2008 August 22Overview Session Welcome Welcome to the professional development sessions that focus on the 9-12 Mathematics Standards for Washington. 1

2008 August 22 Overview Session

Welcome

Welcome to the professional development sessions that focus on the

9-12 Mathematics Standards for Washington.

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Facilitators

INSERT the names and affiliations

of facilitators

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Purposes of the Sessions

1. Present an overview of the 9-12 Mathematics Standards

2. Understand the organization of the Standards

3. Identify content specific to the high school courses

4. Examine the flow of content across grades

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Goals for the this Session

• Present an overview of the 9-12 Mathematics Standards

• Understand the organization of the Standards

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Standards Document

• The 9-12 Mathematics Standards are accompanied by the Mathematics Standards for Grades 6-8.

• It is important to know what knowledge students will bring with them when they enter high school.

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Organization of 6-8 Mathematics Standards

At each grade level:

• 3-4 Core Content areas

• Additional Key Content

• Core Processes (reasoning, problem solving, communication)

For each of these:

• Overview paragraph

• Performance Expectations

• Comments/Examples6


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:

• Overview paragraph

• Performance Expectations

• Comments/Examples7


Paragraphs for 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 or in each course. They provide clear guidance about the mathematics that is to be taught and learned.

Numbering System

Course Core Content Expectation

A1.2.C9


Explanatory Comments and Examples

Explanatory comments and examples, taken together with the Performance Expectations, provide a full context and understanding of the Expectations. The comments and examples expand upon the meaning of the Expectations.

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Detail about Comments and Examples

• Clarify the parameters regarding the type or size of numbers

• Provide more information regarding mathematical understanding

• Give expanded detail to the mathematical definitions, laws, principles, and forms

• Provide example problems typical of those that students should be able to solve, such as limits on expected levels of difficulty

•Serve as instructional illustrations to teachers

Explanatory Comments and Examples are not intended to limit either teaching of content or teaching

methods. 11


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?

When you are finished reading, discuss the information with your neighbors.

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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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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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Fundamental Principle

For all students to learn significant mathematics, content should be taught and

assessed in meaningful situations.

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Find the Content

Choose two ideas from the list below. In small groups, search the Standards to find (a) prerequisite content for each idea, (b) the first mention of each idea, and (c) the last mention of each idea. Keep track of the Performance Expectation numbers and page numbers where you find the information. Begin with Grade 6 standards.

1. domain of a function

2. congruence of triangles

3. exponential functions

4. variability in a set of data

5. rotations and reflections

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What do you notice?

1. What do you notice about how long students are given to “learn” an idea?

2. What are the implications of this for teachers?

3. What are the implications of this for students and parents/families?

4. What are the implications for curriculum?

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Reasons 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.

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Process for Creating the Standards

The State Board of Education contracted with Strategic Teaching to evaluate the GLEs.

That report was approved by the State Board in August 2007.

Then OSPI created a Standards Revision Team to revise the GLEs according to the criteria described in that report.

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Standards Revision Team

The Standards Revision Team (SRT) included teachers, district and ESD mathematics specialists and coaches, 2- and 4-year higher education faculty (mathematics and mathematics education), and business/community representatives.

The SRT worked both as a whole group and in grade-band teams (K-2, 3-5, 6-8, 9-12).

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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 SRT:

• Mathematics Standards from Massachusetts, California, Indiana, Georgia, Florida, Finland, Singapore

• Curriculum Focal Points from NCTM

• 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

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National Mathematics Advisory Panel (NMAP)

Final Report released on March 13, 2008.

• 45 Recommendations and Findings

• List of Major Topics of School Algebra

• List of Critical Foundations of Algebra

• Benchmarks for the Critical Foundations

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National Mathematics Advisory Panel:Major Findings

Teachers: “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.”

Instruction: “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 Panel:Major Findings

Effort: “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.”

Integrated Mathematics: “A search of the literature did not produce studies 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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Algebra for Everyone

The charge to the NMAP was to outline curriculum that would allow students to take Algebra 1 in Grade 8.

There is no policy of Algebra 1 in Grade 8 in Washington, so the “flow” of content in the K-8 Mathematics Standards is slightly different from flow of content outlined in the NMAP report.

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National Mathematics Advisory Panel: Critical Foundations of Algebra

• Fluency with Whole Numbers

• Fluency with Fractions

• Particular Aspects of Geometry and Measurement

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National Mathematics Advisory Panel: Algebra Recommendations

The Panel recommended that school algebra be consistently understood in terms of the Major Topics of School Algebra.

