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1 1 Project TIME Summer Symposium Green River Community College August 25, 2008 Susan Hudson Hull, PhD Dana Center, University of Texas at Austin Washington K-12 Standards in Transition

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2 Goals for this Session Provide 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 Consider implications for instruction and support 2

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3 2008 July 29OSPI Standards Document The WA High School Mathematics Standards are accompanied by the Mathematics Standards for Kindergarten—Grade 8. It is important to know what knowledge students will bring with them when they enter high school. 3

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4 2008 July 29OSPI 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 4

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5 2008 July 29OSPI 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 5

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6 2008 July 29OSPI Core Content Paragraphs for Each Part 6 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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7 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. They are NOT intended to be a course sequence. Numbering System Course Core Content Expectation A1.2.C 2008 July 29OSPI Performance Expectations 7

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8 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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9 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, nor do they always address every part of the standard.

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10 2008 July 29OSPI Balanced Program A well-balanced mathematics program for all students includes: Conceptual understanding Procedural proficiency Mathematical processes 10

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11 2008 July 29OSPI 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. 11

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12 2008 July 29OSPI 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. 12

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13 2008 July 29OSPI 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. 13

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14 2008 July 29OSPI 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. 14

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15 2008 July 29Standards PD: Day 2 AM A Look at the Standards 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. 15

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16 2008 July 29Standards PD: Day 2 AM 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. 16

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17 2008 July 29OSPI 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. 17

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18 2008 July 29OSPI Charge to Standards Revision Team Address these areas of concern: ContentRigor SpecificityClarity DepthCoherence MeasurabilityAccessibility Balance 18

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19 2008 July 29OSPI 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 Washington’s TMP College Readiness Mathematics Standards Benchmarks of National Mathematics Advisory Panel (after March, 2008) 19

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20 2008 July 29OSPI Process for Creating the Standards Oct: SRT met to develop outline of first draft; edit and articulation teams organized pre-draft. Oct–Dec: SRT met to develop drafts; edit and articulation teams organized drafts. Dec–Jan: Draft sent out for field review Feb: Revisions made for March 5 version Mar–July: 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. 20

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21 2008 July 29Standards PD: Day 2 AM 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. 21

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22 2008 July 29OSPI 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. 22

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23 Algebra 1 A1.1.Core Content: Solving Problems A1.2Core 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 A1.7Additional Key Content: Exponentials, Sequences, and Literal Equations A1.8.Core Content: Reasoning, Problem Solving, and Communication

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24 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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25 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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26 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 26

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27 2008 July 29High School Courses 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 27

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28 2008 July 29High School Courses 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 28

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29 2008 July 29High School Courses 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? 29

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30 2008 July 29OSPI Knowledge for College Readiness Let’s look at how the High School Mathematics Standards prepare students for learning mathematics for college readiness. 30

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31 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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32 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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33 2008 July 29High School Courses Course Content 1.As a table group, decide which high school course you want to examine. 2.Identify a core content area that is especially important for the course and read the performance expectations for the core content area. 3.Identify the performance expectations in Grades 6-8 that are “prerequisite” for the expectations in the core content area. 4.Look at the College Readiness Standards to see what correlations exist with the performance expectations in your core content area. What level of proficiency is needed for students to be college ready? 33

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34 2008 July 29OSPI 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. 34

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35 2008 July 29OSPI What makes WA HS Standards unique? There are standards now in WA that are not typically found in standards documents. Examples: Alg 1, Alg 2, M1, M2, M3 all start with solving problems to set the tone for the course Specific standards, such as A1.2.B/M1.6.C and G.3.K/M3.5.C move into 21st century skills Examples and comments exemplify the standards and stretch thinking, such as for G.6.A/M3.7.D What do you find? 35

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36 2008 July 29OSPI Implications for Instruction Find a performance expectation or an example that is new to you or that you think might be challenging to students. What will it take to help students meet this standard? With your group, develop an assessment task that exemplifies the standard. 36

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37 2008 July 29High School Courses 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 don’t understand this set of expectations and they don’t have materials to teach it. What does this mean for your work for next year? 37

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38 2008 July 29OSPI 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) 38

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39 2008 July 29OSPI 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? Change Nothing Everything 39

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