Preparing K-5 Students for the Focus, Coherence and Rigor of the Common Core State Standards for Mathematics

Preparing K-5 Students for the Focus, Coherence and Rigor of the Common Core

State Standards for Mathematics

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Shelbi K. Cole, Ph.D.Smarter Balanced Director of Mathematics

September 24, 2013

"The world is small now, and we're not just competing with students in our county or across the state. We are

competing with the world," said Robert Kosicki, who graduated from a Georgia high school this year after

transferring from Connecticut and having to repeat classes because the curriculum was so different. "This is a move away from the time when a student can be punished for

the location of his home or the depth of his father's pockets."

Excerpt from Fox News, Associated Press. (June 2, 2010) States join to establish 'Common Core' standards for high school graduation.

Common Core State Standards

• Define the knowledge and skills students need for college and career

• Developed voluntarily and cooperatively by states; more than 40 states have adopted

• Provide clear, consistent standards in English language arts/literacy and mathematics

Source: www.corestandards.org

What questions will we try to answer today?

• How can teachers plan lessons that take

into account the shifts in the CCSS-M and

meet the needs of all learners?

• How will the new assessment system help

educators understand what students have

learned and how to support their future

learning?

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The Three Shifts: What do they really mean?

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The Background of the Common Core

Initiated by the National Governors Association (NGA) and Council of Chief State School Officers (CCSSO) with the following design principles:

• Result in college and career readiness

• Based on solid research and practice evidence

• Focused, coherent and rigorous

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The CCSSM Requires 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 conceptual understanding, procedural skill and fluency, and application with equal intensity

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Mathematics topics

intended at each grade by

at least two-thirds of A+

countries

Mathematics topics intended at each grade by at least two-thirds of 21 U.S. states

Shift #1: Focus Strongly where the Standards FocusThe shape of math in A+ countries

1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002). 8

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Shift #1: Focus Traditional U.S. Approach

K 12

Number and Operations

Measurement and Geometry

Algebra and Functions

Statistics and Probability

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GradeFocus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding

K–2Addition and subtraction - concepts, skills, and problem solving and place value

3–5Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving

6Ratios and proportional reasoning; early expressions and equations

7Ratios and proportional reasoning; arithmetic of rational numbers

8 Linear algebra and linear functions

Shift #1: Focus Key Areas of Focus in Mathematics

Shift #1: FocusContent Emphases by Cluster

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The Smarter Balanced Content Specifications help support focus by identifying the content emphasis by cluster. The notation [m] indicates content that is major and [a/s] indicates content that is additional or supporting.

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Shift #2: 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 on 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.

Shift #2: CoherenceThink Across Grades

Example: Fractions

“The coherence and sequential nature of mathematics dictate the foundational skills that are necessary for the learning of algebra. The most important foundational skill not presently developed appears to be proficiency with fractions (including decimals, percents, and negative fractions). The teaching of fractions must be acknowledged as critically important and improved before an increase in student achievement in algebra can be expected.”

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Source: Final Report of the National Mathematics Advisory Panel (2008, p. 18)

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Shift #2: CoherenceThink Across Grades

4.NF.4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

5.NF.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

5.NF.7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

6.NS. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

6.NS.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

Grade 4

Grade 5

Grade 6

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Shift #2: Coherence Link to major work within grade

Example: Data Representation

Standard 3.MD.3

Shift #3: Rigor In Major Topics, Pursue Conceptual

Understanding, Procedural Skill and Fluency, and Application

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• The CCSSM require a balance of: Solid conceptual understanding Procedural skill and fluency Application of skills in problem solving

situations

• Pursuit of all threes requires equal intensity in time, activities, and resources.

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Grade Standard Required Fluency

K K.OA.5 Add/subtract within 5

1 1.OA.6 Add/subtract within 10

2 2.OA.22.NBT.5

Add/subtract within 20 (know single-digit sums from memory)Add/subtract within 100

3 3.OA.73.NBT.2

Multiply/divide within 100 (know single-digit products from memory)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 divisionMulti-digit decimal operations

Shift #3: RigorRequired Fluencies for Grades K-6

• Students can use appropriate concepts and procedures for application even when not prompted to do so.

• Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS.

• Teachers in content areas outside of math, particularly science, ensure that students are using grade-level-appropriate math to make meaning of and access science content.