These topics were not separated by course, and there was little or nothing said about other high school content (geometry, probability, data analysis, statistics or precalculus).

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National Mathematics Advisory Panel: Major Topics of School Algebra

Symbols and Expressions

Linear Equations

Quadratic Equations

Functions

Algebra of Polynomials

Combinatorics and Finite Probability32


Approval of Standards

In 2008, the WA Legislature gave authority for approval of the Standards to the State Board of Education.

On July 30, 2008, the State Board is expected to approve the 9-12 Mathematics Standards.

Because legislation requires that the State Board approve the Standards, it is not possible to make changes in the approved version.

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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.

These professional development sessions are the start of what can become a coordinated effort among WA educators to help WA students learn mathematics better.

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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 9-12 Mathematics Standards are identical.

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Knowledge of Entering 9th Graders

Let’s look at how the K-8 Mathematics Standards “set up” students for learning mathematics in high school.

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Analysis of Grade-level Overview

1. Skim the Grade-Level Overview.

2. How is this “sequencing” of topics different from your perception of what students in K-8 have typically experienced?

3. How will this “sequencing” prepare your students in the future to learn high school mathematics?

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Tracing an Idea

Trace the development of direct variation across the standards, beginning in Grade 6.

1. Where does it start and end?

2. How does understanding develop?

3. Are there any grades/courses where direct variation is not addressed?

4. How would you know whether students understand direct variation?

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Related Policy Decidisions

During 2007-08 there were policy decisions about testing and

graduation requirements that may affect mathematics

instruction in high schools.

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Status of WASL for Grades 3-8

• mandated shortening of tests for grades 3-8

• new tests for grades 3-8

pilot new tests in Spring 2009

administer new tests in Spring 2010

• during 2008-2010 create diagnostic tools for grades 3-8

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Legislated Status of 10th-grade WASL

• By 2010 end-of-course tests will be created for Algebra 1 and Integrated Mathematics 1. Because high school standards were not approved until late July 2008, this schedule cannot be met.

• By 2011 end-of-course tests will be created for Geometry and Integrated Mathematics 2.

• All end-of-course tests should be ready by 2011.

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Legislated Status of 10th-grade WASL

• For the class of 2013, end-of-course tests may substitute for the 10th-grade WASL. The 10th-grade WASL will be based on the new high school standards.

• For the class of 2014, end-of-course tests will replace the 10th-grade WASL. In order to graduate, students will need to pass 2 end-of-course tests.

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Graduation Requirements: State Board of Education

• 3rd mathematics credit required for graduation for class of 2013 (legislated requirement)

• State Board of Education has set Algebra 2 or Integrated Mathematics 3 or CTE equivalents as the requirement (with a career choice option under specific circumstances)

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Graduation Requirements: Segmented Mathematics

Segmented Mathematics was NOT approved as an option to the WASL.

Consequently, Segmented Mathematics will disappear by 2014.

It will likely not be updated to align with the 9-12 Mathematics Standards.

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Graduation Requirements: Collection of Evidence

Collection of Evidence will continue to be an alternate way to meet graduation requirements.

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Curriculum Review Requirements

1. OSPI will recommend three basic curricula to State Board within 6 months of adoption of Mathematics Standards.

2. State Board submits comments about the recommendations to OSPI within 2 months after the recommendations are made.

3. Recommendations are finalized and OSPI adopts the recommendations at a date to be determined.

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Curriculum Review Projected Schedule

K-8:

Basic instructional materials review: June 22 -27, 2008

Supplemental materials review: Late Summer 2008

Finalize results with recommendations: October 2008

9-12:

Basic instructional materials review: To be determined

Supplemental materials review: To be determined47


Three Audiences

Group 1: Recent Adopters with a system in place

Group 2: Pending Adopters

Group 3: Districts with older materials and few resources

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Goals of Curriculum Review

1. Serve school districts –support districts over time with existing and new materials

2. Build a solid, clean, evidence-based process for reviewing basic and supplemental materials

3. Present three basic curricula recommendations for each of elementary, middle, and high school levels

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What to do Next Year

Where would you place yourself on this continuum?

<-------------------------------------------------------------------->

Change Change

Nothing Everything

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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 9-12 Mathematics Standards different from your previous practice? (Differences)

2. What are some benefits of these changes? (Benefits)

3. What are some challenges that you might face? (Challenges)

4. What do you need to learn in order to implement these Standards? (Need to Learn)

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Thank You

We hope you have a good overview of the 9-12 Mathematics Standards.

In later sessions you will focus more on the content of the Standards and develop more detailed understanding of the expectation for specific high school mathematics courses.

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