Washington K12 Standards in Transition

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Washington K-12 Standards in Transition

• Transition Mathematics Project
• August 2008
• Susan Hudson Hull, Dana Center, University of
  Texas at Austin
• Kristen Maxwell, ESD 105
• Yakima, WA

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Goals for the this Session

• Present an overview of the newly adopted WA
  High School Mathematics Standards
• Understand the organization of the Standards
• Discuss correlations with the WA TMP College
  Readiness Standards and implications

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Standards Document

• The WA High School Mathematics Standards are
  accompanied by the Mathematics Standards for
  KindergartenGrade 8.
• It is important to know what knowledge students
  will bring with them when they enter high school.

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Organization of K-8 Mathematics Standards

• At each grade level
• 3-4 Core Content areas
• Additional Key Content
• Core Processes (reasoning, problem solving,
  communication)
• For each of these
• Core Content Paragraph
• Performance Expectations
• Comments/Examples

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Organization of High School Mathematics Standards

• For each high school course
• several Core Content areas
• Additional Key Content
• Core Processes (reasoning, problem solving,
  communication)
• For each of these
• Core Content Paragraph
• Performance Expectations
• Comments/Examples

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Core Content Paragraphsfor Each Part

• The paragraphs are part of the Standards and
  should not be overlooked. They convey the essence
  of the content in a way that should help readers
  get a clear sense of that content. Taken
  together the paragraphs provide the story of
  the course.

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Performance Expectations

• Performance expectations describe what students
  should know and be able to do at each grade level
  or in each course. These statements are the core
  of the document. They provide clear guidance
  about the mathematics that is to be taught and
  learned.
• Numbering System
• Course Core Content
  Expectation
• A1.2.C

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Explanatory Comments and Examples

• Explanatory comments and examples, taken together
  with the performance expectations, provide a full
  context and understanding of the expectation.
  They expand upon the meaning of the expectation.

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Explanatory Comments and Examples

• Clarify the parameters regarding the type or size
  of numbers
• Provide more information regarding mathematical
  understanding
• Give expanded detail to mathematical definitions,
  laws, principles, and forms
• Provide example problems that are typical of
  those that students should be able to solve
  i.e., limits on expected levels of difficulty.
• Serve as instructional illustrations to the
  teacher.
• They are not intended to limit the teaching of
  content or teaching methods.

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Balanced Program

• A well-balanced mathematics program for all
  students includes
• Conceptual understanding
• Procedural proficiency
• Mathematical processes

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Conceptual Understanding(making sense of
mathematics)

• Conceptual understanding is woven throughout the
  standards.
• Performance Expectations with verbs like
  demonstrate, describe, represent, connect, or
  verify ask students to show their understanding.

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Procedural Proficiency(skills, facts, and
procedures)

• Computation is typically carried out by using
  mathematical procedures, or algorithms.
• An algorithm is a set of step-by-step procedures
  that, if followed correctly, always produce a
  correct solution.
• Students should come to understand that
  algorithms are an important part of mathematics.

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Mathematical Processes(using mathematics to
reason and think)

• Students must be able to reason, solve problems,
  and communicate their understanding effectively.
• Content is always embedded in processes, and
  processes are often embedded in content.

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Mathematical Processes

• Are described in
• Core Content 1 in Algebra 1 and 2, and
  Mathematics 1, 2, and 3.
• Core Processes, the last section in each course.
• Process expectations also are embedded in Core
  Content when appropriate.

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Reading

• Read the paragraph, Performance Expectations and
  Comments/Examples for Core Content A1.4 Linear
  functions, equations, and inequalities.
• What surprised you?
• What feels comfortable?
• Where do you find content, procedure, and
  process?
• When you have finished reading, discuss what you
  found in your group.

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Process for Creating the Standards

• In 2007, the WA Legislature decided that improved
  Mathematics Standards were needed, partly because
  of the high number of students who did not pass
  the 10th-grade WASL.
• The State Board of Education contracted with
  Strategic Teaching to evaluate the GLEs.
• That report was approved by the State Board in
  August 2007.

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Process for Creating the Standards

• OSPI contracted with the Dana center in October
  to manage the revision process.
• OSPI created a Standards Revision Team to revise
  the GLEs according to the criteria described in
  that report. The SRT included teachers, district
  and ESD math specialists and coaches, 2- and 4-yr
  higher ed faculty (mathematics and education),
  business representatives.
• SRT subgroups K-2, 3-5, 6-8, 9-12
• Articulation and edit teams, including WA
  representatives on each team, national experts,
  and Dana Center staff, produced draft standards
  from SRT direction.