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Shift #3: RigorApplication

Resources

• www.achievethecore.org

• http://corestandards.org/assets/Math_Publishers_Criteria_K-8_Summer%202012_FINAL.pdf

• www.illustrativemathematics.org

• www.pta.org/4446.htm

• commoncoretools.me

• www.corestandards.org

• http://math.arizona.edu/~ime/progressions/#products

• http://www.smarterbalanced.org/k-12-education/common-core-state-standards-tools-resources/

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http://www.achievethecore.org/

http://corestandards.org/assets/Math_Publishers_Criteria_K-8_Summer%202012_FINAL.pdf

http://corestandards.org/assets/Math_Publishers_Criteria_K-8_Summer%202012_FINAL.pdf

http://www.illustrativemathematics.org/

http://www.pta.org/4446.htm

http://commoncoretools.me/

http://www.corestandards.org/

https://by2prd0811.outlook.com/owa/redir.aspx?C=Y-79v0cLCk-zl92fHN2uycAy80bbY88IBG91sm_G258nR9VNvuwFkDU1yMiJ7GUwZxGOh3bnIIk.&URL=http://math.arizona.edu/~ime/progressions/#products

http://www.smarterbalanced.org/k-12-education/common-core-state-standards-tools-resources/




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Five Basic Characteristics to Support Quality Mathematics Teaching

• Precision: Mathematical statements are clear and unambiguous. At any moment, it is clear what is known and what is not known.

• Definitions: They are the bedrock of the mathematical structure. They are the platform that supports reasoning. No definitions, no mathematics.

• Reasoning: The lifeblood of mathematics. The engine that drives problem solving. Its absence is the root cause of teaching and learning by rote.

• Coherence: Mathematics is a tapestry in which all the concepts and skills are interwoven.

• Purposefulness: Mathematics is goal-oriented, and every concept or skill is therefore a purpose. Mathematics is not just fun and games.

(Wu, 2011)

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“Just as technicians in any kind of engineering must have a ‘feel’ for their profession in order to avert disasters in the myriad of unexpected situations they are thrust into, mathematics teachers need to know something about the essence of mathematics in order to successfully carry out their duties in the classroom.”

(Wu, 2011)

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Topic 1: FractionsThe Progression Across Grades 3-5

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Definition of “fraction”

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3.NF.A Develop understanding of fractions as numbers.

• On a piece of paper, draw a line segment that is 6 inches long.

• Label the left endpoint 0 and the right endpoint 3.

• Locate and label the numbers 1 and 2 on the number line with respect to locations of 0 and 3.

• Locate and label the numbers 1/3, 5/3, and 9/3.

If you were doing this with Grade 3 students, would you change any direction above? What additional support may be needed? Why?

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3.NF.A Develop understanding of fractions as numbers.

• Next, label all fractions with denominator 3 along the part of the number line you have drawn.– How many fractions with denominator 3 do

you have labeled?

• Discuss with your table: What parallels are there between how whole numbers are introduced in kindergarten and this introduction to fractions?

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Which standards were addressed in the activity so far?

• 3.NF.A Develop understanding of fractions as numbers.

• 3.NF.A.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

• 3.NF.A.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

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Which aspects of this standard have been addressed so far?

• 3.NF.A.3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

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A Brief DetourThe Parallel Curriculum Model

What is the Parallel Curriculum Model?

The Parallel Curriculum Model is a set of four interrelated designs that can be used singly, or in combination, to create or revise existing curriculum units, lessons, or tasks. Each of the four parallels offers a unique approach for organizing content, teaching, and learning that is closely aligned to the special purpose of each parallel.

The Parallel Curriculum Model

CURRICULUMOF CONNECTIONS

CURRICULUM OFPRACTICE

CURRICULUMOF

IDENTITY

CORE CURRICULUM

Why Four Parallels?

• Qualitatively differentiated curriculum isn’t achieved by doing only one thing or one kind of thing.

• Students are different.

• Students have different needs at different times in their lives.

• Students’ styles, talents, interests, environments and opportunities are different.

• Students have different levels of expertise.

