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### Content SpecificationsMathematics

### Depth of Knowledge

### Smarter Balanced

Connecting the

ICS-M (CCSS) & Smarter Balanced Assessment

Nichole Hall, Assessment Coordinator

Nancy Thomas Price, Formative/Interim Assessment Coordinator

Learning Targets

I understand….

- specifics of the SBAC balanced assessment system.
- how the Smarter Balanced Content Specifications reflect standards, assessment, and instruction
- ways to use knowledge of the new assessment design, tools and mathematics content to inform classroom instruction.
- how sample “items/tasks” can be used ‘thoughtfully’ to elicit evidence about student understanding and teacher instruction.
- formative assessment strategies that can be used during instruction.

Success Criteria

- I will show understanding of the major components of the SBAC balanced assessment system and the vocabulary used in that system specifications.(DOK1) – Knowledge Target
- I can specify the assessment claim, target, standard, and depth of knowledge for an item or task . (DOK 2)- Skill target Explain response (DOK 3)
- I can use the concepts presented to design classroom instruction and assessments that elicit evidence of student learning, (DOK3) Reasoning, Product targets
- I can relate these concepts to other content areas and / or grade levels (DOK 4) Product target

Depth of Knowledge

- DOK 1: Recall or identify a fact, definition, term; focus on initial comprehension
- DOK 2: Demonstrate conceptual information through explanation, interpretation (make some decisions)
- DOK 3: Strategic Thinking, reasoning, planning, using evidence, interpreting
- DOK 4: Extended thinking, relate concepts to other content areas, new situations...synthesize, show new perspective

Shared understanding

- Balanced Assessment System
- Formative
- Interim
- Summative
- Attributes of Formative Assessment
- Clarify Intended Learning
- Elicit Evidence
- Interpret Evidence
- Act on Evidence

http://www.smarterbalanced.org/smarter-balanced-assessments/

Formative Assessment is a deliberate process used by teachers and students during instruction that provides actionable feedback that is used to adjust ongoing teaching and learning strategies to improve students’ self-assessment, reflection, and attainment of curricular learning targets/goals.

Multiple ways to elicit evidence

- Can be planned for or spontaneous
- Inform: Teacher, peers, or self

- Practice implemented by teachers in collaboration with students
- Learning Targets: Students understand expectations & goals
- Success Criteria: Observable & measurable evidence of learning

The formative assessment process attributes are:

Clarify

Intended

Learning

Elicit

Evidence

- To determine where students are in regards to the learning target and success criteria
- Can be conducted by the teacher, student, or both

- Timely and Actionable
- Provide feedback : Where are students at in regards to learning targets
- Make adjustments to instruction

Interpret

Evidence

Act on

Evidence

Documents we will be using:

- Idaho Core Standards (CCSS) for Mathematics

http://www.sde.idaho.gov/site/common/math/docs/CCSSI_Math_Standards.pdf

- SBAC Math Content Specifications (Draft) & Item Specifications

http://www.smarterbalanced.org/wordpress/wp-content/uploads/2011/12/Math-Content-Specifications.pdf

- Cognitive Rigor Matrix Article (Hess, Carlock, Jones, and Walkup) and Matrix

http://schools.nyc.gov/NR/rdonlyres/D106125F-FFF0-420E-86D9-254761638C6F/0/HessArticle.pdf

Content Specifications

- Create a bridge between standards, assessment, and instruction
- Organize the standards around major constructs and big ideas
- Further describe what students should learn and be able to do to demonstrate evidence of their learning

Content Specifications Claims (p. 18)

Claims

are the broad statements of the assessment system‘s learning outcomes, each of which requires

evidence

that articulates the types of data/observations that will support interpretations of competence towards achievement of the claims.

Interpretations are spelled out in the Achievement Level Descriptors.

Conceptual Framework

- Evidence = Assessment Target
- Assessment Targets align with Standards

The Standard is the Content to be learned while the Assessment Target describes in greater detail, the evidence that will show the content has been mastered.

Relationship among Content Claims, Content Categories, Assessment Targets, and Standards (p.8 ALD Document)

Evidence-Centered Design

The Assessment Triangle (NRC, 2001)

The Assessment Triangle as Represented in the Content Specifications (pp. 14-15)

Content Categories & Assessment Targets

Proposed Reporting Categories

Claims & Rationale

The Assessment Triangle (NRC, 2001)

The Assessment Triangle as Represented in the Content Specifications (pp. 14-15)

Proposed Reporting Categories

Achievement

Level

Descriptors

The Assessment Triangle (NRC, 2001)

POLLCheck for Understanding

- Assessment Claim
- Assessment Target
- Standards
- Evidence-Centered Design
- Depth of Knowledge
- Formative Assessment

Claims & Assessment Targets

Relationship among Content Claims, Content Categories, Assessment Targets, and Standards

How to read the grade level standardsStandards – p. 5

- Standards define what students should understand and be able to do.
- Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject.
- Domains are larger groups of related standards. Standards from different domains may sometimes be closely related.

