Washington K-12 Standards in
Transition
Project TIME Summer Symposium
Green River Community College
August 25, 2008
Susan Hudson Hull, PhD
Dana Center, University of Texas at Austin
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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
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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.
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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 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 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
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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, nor do they always
address every part of the standard.
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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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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.
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Standards PD: Day 2 AM
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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 10thgrade 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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Standards PD: Day 2 AM
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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
Specificity
Depth
Measurability
Balance
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Rigor
Clarity
Coherence
Accessibility
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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
• Washington’s TMP College Readiness Mathematics Standards
• Benchmarks of National Mathematics Advisory Panel
(after March, 2008)
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Process for Creating the Standards
Oct:
Oct–Dec:
Dec–Jan:
Feb:
Mar–July:
May:
July:
Aug:
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SRT met to develop outline of first draft; edit and
articulation teams organized pre-draft.
SRT met to develop drafts; edit and articulation teams
organized drafts.
Draft sent out for field review
Revisions made for March 5 version
Strategic Teaching review and edits; field review
K-8 adopted
Algebra 1, Geometry, Algebra 2 adopted
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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Standards PD: Day 2 AM
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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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Algebra 1
A1.1.
A1.2
A1.3.
A1.4.
A1.5.
A1.6.
A1.7
A1.8.
Core Content: Solving Problems
Core Content: Numbers,Expressions, and
Operations
Core Content: Characteristics and Behaviors of
Functions
Core Content: Linear Functions, Equations, and
Relationships
Core Content: Quadratic Functions and Equations
Core Content: Data and Distributions
Additional Key Content: Exponentials, Sequences,
and Literal Equations
Core Content: Reasoning, Problem Solving, and
Communication
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Geometry
G.1.
G.2.
G.3.
G.4.
G.5.
G.6.
G.7.
Core Content: Logical Arguments and Proofs
Core Content: Lines and Angles
Core Content: Two- and Three-Dimensional
Figures
Core Content: Geometry in the Coordinate
Plane
Core Content: Geometric Transformations
Additional Key Content: Measurement
Core Processes: Reasoning, Problem Solving,
and Communication
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Algebra 2
A2.1.
A2.2.
A2.3.
A2.4.
A2.5.
A2.6.
A2.7.
A2.8.
Core Content: Solving Problems
Core Content: Numbers, Expressions, and
Operations
Core Content: Quadratic Functions and
Equations
Core Content: Exponential and Logarithmic
Functions and Equations
Core Content: Additional Functions and
Equations
Core Content: Probability, Data, and
Distributions
Additional Key Content: Systems and Series
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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High School Courses
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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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High School Courses
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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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High School Courses
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Knowledge for College Readiness
Let’s look at how the High School
Mathematics Standards prepare students
for learning mathematics for college
readiness.
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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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Course Content
1.
2.
3.
4.
As a table group, decide which high school course you
want to examine.
Identify a core content area that is especially important for
the course and read the performance expectations for the
core content area.
Identify the performance expectations in Grades 6-8 that
are “prerequisite” for the expectations in the core content
area.
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?
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High School Courses
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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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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?
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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.
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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 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?
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High School Courses
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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?
<-------------------------------------------------------------------->
Change
Change
Nothing
Everything
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