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Four Facets of Qualitatively Differentiated Curriculum

• Core: The essential nature of a discipline

• Connections: The relationships among knowledge

• Practice: The applications of facts, concepts, principles, skills, and methods as scholars, researchers, developers, or practitioners

• Identity: Developing students’ interests and expertise, strengths, values, and character

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Concepts, Principles and Skills

• Concepts:A general idea or understanding, especially a generalized idea of a thing or class of things; a category or classification

• Principles: Fundamental truths, laws, doctrines, or rules, that explain the relationship between two or more concepts

• Skills: Proficiency, ability, or technique, strategy, method or tool

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Building a CCSS-Aligned Lesson

• Discuss the number line activity. – How would you implement a similar activity

with students in a grade 3 classroom?– How can you determine if students are

successful on individual standards while still building important connections across standards?

– Should there be something that precedes the number line activity in introducing fractions to grade 3 students? If so, what does it look like?

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Learning from the Group

DON’T start filling in the lesson template before hearing the GOOD IDEAS of other educators working on the SAME THING.

The Common Core State Standards offer new opportunity for collaboration so that TOGETHER we can build and gather the BEST RESOURCES for students.

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Work Time

• Begin to populate the template with some of the ideas we’ve heard that represent important learning opportunities for students.

• But first, let’s take a look at the lesson plan template.

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Increasing Engagement, Thinking Across Grades

• Grade 1 – 1.OA.A (standards 5&6)

• Grade 2 – 2.MD.B (standards 5&6)

• Grade 3 – 3.NF.A (standard 3)

• Grade 4 – 4.NF.A (standards 1&2)

• Grade 4 – 4.NF.C (standards 5-7)

• Grade 5 – 5.NF.B (standards 3&4)Create a task or learning opportunity that relates the content of the indicated standards to the number line.Materials allowed: Ruler, Sidewalk chalk

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• And the number line remains relevant even after grade 5…

Grade 3

3.NF.A.3b Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

Grade 7

Grade 8

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Beyond the Number Line: Other Representations that Support Student

Understanding of Fractions

• What fraction is represented by the shaded area?

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Notice the use of “represented.” The shaded area is not “equal” to a fraction.

• The fraction represented by the shaded area is ¾. Based on this:– Draw an area that represents ¼.– Draw an area that represents 1.

• The fraction represented by the shaded area is equal to 3/2. Based on this:– Draw an area that represents ½. – Draw an area that represents 1.

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Linking Operations with Fractions to Operations with Whole Numbers

“Children must adopt new rules for fractions that often conflict with well-established ideas about whole number” (p.156)

Bezuk & Cramer, 1989

Fractions Example

The shaded area represents 3/2. Drag the figures below to make a model that represents 3 x 3/2.

BA C D

Slide 46

Student A drags three of shape B, which is equal in area to the shaded region. This student probably has good understanding of cluster 5.NF.B he knows that 3 x 3/2 is equal to 3 iterations of 3/2. Calculation of the product is not necessary because of the sophisticated understanding of multiplication.

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Slide 47

Student B reasons that 3 x 3/2 = 9/2 = 4 ½. She correctly reasons that since the shaded area is equal to 3/2, the square is equal to one whole, and drags 4 wholes plus half of one whole to represent the mixed number.


Note that unlike the previous chain of reasoning, this requires that the student determines how much of the shaded area is equal to 1.

Slide 48

Student C multiplies 3 x 3/2 = 9/2. She reasons that since the shaded area is 3/2, this is equal to 3 pieces of size ½. Since 9/2 is 9 pieces of size ½, she drags nine of the smallest figure to create her model.


This chain of reasoning links nicely back to the initial development of 3/2 in 3.NF.1 “understand a fraction a/b as the quantity formed by a parts of size 1/b, illustrating the coherence in the standards across grades 3-5.

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How can K-2 work on operations with whole numbers and work on fractions in grade 3 support students’

thinking about these problems in grades 4 & 5?

4 5

2?

4 5

2?

Even before learning the exact sum, can students tell you between which two whole numbers the

answer lies?

Even before learning the exact product, what can students tell you about

the value of the product?

At what grade should students be able to solve these problems?

1

3

1

3

1

?

1

3

2

5

2

3

1

10

4

6

?

?

Explain the flaw in the chain of reasoning.In the first group, 3/5 of the cats have spots. In the second group, 1/3 of the cats have spots. All together, 4/8 of the cats have spots.

Therefore, 3/5 + 1/3 = 4/8.

