Because You Can’t Memorize
Understanding!
Supporting ELL Students in
Common Core Mathematics
Presented by: Katy Absten, K-12 Mathematics Specialist, OSPI Teaching and Learning
Washington Association for Bilingual Educators
April 12, 2014
Goals
• Understand the 3 shifts and 8 math practices
in the Common Core Mathematics Standards
and how they can support English Language
Learners’ mathematical achievement.
• Learn about research-based resources
available to support teachers of English
Language Learners.
• Engage in a math task using these resources!
CCSS - Equity for ALL Students
http://www.portlandoregon.gov/oehr/
Washington’s Vision for Education
Every Washington public school student will
graduate from high school globally
competitive for work and postsecondary
education and prepared for life in the 21st
century.
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Class of 2011: Bridgeport High School
Classroom Impact of CCSS
Content
Culture
Practices
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The Three Shifts in Mathematics
• Focus: Strongly where the
standards focus
• Coherence: Think across
grades and link to major
topics within grades
• Rigor: In major topics, pursue
with equal intensity:
– Conceptual understanding
– Procedural skill and
fluency
– Application
Shift One: Focus
Strongly Where the Standards Focus
• Significantly narrow the scope of
content and deepen how time and
energy is spent in the math classroom
• Focus deeply only on what is
emphasized in the standards, so that
students gain strong foundations
Shift One: Focus
strongly where the Standards focus
•
Move away from "mile wide, inch deep" curricula identified in
TIMSS.
•
Spend more time on foundational concepts to deepen
understanding
•
Focus is necessary in order to achieve the rigor set forth in the
standards
•
Teach less, learn more.
Less topic coverage can be associated with higher scores on those topics covered
because students have more time to master the content that is taught.”
– Ginsburg et al., 20059
WaToToM – March 7th-9th, 2014
Attaining Focus in early grades
K-2 is a deep focus on number, place value, and operation (addition
and subtraction) - concepts, skills and problem solving
3-5 builds on these foundational concepts and focuses on
multiplication and division of whole numbers and fractions concepts, skills and problems solving
There is very little data work in K-5, and what’s there is tightly
connected with core progressions in number systems, the number
line, and problem solving using the four operations
Concentration on arithmetic and the aspects of
measurement that support it
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Traditional K-12 U.S. Approach
K
Number and
Operations
Measurement
and Geometry
Algebra and
Functions
Statistics and
Probability
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Focus by Grade Level
Pre-K-8 Domains Progression
Domains
Counting and Cardinality
Operations and Algebraic Thinking
Number and Operations in Base Ten
Number and Operations - Fractions
Ratios and Proportional Relationships
The Number System
Expressions and Equations
Functions
Geometry
Measurement and Data
Statistics and Probability
PK
K
1
2
3
4
5
6
7
8
Grade Level Focus
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Shift Two: Coherence
Think across grades, and link to major topics
within grades
• Carefully connect the learning within and across grades so
that students can build new understanding onto foundations
built in previous years.
• Begin to count on solid conceptual understanding of core
content and build on it. Each standard is not a new event, but
an extension of previous learning.
Coherence
“The Standards are not so much
built from topics as they are woven
out of progressions.”
Structure is the Standards, Publishers’ Criteria for Mathematics, Appendix
http://ime.math.arizona.edu/progressions/
Progression of Learning
Grade 3
Grade 4
Grade 5
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K-5 – NBT Progression Document
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Coherence Within Grades
3.OA.B
3.MD.C.7
Relate area to the
operations of
multiplication &
addition.
Understand
properties of
multiplication …
3.G.A
Reason with
shapes and their
attributes.
The standards make explicit connections
at a single grade
Shift Three: Rigor
Equal intensity in conceptual understanding,
procedural skill/fluency, and application
• The CCSSM require:
– Solid conceptual understanding
– Procedural skill and fluency
– Application of mathematics to problem solving
situations
• In the major work of the grade, this requires
equal intensity in time, activities, and
resources in pursuit of all three.