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Charge to Standards Revision Team

• Address these areas of concern
• Content Rigor
• Specificity Clarity
• Depth Coherence
• Measurability Accessibility
• Balance

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Comparison Documents

• These documents were available for use by members
  of the Standards Revision Team
• Mathematics Standards from
• Massachusetts, California, Indiana, Georgia,
• Florida, Finland, Singapore
• NCTM Curriculum Focal Points
• NAEP Framework
• Achieve Secondary Mathematics Expectations and
  Algebra 2 End-of-Course Exam core content
• College Board Standards for College Success
• Washingtons TMP College Readiness Mathematics
  Standards
• Benchmarks of National Mathematics Advisory
  Panel (after March, 2008)

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National Mathematics Advisory PanelMajor
Findings

• Teachers Mathematically knowledgeable classroom
  teachers have a central role in mathematics
  education attracting, preparing, evaluating, and
  retaining high quality teachers is essential.
• Instruction Instructional practice should be
  informed by high-quality research, when
  available, and by the best professional judgment
  and experience of accomplished classroom
  teachers research does not support either
  entirely student centered or teacher directed
  instruction.

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National Mathematics Advisory PanelMajor
Findings

• Effort Research about how children learn should
  be used, especially by recognizing
• the advantages for children in having a strong
  start
• the mutually reinforcing benefits of conceptual
  understanding, procedural fluency, and automatic
  recall of facts and
• that effort, not just inherent talent, counts in
  mathematical achievement.
• Integrated Mathematics No studies were found
  that clearly examined whether an integrated
  approach or a single-subject sequence is more
  effective for algebra and more advanced
  mathematics course work. The Panel finds no basis
  in research for preferring one or the other.

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National Mathematics Advisory PanelSpecific
Recommendations

• Specific content recommendations for K-7. WA K-7
  Standards align with almost all of these.
• Algebra recommendations
• Charge to the committee assumes 8th grade
  algebra
• Report lists major topics of school algebra
• Little or no mention of other high school
  content (geometry, probability, data analysis,
  statistics, or precalculus content)

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Process for Creating the Standards

• Oct SRT met in October to develop outline of
  first draft edit and articulation teams
  organized pre-draft.
• OctDec SRT met to develop drafts edit and
  articulation teams organized drafts.
• DecJan Draft sent out for field review
• Feb Revisions made for March 5 version
• MarJuly Strategic Teaching review and edits
  field review
• May K-8 adopted
• July Algebra 1, Geometry, Algebra 2 adopted
• Aug SRT, OSPI, and Dana Center finalize
  Mathematics 1, 2, and 3.

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Appropriateness of Expectations

• Each Performance Expectation was compared to
  standards from other states and nations.
• Information from research literature and
  knowledge of national experts influenced the
  placement of Expectations appropriately into each
  grade level.
• Washington is not the only state working to
  increase the rigor of mathematics instruction.

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WA Mathematics Standards Traditional vs.
Integrated Mathematics

• Across the three years of either traditional or
  integrated mathematics courses, the Performance
  Expectations in the High School Mathematics
  Standards are identical.

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Knowledge for College Readiness

• Lets look at how the High School Mathematics
  Standards prepare students for learning
  mathematics for college readiness.

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Algebra 1

• A1.1. Core Content Solving Problems
• A1.2 Core Content Numbers,Expressions and
  Operations
• A1.3. Core Content Characteristics and Behaviors
  of Functions
• A1.4. Core Content Linear Functions, Equations
  and Relationships
• A1.5. Core Content Quadratic Functions and
  Equations
• A1.6. Core Content Data and Distributions
• A1.7 Additional Key Content Exponentials,
  Sequences and Literal Equations
• A1.8. Core Content Reasoning, Problem Solving
  and Communication

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Geometry

• G.1. Core Content Logical Arguments and Proofs
• G.2. Core Content Lines and Angles
• G.3. Core Content Two- and Three-Dimensional
  Figures
• G.4. Core Content Geometry in the Coordinate
  Plane
• G.5. Core Content Geometric Transformations
• G.6. Additional Key Content Measurement
• G.7. Core Processes Reasoning, Problem Solving
  and Communication