Closing Task – Fractions

• You have 4 strips of paper each 1 foot in length.– Partition one into thirds.– Partition one into fifths.– Partition one into eighths.

– Use the ruler as needed. – How can the strips be used to compare fractions? – What is the length, in inches, of each partition?

Assume that the strip is exactly one foot and each of your partitions is exactly equal.

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53

Topic 2: Whole Numbers

0

3/2

1 + 3 = ?

Operations with fractions should be a natural extension of operations with whole numbers

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2 4 5

0

1 3

1

2

3

2?

1/2 2/2 4/2

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Future impact

1.OA.B Understand and apply properties of operations and the relationship between addition and subtraction.1.OA.B.3. Apply properties of operations as strategies to add and subtract.3 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)1.OA.B.4. Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8..

Future impact

1.OA.C Work with addition and subtraction equations.1.OA.C.7. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.1.OA.C.8. Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? – 3, 6 + 6 = ?

Within grade impact

• Look at the grade 2 standards in the domains NBT and OA. Discuss how the standards in NBT might be integrated with the standards for OA to create problems that challenge mathematically talented students.

• Develop a problem that integrates concepts and skills from the two domains to increase the level of challenge. (You may use online resources such as Illustrative Math to find a base task and then further differentiate.)

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Smarter Balanced Assessment Consortium

An Assessment System to Support Teaching and Learning

The Assessment Challenge

How do we get from here... ...to here?

All studentsleave high school

college and career ready


specify K-12 expectations for

college and career readiness

...and what can an assessment system

do to help?

Concerns with Today's Statewide Assessments

• Each state bears the burden of test development; no economies of scale

Each state pays for its own assessments

• Students in many states leave high school unprepared for college or careerBased on state standards

• Inadequate measures of complex skills and deep understandingHeavy use of multiple choice

• Tests cannot be used to inform instruction or affect program decisions

Results delivered long after tests are given

• Difficult to interpret meaning of scores; concerns about access and fairness

Accommodations for special education and ELL students vary

• Costly, time consuming, and challenging to maintain securityMost administered on paper

The Purpose of the Consortium

• To develop a comprehensive and innovative assessment system for grades 3-8 and high school in English language arts and mathematics aligned to the Common Core State Standards, so that...

• ...students leave high school prepared for postsecondary success in college or a career through increased student learning and improved teaching

[The assessments shall be operational across Consortium states in the 2014-15 school year]

• 26 member states and territories representing 39% of K-12 students

• 22 Governing States, 3 Advisory States, 1 Affiliate Member

• Washington state is fiscal agent

• WestEd provides project management services

A National Consortium of States

Theory of Action Built on Seven Key Principles

1. An integrated system2. Evidence-based approach3. Teacher involvement4. State-led with transparent governance5. Focus: improving teaching and learning6. Actionable information – multiple

measures7. Established professional standards

A Balanced Assessment System


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

learningInterim assessments

Flexible, open, used for actionable

feedback

Summative assessments

Benchmarked to college and career

readiness

Teacher resources for formative

assessment practices

to improve instruction

A Balanced Assessment System

School Year Last 12 weeks of the year*

DIGITAL LIBRARY of formative tools, processes and exemplars; released items and tasks; model curriculum units; educator training; professional development tools and resources; scorer training modules; and teacher collaboration tools.

ELA/Literacy and Mathematics, Grades 3-8 and High School

Computer AdaptiveAssessment and

Performance Tasks

Computer AdaptiveAssessment and

Performance Tasks

Scope, sequence, number and timing of interim assessments locally determined

*Time windows may be adjusted based on results from the research agenda and final implementation decisions.

Performance Tasks

• ELA/literacy• Mathematics

Computer Adaptive

Assessment• ELA/literacy• Mathematics

Optional InterimAssessment

Optional InterimAssessment

Re-take option available

Summative Assessment for Accountability

Using Computer Adaptive Technology for Summative and Interim Assessments

• Provides accurate measurements of student growth over timeIncreased precision

• Item difficulty based on student responsesTailored for Each

Student

• Larger item banks mean that not all students receive the same questionsIncreased Security

• Fewer questions compared to fixed form testsShorter Test Length

• Turnaround time is significantly reducedFaster Results

• GMAT, GRE, COMPASS (ACT), Measures of Academic Progress (MAP)Mature Technology

What is CAT?