Required Fluencies in K-6
Grade
Standard
Required Fluency
K
K.OA.5
Add/subtract within 5
1
1.OA.6
Add/subtract within 10
2.OA.2
Add/subtract within 20 (know single-digit sums from memory)
2
3
2.NBT.5
3.OA.7
Add/subtract within 100
Multiply/divide within 100 (know single-digit products from memory)
3.NBT.2
Add/subtract within 1000
4
4.NBT.4
Add/subtract within 1,000,000
5
5.NBT.5
Multi-digit multiplication
6
6.NS.2,3
Multi-digit division
Multi-digit decimal operations
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Conceptual Understanding is more
than explaining
What are two
different
equations with
the same solution
as 3(y – 1) = 8?
Asking students to show work
and explain can be
informative, but it isn’t the
only way to assess conceptual
understanding and can
become tiring for students.
Procedural Fluency is not all about
Timed Tests
Find the number
that goes into each
box:
A) 𝟑 + 𝟒 = □
B) 5 + □ = 8
C) □ - 2 = 6
D) 9 - □ = 5
E) □ + □ = 10
“Reasoning and pattern
searching are never
facilitated by restricted
time….strategy
development and general
number sense are the best
contributors to fact
mastery.”
--Van de Walle
Applications should be motivating for
students
What is the
relationship
between the
height you drop a
ball and it’s
corresponding
bounce height?
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of
others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
The practices live within the content.
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Describes mathematical “habits of mind” that
students at ALL grade levels should develop.
STATE-WIDE NETWORK
Ongoing: Statewide Coordination and Collaboration to
Support Implementation
(Professional Learning Providers and Partners Across WA )
Washington
Including:
• School Districts (CCSS District Implementation Network)
• Higher Education
• Education and Educator Content Associations
• Business Partners
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OSPI Math Webinar_Part 3_ 3-26-2014
• I will send another slide about signing up for
movers and shakers—how to stay connected.
RESOURCES
CCSS Implementation Resources
Top Resources – Big Picture
Achieve The Core www.achievethecore.org
Resources included annotated tasks, practice guides, assessment guides,
instructional materials toolkit
Assessment System Resources www.smarterbalanced.org
Smarter Balanced Released Sample Items / Performance. Tasks
Smarter Balanced Practice & Training Tests
http://www.smarterbalanced.org/practice-test/
Achieve www.achieve.org
Multiple array of resources to support implementation of CCSS
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Top Resources - Math
Illustrative Mathematics Project www.illustrativemathematics.org
Takes available aligned to the CCSS that illustrate the standards. These tasks have been vetted by
leaders in the nation for alignment and quality.
Progression Documents http://ime.math.arizona.edu/progressions/
These documents give the narrative or story of how the domains progress both in a particular grade
and through several grades.
Engage NY http://www.engageny.org/
Engage NY is building out units in ELA and mathematics that are aligned to the CCSS
Inside Mathematics http://www.insidemathematics.org/
Video excerpts of mathematics lessons correlated with the practice standards, resources on content
standards alignment, and videos of exemplary lessons in both elementary and secondary settings.
Publishers Criteria http://www.achievethecore.org/downloads/Math_Publishers_Criteria_K8_Summer_2012.pdf Provides criteria for aligned materials to CCSS. Based on the two major evidencebased design principles of the CCSSM, focus and coherence, the document intends to guide the work of
publishers and curriculum developers, as well as states and school districts, as they design, evaluate,
and select materials or revise existing materials.
NWMC 10/11/13
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CCSS-M Implementation Resources
Top Resources – Big Picture
Achieve The Core www.achievethecore.org
Resources included annotated tasks, practice guides, assessment guides,
instructional materials toolkit
Illustrative Mathematics Project www.illustrativemathematics.org
Takes available aligned to the CCSS that illustrate the standards. These tasks
have been vetted by leaders in the nation for alignment and quality.
Achieve www.achieve.org
Multiple array of resources to support implementation of CCSS
Assessment System Resources www.smarterbalanced.org
Smarter Balanced Practice Test/Released Sample Items & Performance Tasks
CCSS-M Implementation Resources
Top Resources - Math
Progression Documents http://ime.math.arizona.edu/progressions/
These documents give the narrative or story of how the domains progress both in a
particular grade and through several grades.