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Algebra 2

• A2.1. Core Content Solving Problems
• A2.2. Core Content Numbers, Expressions, and
  Operations
• A2.3. Core Content Quadratic Functions and
  Equations
• A2.4. Core Content Exponential and Logarithmic
  Functions and Equations
• A2.5. Core Content Additional Functions and
  Equations
• A2.6. Core Content Probability, Data and
  Distributions
• A2.7. Additional Key Content Systems and Series
• A2.8. Core Processes Reasoning, Problem Solving
  and Communication

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Mathematics 1

• M1.1. Core Content Solving problems
• M1.2. Core Content Characteristics and behaviors
  of functions
• M1.3. Core Content Linear functions, equations,
  and relationships
• M1.4. Core Content Proportionality, similarity,
  and geometric reasoning
• M1.5. Core Content Data and distributions
• M1.6. Numbers, expressions, and operations
• M1.7 Additional Key Content Exponential
  functions and expressions
• M1.8. Core Processes Reasoning, problem solving,
  and communication

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Mathematics 2

• M2.1. Core Content Modeling situations and
  solving problems
• M2.2. Core Content Quadratic functions,
  equations, and relationships
• M2.3. Core Content Conjectures and proofs
• M2.4. Core Content Probability
• M2.5. Additional Key Content Algebra and
  measurement
• M2.6. Core Processes Reasoning, problem solving,
  and communication

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Mathematics 3

• M3.1. Core Content Solving problems
• M3.2. Core Content Transformations and functions
• M3.3. Core Content Functions and modeling
• M3.4. Core Content Quantifying variability
• M3.5. Core Content Three-dimensional geometry
• M3.6. Core Content Algebraic properties
• M3.7. Additional Key Content Circles and
  measurement
• M3.8. Core Processes Reasoning, problem solving,
  and communication

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WA State TMP College Readiness Standards

• Process Standards
• 1. Reasoning/Problem Solving The student uses
  logical reasoning and mathematical knowledge to
  define and solve problems
• 2. Communication The student can interpret and
  communicate mathematical knowledge and
  relationships in both mathematical and everyday
  language.
• 3. Connections The student extends mathematical
  thinking across mathematical content areas, and
  to other disciplines and real life situations.

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WA State TMP College Readiness Standards

• Content Standards
• 4. Number Sense The student accurately describes
  and applies concepts and procedures related to
  real and complex numbers.
• 5. Geometry The student makes hypotheses, models
  situations, draws conclusions, and supports
  claims using geometric concepts and procedures.
• 6. Probability/Statistics The student accurately
  describes and applies concepts and procedures
  from probability and statistics to analyze data.
• 7. Algebra The student accurately describes and
  applies concepts and procedures from algebra.
• 8. Functions The student accurately describes
  and applies function concepts and procedures to
  understand mathematical relationships.

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Paragraphs as a Story of the Course

• 1. Choose a course to study with your table
  partners.
• 2. Read the paragraphs for each content area for
  this course and then discuss them with your
  neighbors.
• 3. What is the image or story of this course as
  portrayed in the paragraphs?

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Course Goals

• 1. As a table group, identify the 3 or 4 most
  important goal statements for this course.
• 2. Choose one goal and find the Performance
  Expectations in the Grades 6-8 standards that are
  prerequisite for this goal.
• 3. Look at the College Readiness Standards to see
  what correlations exist with this goal. What
  level of proficiency is needed for students to be
  college ready?

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Readiness Assessment

• Look at the content areas of Performance
  Expectations for your course.
• For each content area, rate how well-prepared you
  think that the teachers you work with (or
  yourself as a teacher) are to teach it
• 5 Teachers will know what this set of
  expectations is asking of students and they have
  materials to teach it.
• 1 Teachers dont understand this set of
  expectations and they dont have materials to
  teach it.
• What does this mean for your work for next year?

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Improving Mathematics Instruction in WA

• There are important differences between the GLEs
  and the Standards, so the changeover is an
  opportunity to rethink how mathematics is taught
  throughout Washington.

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Changing Expectations Reflection

• Each group discusses one question, records
  answers on chart paper, and posts the charts.
• 1. How are expectations in the High School
  Mathematics Standards different from the GLEs?
  (Differences)
• 2. What are some benefits of these changes?
  (Benefits)
• 3. What are some challenges that teachers might
  face? (Challenges)
• 4. What more do you need to learn to support
  implementation of these Standards? (Need to
  Learn)

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What to do Next Year From Your Perspective

• What will be the implications of the WA Standards
  on what you do or how you support teachers?
• What would you recommend for the teachers and
  campuses with whom you work?
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• Change
  Change
• Nothing
  Everything