Administered by computer, a Computerized Adaptive Test (CAT) dynamically adjusts to the trait level of each examinee as the test is being administered.

How CAT Works (Binet’s Test)

Rating Item Difficulty

A) 9 x 4 = 2 x □ B) 9 x 4 = □ x 9C) 4 x □ = 40 – 8 D) 8 x 5 = □E) 8 x □ = 4 x □Give two different pairs of numbers that could fill the boxes to make a true equation.F) 8 x □ = 40

0

3/2

Put a point at the number 1.

Some Important “Constraints” in the Smarter Balanced Summative

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2 4

0 3

0

0

3/5

Grade 1Add and subtract within 20.6. Add and subtract within 20, demonstrating

fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Work with addition and subtraction equations.7. Understand the meaning of the equal

sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

8. Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? – 3, 6 + 6 = ?.

Grade 4Understand decimal notation for fractions, and compare decimal fractions.5. Express a fraction with denominator

10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.4

For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

K-12 Teacher Involvement

• Support for implementation of the Common Core State Standards (2011-12)

• Write and review items/tasks for the pilot test (2012-13) and field test (2013-14)

• Development of teacher leader teams in each state (2012-14)

• Evaluate formative assessment practices and curriculum tools for inclusion in digital library (2013-14)

• Score portions of the interim and summative assessments (2014-15 and beyond)

Higher Education Collaboration

• Involved 175 public and 13 private systems/institutions of higher education in application

• Two higher education representatives on the Executive Committee

• Higher education lead in each state and higher education faculty participating in work groups

• Goal: The high school assessment qualifies students for entry-level, credit-bearing coursework in college or university

Assessment System Components

Summative Assessment (Computer Adaptive)

• Assesses the full range of Common Core in English language arts and mathematics for students in grades 3–8 and 11 (interim assessments can be used in grades 9 and 10)

• Measures current student achievement and growth across time, showing progress toward college and career readiness

• Can be given once or twice a year (mandatory testing window within the last 12 weeks of the instructional year)

• Includes a variety of question types: selected response, short constructed response, extended constructed response, technology enhanced, and performance tasks


Interim Assessment (Computer Adaptive)

• Optional comprehensive and content-cluster assessment to help identify specific needs of each student

• Can be administered throughout the year• Provides clear examples of expected performance on

Common Core standards• Includes a variety of question types: selected response,

short constructed response, extended constructed response, technology enhanced, and performance tasks

• Aligned to and reported on the same scale as the summative assessments

• Fully accessible for instruction and professional development


• Extended projects demonstrate real-world writing and analytical skills

• May include online research, group projects, presentations

• Require 1-2 class periods to complete

• Included in both interim and summative assessments

• Applicable in all grades being assessed

• Evaluated by teachers using consistent scoring rubrics

The use of performance

measures has been found

to increase the intellectual

challenge in classrooms

and to support higher-

quality teaching.

- Linda Darling-Hammond and Frank Adamson, Stanford University

“

”

Performance Tasks


Few initiatives are

backed by evidence

that they raise

achievement.

Formative assessment

is one of the few

approaches proven to

make a difference.

- Stephanie Hirsh, Learning Forward

Formative Assessment Practices

• Research-based, on-demand tools and resources for teachers

• Aligned to Common Core, focused on increasing student learning and enabling differentiation of instruction

• Professional development materials include model units of instruction and publicly released assessment items, formative strategies

“

”


Data are only useful if

people are able to

access, understand and

use them… For

information to be useful,

it must be timely, readily

available, and easy to

understand.

- Data Quality Campaign

Online Reporting

• Static and dynamic reports, secure and public views

• Individual states retain jurisdiction over access and appearance of online reports

• Dashboard gives parents, students, practitioners, and policymakers access to assessment information

• Graphical display of learning progression status (interim assessment)

• Feedback and evaluation mechanism provides surveys, open feedback, and vetting of materials

“

”

Support for Special Populations

• Accurate measures of progress for students with disabilities and English Language Learners

• Accessibility and Accommodations Work Group engaged throughout development

• Outreach and collaboration with relevant associations

Common-

Core Tests

to Have Built-in

Accommodations

- June 8, 2011

“

”

“Students can demonstrate progress toward college and career readiness in English Language arts and literacy.”