Engage NY http://www.engageny.org/
Engage NY is building out units in ELA and mathematics that are aligned to the CCSS
Inside Mathematics http://www.insidemathematics.org/index.php/home
Classroom examples and tools for innovative instruction, and videos of instructional
practices aligned to the CCSS
Mathematics Assessment Project http://map.mathshell.org/materials/index.php
The Mathematics Assessment Program (MAP) aims to bring to life the Common Core State
Standards (CCSSM and exemplify CCSSM in engaging tasks, performance assessments and
lessons grounded in formative assessment.
Opportunities to be involved
Movers and Shakers
http://k12.wa.us/Mathematics/default.aspx
OSPI CCSS Webinar Series
https://www.k12.wa.us/CoreStandards/updatesevents.aspx
PD Offered through all 9 ESDs
Check with your local ESD to determine what professional
learning opportunities are available.
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Resources to support English
Language Learners in Mathematics
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Goal of the Understanding Language
materials
Illustrate how mathematics tasks that are
aligned with the Common Core State
Standards (CCSS) for Math can be used to
support mathematics instruction and the
learning of English Language Learners (ELLs),
at three grade spans (elementary, middle,
and high school).
ELLs develop mathematical proficiency as well as the linguistic
resources to express that proficiency by actively participating in
mathematical practices and rigorous mathematical reasoning that is
well scaffolded by instruction.
These resources are based on the premise that the
eight Common Core Standards for Mathematical
Practice focus on key aspects of mathematical
expertise and set expectations for students to be
engaged in mathematical activities that, over time,
simultaneously build:
• procedural fluency,
• conceptual understanding, and
• mathematical reasoning and sense making
Although learning vocabulary may be
necessary, it is not sufficient.
• Learning to communicate mathematically and
participate in mathematical discussions is not
simply a matter of learning vocabulary.
• During discussions in mathematics
classrooms, students are learning to describe
relationships, make generalizations, and use
representations to support their claims.
The question is not whether students who are ELLs
should learn vocabulary but rather how instruction
can best support students to learn vocabulary as they
actively engage in mathematical reasoning about
important mathematical topics.
Therefore, these materials and recommendations
stress the importance of creating (and supporting
students in) engaging rich mathematical
discussions.
Key Principles
• Focus on students’ mathematical reasoning,
not accuracy in using language
• Focus on mathematical practices, not
language as single words or definitions
• Recognize the complexity of language in
mathematics classrooms & supports students
in engaging in this complexity
• Treat everyday and home languages as
resources, not obstacles
Sample Mathematics Tasks
• We used or adapted tasks from two publicly
accessible curriculum projects, Inside
Mathematics and Mathematics Assessment
Project.
• The mathematics tasks with annotations
(available on the UL web site) provide
examples of how teachers can use a
mathematics task that is aligned with the CCSS
when working with ELLs.
Language of Mathematics Tasks
TASKS TO SUPPORT READING MATHEMATICS
PROBLEM
• Reading and Understanding a Mathematics
Problem
• Jigsaw Reading
TASKS TO SUPPORT VOCABULARY FOR
MATHEMATICAL COMMUNICATION
• Vocabulary Review Jigsaw
• Mathematically Speaking
• Vocabulary Pieces, Roots, and Families
READING AND UNDERSTANDING A
MATHEMATICS PROBLEM
• Step 1. Read the problem out loud to a peer. Try to answer this
question: What’s the problem about?
• Step 2. Read the problem again. Talk to your partner about these
questions: What is the question in the problem? What are you
looking for? (Hint: Look at the end of the problem for question.)
• Step 3. Read the problem a third time. Talk to your partner about
these questions.
– What information do you need to solve the problem? (What do you
want to know?)
– What information do you have? (What do you know?)
– What information are you missing? (What don’t you know?)