Number and Operations in Base Ten 3.NBT

Use place value understanding and properties of operations to

perform multi-digit arithmetic.

1. Use place value understanding to round whole numbers to the nearest 10 or 100.

2. Fluently add and subtract within 1000 using strategies and algorithms based on

place value, properties of operations, and/or the relationship between addition

and subtraction.

3. Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 ×

80, 5 × 60) using strategies based on place value and properties of operations

Domain

Cluster Heading

Cluster of Standards

Grouping the Standards for Mathematical PracticeStandards – p. 6-8

- Mathematical Practices
- The same across all grade levels
- Different levels of expertise that educators should seek to develop in their students
- The Practices are how students are expected to engage in items or tasks

Overarching habitsofmindofaproductivemathematicalthinker.

William McCallum – The University of Arizona

Relationship among Content Claims, Content Categories, Assessment Targets, and Standards

Can a Task or Assessment Item be Aligned to More Than One Claim?STOP!

“Mathematics is not a collection of separate strands or standards, though it is often partitioned and presented in this manner. Rather, mathematics is an integrated field of study.

Viewing mathematics as a whole highlights the need for studying and thinking about the connections within the discipline, as reflected both within the curriculum of a particular grade and between grade levels.”

Principles and Standards for School Mathematics; NCTM, 2000

Claim Alignment Practice: Grade 7 Item

Part A Determine if each of these statements is always true, sometimes true, or never true. Circle your response.

- The sum of the measures of two complementary angles is 90°.

Always True Sometimes True Never True

Part B For each statement you chose as “Sometimes True,” provide one example of when the statement is true and one example of when the statement is not true.

Your examples should be a diagram with the angle measurements labeled. If you did not choose any statement as “Sometimes True,” write “None” in the work space below.

What claim does this item align to?POLL

- Claim 3: Communicating Reasoning

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

Secondary Claim?

- Claim 1: Concepts and Procedures

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

What claim does this item align to?POLL

- Claim 1: Concepts and Procedures

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

Secondary Claim?

- No secondary claim

Relationship among Content Claims, Content Categories, Assessment Targets, and Standards

Relationship among Content Claims, Content Categories, Assessment Targets, and Standards

Math Domains in the Content Standards

Claims 2, 3, & 4:

Derived from the Mathematical Practices

Claim 1 - Assessment TargetsContent Specifications, p. 30

m = major

a/s = additional/supplemental

Content Category: CCSS-M Domain (p. 23)

Depth of Knowledge

Assessment Target: CCSS-M Cluster Heading

Description of Evidence

Relationship between the Idaho Core Standards & the Content Specifications

CCSS, p. 23

Content Specs, p. 30

Domain = Content Category

Cluster Heading 1 = Target A

Standards = Evidence

Cluster Heading 2 = Target B

CLAIM 1 – Grade 3: Content Categories, Assessment Targets, and Standards

CLAIM 1 – Grade 3: Content Categories, Assessment Targets, and Standards

CLAIM 1 – Grade 3: Content Categories, Assessment Targets, and Standards

Claims 2, 3, & 4 – Assessment TargetsContent Specifications, p. 59

Aligned to the Mathematical Practices

Relevant Verbs

Depth of Knowledge

Description of Engagement

Update #2 to the Content Specifications for Mathematics

- Provide a more explicit connection between the content standards and
- Claim 2 (Problem Solving), Claim
- 3 (Communicating Reasoning), and
- Claim 4 (Modeling and Data Analysis)
- by including the standards for each claim by grade level.

Content standards for each grade that support the collection of evidence for Claim 4.

POLL:Assessment Target: Grade 7 Item

Part A Determine if each of these statements is always true, sometimes true, or never true. Circle your response.

- The sum of the measures of two complementary angles is 90°.

Always True Sometimes True Never True

Part B For each statement you chose as “Sometimes True,” provide one example of when the statement is true and one example of when the statement is not true.

Your examples should be a diagram with the angle measurements labeled. If you did not choose any statement as “Sometimes True,” write “None” in the work space below.

What assessment target does this item align to? Please type your answer in the Question Box

- 3 B: Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures.
- 3 F: Base arguments on concrete referents such as objects, drawings, diagrams, and actions.
- 1 F: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

This item aligns to which assessment target? Write your answer in the question box.

- 1 I: Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

What are the Implications for Instruction?