“Students can demonstrate college and career readiness in English language arts and literacy.”

“Students can read closely and analytically to comprehend a range of increasingly complex literary and informational texts.”

“Students can produce effective and well-grounded writing for a range of purposes and audiences.”

“Students can employ effective speaking and listening skills for a range of purposes and audiences.”

“Students can engage in research and inquiry to investigate topics, and to analyze, integrate, and present information.”

Overall Claim for Grades 3-8

Overall Claim for Grade 11

Claim #1 - Reading

Claim #2 - Writing

Claim #3 - Speaking and Listening

Claim #4 - Research/Inquiry

Claims for the ELA/Literacy Summative Assessment

“Students can demonstrate progress toward college and career readiness in mathematics.”

“Students can demonstrate college and career readiness in mathematics.”

“Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.”

“Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.”

“Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.”

“Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.”

Overall Claim for Grades 3-8

Overall Claim for Grade 11

Claim #1 - Concepts & Procedures

Claim #2 - Problem Solving

Claim #3 - Communicating Reasoning

Claim #4 - Modeling and Data Analysis

Claims for the Mathematics Summative Assessment

April 2012 Item/task specifications and guidelines v1.0 completed

May 2012 Training materials for writing & reviewing items/tasks completed

May-June 2012 Automated scoring models developed

June 2012 Engage students in “cognitive labs” for new and innovative items/tasks

June 2012 Recruit classrooms for small scale trials

Aug-Oct 2012 Conduct small scale trials

May 2012 Recruit teachers to write and review first ~10,000 items/tasks (“Pilot” Phase)

May-July 2012 Teachers trained and write pilot items/tasks

Sept-Oct 2012 Teachers review pilot items/tasks

Oct-Nov 2012 Solicit classrooms for pilot testing

Feb-Mar 2013 Pilot testing of items/tasks

May 2013 Recruit teachers to write/review next ~35,000 items/tasks (“Field Test” Phase)

May-July 2013 Teachers trained and write field test items/tasks

Sept-Oct 2013 Teachers review field test items/tasks

Oct-Nov 2013 Solicit classrooms for field testing

April-June 2014 Field testing of items/tasks

Development of Items and Tasks

Viewing Sample Items & Tasks

• Preliminary Sample Items– http://sampleitems.smarterbalanced.org/itemp

review/sbac/

• Full Practice Tests Available– http://sbac.portal.airast.org/practice-test/

http://sampleitems.smarterbalanced.org/itempreview/sbac/

http://sampleitems.smarterbalanced.org/itempreview/sbac/

http://sbac.portal.airast.org/practice-test/

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Usability, Accessibility, Accommodations

Overall New Document

• Introduction– Purpose and intended audience– Briefly addresses Framework and ISAAP, includes links

• Three main sections on supports– Universal Accessibility Tools– Designated Accommodations– Documented Accommodations

• Resources (References)• Appendices

– Summary of supports– Research lessons

Speech-to-Text

• Available as a documented accommodation on all math and ELA items:– Available for students providing a response, as a

documented accommodation included in an IEP or 504.

– Available to students when taking notes in preparation for a written response, included in an IEP or 504.

• Students to use own Assistive Technology (AT) device, with AT device certification

Note: Conventions not a challenge to the construct.

American Sign Language

• Available for students who are hard of hearing or deaf as a documented accommodation

• Available on math items• Available on ELA listening items

Closed Captioning

• Available for students who are hard of hearing or deaf as a documented accommodation

• Available on ELA listening items

Calculator• Universal embedded calculator: available on

items as per Smarter Balanced item specifications and targets

• Non-embedded calculator is a documented accommodation (i.e., Brailled calculator)– Student can use own device

• Calculator is not allowed on non-calculator items– Decision based on intended construct to be

measured by assessment targets.

Survey Feedback—Participation

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Universal Tools, Designated Supports, and Accommodations

• Universal tools are access features of the assessment that are either provided as digitally-delivered components of the test administration system or separate from it. Universal tools are available to all students based on student preference and selection.

• Designated supports for the Smarter Balanced assessments are those features that are available for use by any student for whom the need has been indicated by an educator (or team of educators with parent/guardian and student).

