1 making sense of the math revisions george w. bright, ph.d. special assistant to the superintendent...

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Making Sense of the Math Revisions

George W. Bright, Ph.D.Special Assistant to the

SuperintendentOSPI

George.Bright@k12.wa.us

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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

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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

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National Mathematics Advisory PanelK-8 Curriculum

“The mathematics curriculum in Grades PreK–8 should be streamlined and should emphasize a well-defined set of the most critical topics in the early grades.”

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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.”

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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.”

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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.”

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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 ExpressionsPolynomial expressions, Rational expressions, Arithmetic and finite geometric series

Linear EquationsReal 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 EquationsFactors 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)

FunctionsLinear functions, Quadratic functions—word 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 PolynomialsRoots and factorization of polynomials, Complex numbers and operations, Fundamental theorem of algebra, Binomial coefficients (and Pascal’s Triangle), Mathematical induction and the binomial theorem

Combinatorics and Finite ProbabilityCombinations and permutations

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Critical Foundations of Algebra

• Fluency with Whole Numbers

• Fluency with Fractions

• Particular Aspects of Geometry and Measurement

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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 consultant’s review of Feb 29 version of Standards

• consult WA Mathematics Panel about the consultant’s recommendations

• hold public hearing

• direct modifications to consultant’s 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 Plattner’s 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 K–12 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 K–8 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 OSPIʼs January version, further revision is needed. Some areas, such as occasional imprecision of language, is similar to grades K–8 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

Recommendations1. An exemplar review of the OSPI February standards K–8 and 9–12, similar

to last yearʼs 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 K–8. 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 K–8 work.

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The Substance of the Revised Standards

Given the pivotal role of standards in testing, curriculum review, and instruction, let’s 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

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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 State’s Revised K-12 Mathematics Standards.

• Support local teachers as they learn about the revised standards and begin to implement them.