LINKING STANDARDS, ASSESSMENTS, AND
INSTRUCTION IN MATHEMATICS
Presented by Gabriela Orozco Gonzalez
April 5, 2014Stockton Common Core Seminar
WELCOME Educator, I have taught K-6th Grade, currently teach 1st &
2nd Grade Combination class Language Arts Performance Task Writer & Mathematics
Item Reviewer for the Smarter Balanced Assessment Consortium
CTA Teacher Leadership Cohort and Professional Learning Trainer
NEA Teacher Ambassador for SBAC Representing California
Presentation Materials on my blog:
Commoncorecafe.blogspot.com
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LEARNING TARGETS Gain an awareness of the content and structure of the Common Core State Standards for Mathematics Understand the meaning of the Mathematical Practices in the CCSSM and apply the practices to your current classroom instruction Become familiar with a performance task and task planner
A BALANCED ASSESSMENT SYSTEM
Common Core State Standards
specify K - 12
expectations for college and career readiness
Common Core State Standards
specify K - 12
expectations for college and career readiness
All students leave
high school college -
and career- ready
All students leave
high school college -
and career- ready
Teachers and schools have
information and tools they need
to improve teaching and
learning
Interim assessments
Flexible, open, used for actionable
feedback
Interim assessments
Flexible, open, used for actionable
feedback
Summative assessments
Benchmarked to college and career
readiness
Summative assessments
Benchmarked to college and career
readiness
Teacher resources for formative
assessment practices
to improve instruction
Teacher resources for formative
assessment practices
to improve instruction
SIX ITEM TYPES
• Selected Response• Short Constructed Response• Extended Constructed Response• Performance Tasks
• Technology-Enabled• Technology-Enhanced
Focus for today
THE ASSESSMENT CHALLENGE
How do we get from here . . . . . . to here?
All studentsleave high school
college- and career-ready
All studentsleave high school
college- and career-ready
Common Core State Standards
specify K-12 expectations for
college and career readiness
Common Core State Standards
specify K-12 expectations for
college and career readiness
. . . and what can an assessment system
do to help?
Standards based NOT textbook basedYour text book is an AWESOME
resource/ reference book.
SMARTER BALANCED ASSESSMENTS ARE:
STANDARDS BASED INSTRUCTION Standards-based education is a process for planning,
delivering, monitoring and improving academic programs in which clearly defined academic content standards provide the basis for content in instruction and assessment.
Standards help ensure students learn what is important, rather than allowing textbooks to dictate classroom practice.
Student learning is the focus - aiming for a high and deep level of student understanding that goes beyond traditional textbook-based or lesson-based instruction.
TEACHERS GUIDE INSTRUCTION BASED ON STANDARDS
“The standards come alive when teachers study student work, collaborate with other teachers to improve their understanding of subjects and students’ thinking, and develop new approaches to teaching that are relevant and useful for them and their students.”
- Linda Darling-Hammond, 1997
CURRICULUMCurriculum Mapping is a long-range plan captured in a graphic organizer that represents a collection of Standards-based units. It is informed by the benchmarks and curriculum objective, student data, including an analyses of student work and projected assessment timelines. It is a document that should be modified based on student needs and reviewed and revised yearly.
CCSSM PLANNING AND IMPLEMENTATION Planning meetings with
grade level representatives: Examine Standards, then
Prioritize Pacing Overviews Assessment Calendar Unit Overviews and/or Unit
Plans Create Assessments Revise Assessments
DESIGN AND ORGANIZATIONStandards for Mathematical Practice Carry across all grade levels Describe habits of mind of a mathematically expert
student
Standards for Mathematical Content K-8 standards presented by grade level Domains:
Number and Operations Counting and Cardinality Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations—Fractions Measurement and Data
Geometry
DESIGN AND ORGANIZATION Content standards define what students should
understand and be able to do Clusters are groups of related standards Domains are larger groups that progress across grades
FOCAL POINTS & CRITICAL AREAS
Focal PointsFocal Points
Critical Area
PRIORITIZING THE CCSS STANDARDS
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WEBB'S DEPTH OF KNOWLEDGE (DOK) BLOOM'S TAXONOMY VS.
