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.

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

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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/