Washington K-12 Standards in Transition Transition Mathematics Project August 2008 Susan Hudson Hull, Dana Center, University of Texas at Austin Kristen

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 1

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

2

2008 July 29 OSPI

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

2008 July 29 OSPI

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/Examples4

2008 July 29 OSPI

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/Examples5

2008 July 29 OSPI

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.

6

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

2008 July 29 OSPI

Performance Expectations

7

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.

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.

2008 July 29 OSPI

Balanced Program

A well-balanced mathematics program for all students includes:

• Conceptual understanding

• Procedural proficiency

• Mathematical processes

10

2008 July 29 OSPI

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

2008 July 29 OSPI

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

2008 July 29 OSPI

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

2008 July 29 OSPI

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

2008 July 29 Standards PD: Day 2 AM

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.

15


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

2008 July 29 OSPI


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

2008 July 29 OSPI

Charge to Standards Revision Team

Address these areas of concern:

Content Rigor

Specificity Clarity

Depth Coherence

Measurability Accessibility

Balance

18

2008 July 29 OSPI

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

National Mathematics Advisory Panel:Major 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.

20

National Mathematics Advisory Panel:Major Findings

Effort: Research about how children learn should be used, 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 recall of facts; and

c) 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.

21

National Mathematics Advisory Panel:Specific 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)

22

2008 July 29 OSPI


Oct: SRT met in October 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.

23


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.

24

2008 July 29 OSPI

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.

25

2008 July 29 OSPI

Knowledge for College Readiness

Let’s look at how the High School Mathematics Standards prepare students for learning mathematics for college readiness.

26

Algebra 1 A1.1. Core Content: Solving ProblemsA1.2 Core Content: Numbers,Expressions and

OperationsA1.3. Core Content: Characteristics and Behaviors of

FunctionsA1.4. Core Content: Linear Functions, Equations and

RelationshipsA1.5. Core Content: Quadratic Functions and EquationsA1.6. Core Content: Data and DistributionsA1.7 Additional Key Content: Exponentials, Sequences

and Literal EquationsA1.8. Core Content: Reasoning, Problem Solving and

Communication

Geometry

G.1. Core Content: Logical Arguments and ProofsG.2. Core Content: Lines and AnglesG.3. Core Content: Two- and Three-Dimensional

FiguresG.4. Core Content: Geometry in the Coordinate

PlaneG.5. Core Content: Geometric TransformationsG.6. Additional Key Content: MeasurementG.7. Core Processes: Reasoning, Problem Solving

and Communication

Algebra 2 A2.1. Core Content: Solving ProblemsA2.2. Core Content: Numbers, Expressions, and

OperationsA2.3. Core Content: Quadratic Functions and

EquationsA2.4. Core Content: Exponential and Logarithmic

Functions and EquationsA2.5. Core Content: Additional Functions and

EquationsA2.6. Core Content: Probability, Data and

DistributionsA2.7. Additional Key Content: Systems and SeriesA2.8. Core Processes: Reasoning, Problem Solving

and Communication

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 30

2008 July 29 High 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

31


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

32

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.

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.


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?

35


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?

36


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

2008 July 29 OSPI

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.

38

2008 July 29 OSPI

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)

39

2008 July 29 OSPI

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 Change

Nothing Everything

40