NORMAN WEBB'S DEPTH OF KNOWLEDGE
The Common Core Standards are the cornerstones of the Smarter Balanced assessments, Webb’s Depth of Knowledge (scale of cognitive demand) and Blooms Revised Taxonomy (levels of intellectual ability) are the framework and the structures that will be used to evaluate students.
Depth of knowledge, and complexity of knowledge is the heart of the more rigorous assessments being implemented in 2014. They share many ideas and concepts yet are different in level of cognitive demand, level of difficulty, complexity of verbs vs. depth of thinking required, and the scale of cognitive demand.
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During the planning process, refer to the DOK Levels
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3rd Grade Big Ideas
FORMATIVE: checking on learningas students progress
SUMMATIVE: checking on learningat the end of the learning experience
“When the cook tastes the soup, that’s formative; when the guests taste the soup, that’s summative.”
(Stake, 2005)
UNDERSTANDING ASSESSMENTS
CHALLENGES
Curriculum Collection of
Resources Assessments Professional
Learning
TEACHER STUDENT
Collaboration Explain/Justify
Problem Solving
PERFORMANCE TASK PLANNER
PERFORMANCE TASK PLANNER (SECOND PAGE)
COMMUNICATION, ENGAGEMENT, AND LEARNING
Model (Draw a picture or diagram, or make a
list, table, chart, or graph).
Numbers(Show how worked each part of the problem).
WordsTo solve this problem, first I had to
_____________________________. Then, I________________________. Next, I _______________________.After that, I ___________________. Finally, I found out that ________________________________________.
Answer
CCSSM AND REAL LIFE APPLICATION
I get a… If I…
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do nothing -or- just copy the prompt.
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write a number sentence that doesn’t go along with the prompt.do not write an explanation.
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use numbers from the prompt with an operation included.write an explanation telling what I did.
3
use numbers from the prompt.write number sentences that make sense, even if they are not the right answer.write a simple paragraph explaining what I did.
4
correctly answer most of computation that I write.write a paragraph explaining what I did. It can have minor mistakes, but it still makes sense. Anyone should be able to understand how I solved the prompt.
5
get the correct answer.make more than one table, diagram, chart, etc.write a detailed paragraph telling step-by-step what I did to solve the problem…and include what I was thinking as I solved it! (“I did this because…”)
Student Problem Solving
Rubric
STUDENTS NEED TO ENGAGE WITH
Grade-appropriate materials for exposure to structures, content, vocabulary;
Instructional-level materials that allow them to progress;
Easy materials that allow them to practice.If familiar/interesting, material can be more
challenging.
– More at K-12 Teachers: Building Comprehension in the Common Core
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TIMING MATTERS
Greater scaffolding is provided at the beginning of tasks.
Scaffolding supports an increasing level of complexity.
Include a plan for removing the scaffolding.
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ADVICE Time for Planning Ongoing Professional Development
Follow-up Coaching Patience and Understanding
CCSSM RESOURCES
Books Magazines
Technology Resources
DPI Wikihttp://www.ncdpi.wikispaces.net/http://maccss.ncdpi.wikispaces.net/home
CCSSM RESOURCES
Common Core State Standards Live Binder:http://www.livebinders.com/edit?id=133724
Resources: 21st Century Skills Common Core State Standards & Essential Standards Crosswalks Unpacking Documents Investigations & CCSSM Websites
MATH RESOURCESAegom Interactive Smartboard Lessonswww.aegom.com/
Video Resources
Annenberg Media Videos & Resources http://www.learner.org/resources/ browse. html?discipline=6
Discovery Education/United Streaming http://streaming.discoveryeducation.com/
MATH RESOURCES National Council of Teachers of Mathematics (NCTM)
www.nctm.org
http://illuminations.nctm.org/
Teaching Children Mathematics Magazines
COMMON CORE RESOURCES Tools for the Common Core Standardshttp://commoncoretools.wordpress.com/ Illustrative Mathematics (CCSS Tools & Resources)http://illustrativemathematics.org/standards Common Core Wiki (by Drew Polly)http://elemath.pbworks.com/w/page/30621644/common-core National Council of Teachers of Mathematicswww.nctm.orgwww.nctm.org/standards/mathcommoncore/