
  1 and Integrated Mathematics 1
• by 2011 create end-of-course tests for Geometry
  and Integrated Mathematics 2
• in 2013 end-of-course tests may substitute for
  10th grade WASL
• in 2014 end-of-course tests replace the 10th
  grade WASL

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Issues of Scheduling WASL

• In order to have end-of-course tests ready for
  use in Spring 2010, the standards for Algebra 1
  and Integrated Mathematics 1 must be approved by
  May 15.
• Any delay beyond that date would put new
  creation of new tests in jeopardy.
• This puts some urgency into the discussion of
  standards by the State Board of Education.

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Graduation Requirements State Board of Education

• 3rd mathematics credit required for graduation
  in 2013
• The State Board of Education will determine the
  list of permissible courses.
• The expectation is that these decisions will be
  made in July 2008.

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Revised K-12 Mathematics StandardsFeb 29
version Organization

• K-8 organized by grade
• Core Content, Additional Key Content, Core
  Processes
• High School organized by courses
• Algebra 1, Geometry, Algebra 2
• Mathematics 1, Mathematics 2, Mathematics 3
• also, topics for possible 4th year courses

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Review of the Feb 29 Version

• The State Board of Education asked Linda
  Plattner to review the Feb 29 version of the
  Revised K-12 Mathematics Standards. Report
  submitted to Legislature on March 10, 2008.
• Linda Plattner reviewed the GLEs in Summer 2007
  and the Jan 21 version of the Revised K-12
  Mathematics Standards.
• The Legislature delayed action until after
  Linda Plattners review of the Feb 29 version.

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Revised K-12 Mathematics StandardsFeb 29
version Plattner Review

• We first want to commend the substantial work of
  Washington educators and community leaders, OSPI,
  and the Dana Center. Washington has broken new
  ground in its approach to organizing grade level
  content by priorities rather than mathematical
  strands. The writing teams were inclusive, the
  stakeholder feedback extensive. The document
  clearly is thoughtful and written with
  mathematical expertise.

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Revised K-12 Mathematics StandardsFeb 29
version Plattner Review

• Standards inherently involve tensions. They are
  goal statements about which different people,
  even different experts, will have varied
  opinions. They require negotiations, and
  represent compromises among varied legitimate
  participants and groups.
• Confrey, Jere, Tracing the Evolution of
  Mathematics Content Standards in the United
  States Looking Back and Projecting Forward
  towards National Standards, a paper prepared for
  the Conference on K12 Mathematics Curriculum
  Standards, sponsored by CSMC, NCTM, Achieve,
  College Board, MAA, ASA (February 2007).

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Revised K-12 Mathematics StandardsFeb 29
version Plattner Review

• The new mathematics standards for grades K8 are
  very close to excellent. These standards do
  compare favorably with the best in the nation and
  the world. The Performance Expectations are
  specific, measurable, important mathematical
  topics that are both focused at particular grades
  and developed across grade levels.

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Revised K-12 Mathematics StandardsFeb 29
version Plattner Review

• While they the high school standards are much
  improved from OSPI's January version, further
  revision is needed. Some areas, such as
  occasional imprecision of language, is similar to
  grades K8 and just as easily fixed. Other areas,
  such as missing content and content organization,
  are more problematic.

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Revised K-12 Mathematics StandardsFeb 29
version Plattner Recommendations

• 1. An exemplar review of the OSPI February
  standards K8 and 912, similar to last year's
  comparison to other states, countries and
  national frameworks using the nine criteria to
  provide external validation that these are the
  best standards. In order to compress the timeline
  we suggest fewer grade levels and fewer
  documents.
• 2. Substantive edit for grades K8. The content
  is very good language is almost ready. These
  standards are so close that work could be
  completely very quickly.
• 3. A revision of the high school standards.
  The core content of the subjects is in the
  document and many of the examples are excellent.
  The language needs to be tightened and there is
  some more work to be done on the content. This
  means it will take slightly longer than the grade
  K8 work.

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The Substance of the Revised Standards

• Given the pivotal role of standards in testing,
  curriculum review, and instruction, lets turn
  our attention to what mathematics Washington
  educators have said is important for students to
  learn.
• Attend first to K-8 standards.

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Depth of Content

• Where is the first mention of each of the
  following ideas? Where is the last mention?
• multiplication of whole numbers
• mean of a set of data
• area formulas for triangles
• What do you notice about the range of grades for
  these topics?

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Debriefing Depth of Content

• multiplication of whole numbers
• mean of a set of data
• area formulas for triangles

35
Grade Band Discussions K-2, 3-5, 6-8

• What key mathematics would students in your grade
  band learn for each of the following?
• operations, geometry, data
• How do the main ideas develop across your grade
  band for each of the following?
• operations, geometry, data

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Debriefing Grade Band Discussions

• operations
• geometry
• data

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Student Learning

• What is the image of mathematics that the
  Standards for this grade band communicate?
• What is the residual learning that students
  will have as they leave this grade band?

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Debriefing Student Learning

• image of mathematics
• residual learning

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High School Standards

• If Algebra 2 is for ALL students, what content
  should it include?
• If Algebra 2 is for COLLEGE-BOUND students,
  what content should it include?
• What options to Algebra 2 should there be?

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Revised High School Standards

• How well do the High School Revised Mathematics
  Standards reflect what students should know?
• Tentatively, Algebra 2 standards should be
  approved about July 2008.

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Closing Comments

• Share this information with colleagues.
• Communicate with Legislators and members of the
  State Board of Education about what should be in
  Washington States Revised K-12 Mathematics
  Standards.
• Support local teachers as they learn about the
  revised standards and begin to implement them.