LINKING STANDARDS, ASSESSMENTS, AND INSTRUCTION IN MATHEMATICS Presented by Gabriela Orozco Gonzalez April 5, 2014 Stockton Common Core Seminar

WELCOME  Educator, I have taught K-6 th Grade, currently teach 1 st & 2 nd 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 Commoncorecafe.blogspot.com 2

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 Teachers and schools have information and tools they need to improve teaching and learning 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 students leave high school college- and career-ready 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 based Your text book is an AWESOME resource/ reference book. SMARTER BALANCED ASSESSMENTS ARE:

Standard Activities that address Standard Assessment

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

CURRICULUM Curriculum MappingCurriculum 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 ORGANIZATION Standards 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 Points Critical Area

PRIORITIZING THE CCSS STANDARDS 16

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 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. 17

During the planning process, refer to the DOK Levels 18

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3 rd Grade Big Ideas Standard Activities that address Standard Assessment

 FORMATIVE : checking on learning as students progress  SUMMATIVE: checking on learning at 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

Students experience inquiry-based methods of understanding key concepts Use of concrete representation when introducing new concepts Problem-based interactive learning should be the foundation in teaching for understanding Teachers implement strategies that help students develop understanding Utilize resources and methods beyond the adopted textbook Opportunities to work with small group instruction, enrichment, etc.

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). Words To solve this problem, first I had to _____________________________. Then, I________________________. Next, I _______________________. After that, I ___________________. Finally, I found out that __________ ______________________________. Answer

CCSSM AND REAL LIFE APPLICATIO N

I get a…If I… 0  do nothing -or-  just copy the prompt. 1  write a number sentence that doesn’t go along with the prompt.  do not write an explanation. 2  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 31

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. 32

ADVICE  Time for Planning  Ongoing Professional Development  Follow-up Coaching  Patience and Understanding

CCSSM RESOURCES Books Magazines Technology Resources

DPI Wiki

CCSSM RESOURCES Common Core State Standards Live Binder:  Resources:  21 st Century Skills  Common Core State Standards & Essential Standards  Crosswalks  Unpacking Documents  Investigations & CCSSM  Websites

MATH RESOURCES Aegom Interactive Smartboard Lessons

Video Resources  Annenberg Media Videos & Resources  browse. html?discipline=6  Discovery Education/United Streaming 

MATH RESOURCES  National Council of Teachers of Mathematics (NCTM)  Teaching Children Mathematics Magazines

COMMON CORE RESOURCES  Tools for the Common Core Standards  Illustrative Mathematics (CCSS Tools & Resources)  Common Core Wiki (by Drew Polly)  National Council of Teachers of Mathematics