• Accommodations are changes in procedures or materials that increase equitable access during the Smarter Balanced assessments. They are available for students for whom there is documentation of the need for the accommodations on an Individualized Education Program (IEP) or 504 accommodation plan.

New Graphic

General Table, Appendix A

Text-to-Speech

• On Items• Designated support for math items• Designated support for ELA items

• On ELA Reading Passages• Grades 3-5, TTS for passages is not available• Grades 6-HS: for passages available

accommodation for students whose need is documented in an IEP or 504 plan

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Guidelines & Frameworks

• Smarter Balanced Usability, Accessibility and Accommodations Guidelines http://www.smarterbalanced.org/wordpress/wp-content/uploads/2013/09/SmarterBalanced_Guidelines_091113.pdf

• Smarter Balanced Translation Framework

• http://www.smarterbalanced.org/wordpress/wp-content/uploads/2012/09/Translation-Accommodations-Framework-for-Testing-ELL-Math.pdf 96

http://www.smarterbalanced.org/wordpress/wp-content/uploads/2013/09/SmarterBalanced_Guidelines_091113.pdf




http://www.smarterbalanced.org/wordpress/wp-content/uploads/2012/09/Translation-Accommodations-Framework-for-Testing-ELL-Math.pdf





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Making Items More Accessible

Drag and Drop

Equal to 5.42 NOT Equal to 5.42

2.36 + 3.06

1.80 x 3

2.16 + 3.36

9.53 – 4.11

2.71 x 2

8.01 – 2.69

Table

Translation

Translation

Translation

Translation

Embedded

Embedded

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Important Notes on Item Development

107http://commoncoretools.me/2012/02/16/the-structure-is-the-standards/For an essay on similar themes, see

Features of CCSSM and Implications for Assessment Assessing Individual Content Standards or Parts of Standards Alignment in Context: Cluster, Domain, and Grade

3.c

http://commoncoretools.me/2012/02/16/the-structure-is-the-standards/

What are progressions?

Many or most of the content standards in K-8 represent steps or stages along a progression of learning and performance.

Why are progressions important for item writers?

They are context for alignment questions. Progression-sensitive tasks will help teachers implement the standards with fidelity.

Where can I find more information?

Progressions documents are narratives of the standards across grade levels, informed by research on children's cognitive development and by the logical structure of mathematics.

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Features of CCSSM and Implications for Assessment Assessing Individual Content Standards or Parts of Standards Alignment in Context: Neighboring Grades and Progressions

http://math.arizona.edu/~ime/progressions/#products

http://math.arizona.edu/~ime/progressions/

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Features of CCSSM and Implications for Assessment Assessing at All Levels of the Content Hierarchy

Standards in number and operations that involve place value of decimals

Items requiring procedural skill in expanded form, reading/writing, and comparing decimals, and rounding

Q QQ

How Standards and Tests Used To Be Designed: Tossing Items Into Buckets

Q

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Number and Operations in Base Ten—Understand the Place Value System

5.NBT.1 5.NBT.2 5.NBT.3a 5.NBT.3b 5.NBT.4

QQ QQ

QQ

Using the Design of CCSSM to Make Better TestsStep 1: Better Buckets!

1) Standards complement procedural skill with explicit expectations for conceptual understanding of specific content, and connections to practices such as constructing mathematical arguments (MP.3)

2) Individual standards make important connections explicit and inescapable—e.g., 3.MD.7 connects area to multiplication, division, and the distributive property. Buckets that connect buckets.

3) Standards are given a coherent context within and across grades through cluster headings

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5.NBT.1 5.NBT.2 5.NBT.3a 5.NBT.3b 5.NBT.4

QQ QQ

QQ

Using the Design of CCSSM to Make Better TestsStep 2: Where Appropriate, Treat Headings As Buckets

Where appropriate, aim some of the item development at the cluster level

Where appropriate, aim some of the item development at the domain level

Q Q

5.NBT.A 5.NBT

• There are a finite set of key opportunities to assess at the cluster, domain, and grade levels. Smarter Balanced is exploring this feature of the Standards. Such opportunities should be identified carefully and must make

obvious educational and mathematical sense within the framework of the standards. For example, the first two clusters in NBT are often important to link; and doing simple word problems to apply developing NBT skills requires some grade-level tasks that blend OA and NBT.