– Draw a diagram of the problem and label all the information you
know.
http://mathandlanguage.edc.org/
Mathematical Thinking: Supports for
English Language Learners
A website born from the Fostering Mathematical
Success for English Language Learners1(FMSELL)
project carried out by the Education
Development Center, Inc. in collaboration with
Horizon Research, Inc. The site is primarily
designed for math educators of English Learners
in the middle grades. The site's content includes
14 mathematics tasks from The Fostering
Geometric Thinking Toolkit2, as well as a set of
support tools for each of the tasks.
5 types of support tools accompany each task.
Printable PDFs are of sets of tasks and tools
available for free download.
• Warm-ups help give teachers an idea of students' prior knowledge,
provide scaffolding, and reinforce some of the academic language
used in the task.
• Sentence starters & frames help reinforce some of the
mathematical sentence structures useful in solving the problem and
facilitate the development of academic language.
• Word charts break down key words and phrases in the task,
identifying cognates, related terms, and meanings in Common
English versus Academic English.
• Support notes help make teachers aware of the nuances and other
potential points of confusion in the language used in the task.
• Spanish translation of the task
Communications Campaign
• Ready Washington is a coalition of state
and local education agencies,
associations and advocacy organizations
that support college- and career-ready
learning standards. Their audience is public
(parents, community, educators, lawmakers)
to build awareness and support for CCSS,
prepare for initial decline in test scores in
transition to more rigorous assessments and
counter misinformation/myths.
*
www.ReadyWA.org
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Current Resources for Communities
and Families
• Website designed to provide accurate information on the CCSS:
• http://thecommoncore.com/
• The Common Core State Standards: An Introduction for Families
and Other Stakeholders (from the Aspen Institute)
http://www.aspeninstitute.org/publications/common-core-state-standardsintroduction-families-other-stakeholders
– Flyers in Spanish and English for download
• OSPI’s CCSS Web Site:
http://www.k12.wa.us/CoreStandards/Families/default.aspx
• National PTA Parent Guides
• Parent Roadmaps to the CCSS – from the Council
for Great City Schools
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SMARTER BALANCED ASSESSMENT
SYSTEM
Improving Teaching & Learning
Common
Core State
Standards
specify
K-12
expectations
for college
and career
readiness
Summative:
College and career
readiness
assessments for
accountability
Teachers and
schools have
information and
tools they need to
improve teaching
and learning
Formative
Interim:
resources:
Flexible and open
Digital Library with
assessments, used
instructional and
for actionable
professional learning
feedback
resources for
educators to improve
instructionOSPI Math Webinar_Part 3_ 3-26-2014
All students
leave
high school
college
and career
ready
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✔
Balanced Assessment
Summative
Assessments for
Accountability
✔
✔
•Coverage of full breadth/depth of Common Core
•Computer Adaptive Testing (CAT)
• Precise assessment of all students
• More engaging assessment experience
•Performance Tasks – real world problems
Interim
Assessments to
Signal Improvement
Formative Tools and
Resources for
Improved
Instruction
•Optional for district, school or classroom use
•Fully aligned with Common Core – same item pool
•Focus on set of standards or mirror summative test
•Teachers can review and score responses
•Digital library gives access to high-quality resources
•Tools/materials for classroom-based assessments
•Professional social networking (Web-based PLCs)
•Useful for in-service and pre-service development
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Resources in the Digital Library
Assessment
Literacy Modules
Exemplar
Instructional Modules
• Commissioned professional development modules
• Resources for students and families
• Frame formative assessment within a balanced assessment system
• Articulate the formative assessment process
• Highlight formative assessment practices and tools
• Commissioned professional development modules
• Instructional materials for educators
• Instructional materials for students
• Demonstrate/support effective implementation of the formative process
• Focus on key content and practice from the Common Core State
Standards for Mathematics and English Language Arts
• High-quality vetted instructional resources and tools for educators
• High-quality vetted resources and tools for students and families
Education Resources
• Reflect and support the formative process
• Reflect and support the Common Core State Standards for Mathematics
and English Language Arts
• Create Professional Learning Communities
* Resources include the following file types: Video, HTML5, Audio,
PPT,Math
Excel,Webinar_Part
Word, and PDF. 3_
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