This is not a recommendation to make loose interpretations of the standards or go beyond what is written in the standards. Rather, it is an opportunity to measure plausible and immediate implications of what is written in the standard, without ever slipping into the imposition of additional requirements.

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http://tinyurl.com/mathpubcrit

Coherent Connections

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Features of CCSSM and Implications for Assessment

Minimizing pitfalls of traditional multiple choice questions• High-quality machine-scoreable tasks are critical.• Some examples of how to do this in CBT that are

machine scored: Gridded response True/False with multiple options Drag and drop

Some considerations: Risks of technology in assessing of the Standards. • Technology for technology’s sake - The construct should

drive the task design, not functionality

• Overuse of tech-friendly content - Technology can threaten focus; consider how technology can support focus and not dilute it

• Innovative does not equal more difficult. Many tasks should give kids credit for learning the basics of the grade

• Need cognitive labs or other tryouts to make sure the technology is adding value to the task

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Grade 3

Grade 3

Grade 5

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Fluency as a special case of assessing individual content standards.

• Fluent in the standards means fast and accurate.

• The word fluency was used judiciously in the Standards to mark the endpoints of progressions of learning that begin with solid underpinnings and then pass upward through stages of growing maturity.

• Assessing the full range of the standards means assessing fluency where it is called for in the standards. Some of these fluency expectations are meant to be mental and others

with “pencil and paper.” But for each of them, there should be no hesitation in getting the answer with accuracy.


Topics for Discussion

1. Assessing individual content standards or parts of standards

2. Assessing at all levels of the content hierarchy

3. Identifying ways in which technology can promote quality assessment of the standards

4. Connecting mathematical practice standards and content standards

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“Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.” (CCSSM, pg. 8)

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Features of CCSSM and Implications for Assessment Assessing through authentic connections of content and practices

Features of CCSSM and Implications for AssessmentSmarter Balanced’s Claims Embody Specific MathematicalPractices in the Presence of Content Standards

Claim #2: Problem Solving. Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.

Claim #3: Communicating Reasoning. Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.

Claim #4: Modeling and Data Analysis. Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.

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A Closer Look at Claim #3: Communicating Reasoning

Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.(Connection to MP.3: Construct viable arguments and critique the reasoning of others)

Features of CCSSM and Implications for Assessment Connecting Content Standards and Mathematical Practices in Assessment

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Reasoning is a refrain in the content standards

Note generally such words as justify a conclusion, prove a statement, explain the mathematics; also derive, assess, illustrate, and analyze.


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Claim #3 tasks have fine “grain size.”

The Standards ask students not just to Reason, but to “reason about X,” where X is key grade-level mathematics such as properties of operations, relationships between addition and subtraction or between multiplication and division, fractions as numbers, variable expressions, linear/nonlinear functions, etc.


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A Closer Look at Claims #2 and #4Problem SolvingStudents can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.Modeling & Data AnalysisStudents can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.


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Modeling is a mathematical practice (MP.4) – and in high school, it is also a content category. Therefore it is reasonable to say that modeling is enhanced in high school as compared to K-8, with more elements of the modeling cycle (CCSSM, p. 72, 73) – and equivalently, that modeling builds more slowly across K-8 and is less sophisticated there.


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• Contextual word problems involving ideas that are currently at the forefront of the student’s developing mathematical knowledge.

• Multi-step contextual word problem in which the problem isn’t broken into steps or sub-parts

• Micro models: These tasks define goals that can be met by autonomously apply a known technique from pure mathematics to a real-world situation in which the technique yields valuable results though it is obviously not applicable in a strict mathematical sense

• Reasoned estimates: these tasks require students to use reasonable estimates of know quantities in a chain of reasoning that yield an estimate of unknown quantity.

• Decisions from data: These tasks require students to select from a data source, analyze the data and draw reasonable conclusions from it. This will often result in an evaluation or recommendation.

• Full models: These tasks require execution of some or all of the modeling cycle in high school.

Source: Excerpted from Smarter Balanced Content Specifications, PARCC Item Development ITN, Appendix F

Features of CCSSM and Implications for Assessment Modeling and Problem Solving tasks may come in a variety of types

Grade 5

Grade 5

Grade 5

Grade 3

Find Out More

Smarter Balanced can be found online at:

SmarterBalanced.org

Contact Information: [email protected] 133