Claims & Assessment Targets

Cognitive Rigor Matrix

Cognitive Rigor Matrix – Karin Hess

- http://vimeo.com/20998609

Assessment Target: Grade 7 Item

Part A Determine if each of these statements is always true, sometimes true, or never true. Circle your response.

- The sum of the measures of two complementary angles is 90°.

Always True Sometimes True Never True

Part B For each statement you chose as “Sometimes True,” provide one example of when the statement is true and one example of when the statement is not true.

Your examples should be a diagram with the angle measurements labeled. If you did not choose any statement as “Sometimes True,” write “None” in the work space below.

What depth of thinking? POLL

- DOK 1: Recall and Reproduction
- DOK 2: Basic Skills and Concepts
- DOK 3: Strategic Thinking/Reasoning
- DOK 4: Extending Thinking

WHY?

What type of thinking?

What depth of thinking?

- DOK 1: Recall and Reproduction
- DOK 2: Basic Skills and Concepts
- DOK 3: Strategic Thinking/Reasoning
- DOK 4: Extending Thinking

WHY?

What type of thinking?

Depth of Knowledge

Implications for Instruction

Understanding the Item Specifications

- Content & Grade
- Type of Question
- SR – Selected Response
- Claim
- Domain : RP – Ratios and Proportional Relationships
- Assessment Target for Grade Level – Target A
- Internal Number - 181
- Claim – C1, C2, C3, or C4 & Target

Understanding the Item Specifications

“Claims are the broad statements of the assessment system’s learning outcomes, each of which requires evidence that articulates the types of data/observations that will support interpretations of competence towards achievement of the claims.” p. 18 – Content Specifications

“Cluster level headings of the standards in the CCSS-M are used in order to allow for the creation and use of assessment tasks that require proficiency in a broad range of content and practices. Use of more fine-grained descriptions would risk a tendency to atomize the content, which might lead to assessments that would not meet the intent of the standards.” Content Specs., p. 20

Understanding the Item SpecificationsUnderstanding the Item Specifications

Domain

Domains, as found in the CCSS-M, are larger groups of related standards.

Defines what students should understand and be able to do

Understanding the Item SpecificationsUnderstanding the Item Specifications

Standards for Mathematical Practice

“Describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.” CCSS-M pp. 6-8

Make sense of problems & persevere in solving them.

Reason abstractly and quantitatively.

Understanding the Item Specifications

Depth of Knowledge

The cognitive rigor that a student needs to bring to the item/task, as determined by the Cognitive Rigor Matrix, Math Content Specifications, Appendix C, p. 92

Understanding the Item Specifications

- Selected Response
- Includes computer-enhanced items
- Distractors are chosen to embody common misconceptions
- Designed to make sure that students do not obtain correct answers because of test-taking skills

Understanding the Item Specifications

Range of Difficulty -

Estimation until pilot assessment occurs.

Understanding the Item Specifications

Key – Correct Answer

Now you try it:ACTIVITY

- Select one or more items with attached blank answer sheet.
- In your teacher team use the content specifications document to determine the item specifications.
- Use the answer key to check your answers when you are finished.

Work as a team to determine critical specifications for each item

Use the standards and content specifications document to determine:

- …...the item type
- ….. the grade level
- ….. the content domain
- ….. the standard cluster heading
- ….. the assessment target(s)
- ….. the claim(s)
- ….. the mathematical practice(s)
- ….. the depth of knowledge

Navigation of Website

Three locations for sample items

Practice and Pilot TestsSample items and performance tasks

Item Writing and Review

Achievement Level Descriptors and College Content-ReadinessComputer Adaptive Testing

Technology

Test Administration

Learning Targets

I understand….

- specifics of the SBAC balanced assessment system.
- how the Smarter Balanced Content Specifications reflect standards, assessment, and instruction
- ways to use knowledge of the new assessment design, tools and mathematics content to inform classroom instruction.
- how sample “items/tasks” can be used ‘thoughtfully’ to elicit evidence about student understanding and teacher instruction.
- formative assessment strategies that can be used during instruction.

Success Criteria

- I will show understanding of the major components of the SBAC balanced assessment system and the vocabulary used in that system specifications.(DOK1) – Knowledge Target
- I can specify the assessment claim, target, standard, and depth of knowledge for an item or task . (DOK 2)- Skill target Explain response (DOK 3)
- I can use the concepts presented to design classroom instruction and assessments that elicit evidence of student learning, (DOK3) Reasoning, Product targets
- I can relate these concepts to other content areas and / or grade levels (DOK 4) Product target

Next Steps

- Become more familiar with the content in all of the documents discussed today.
- Begin using the documents and the identified implications for instruction when adjusting current activities, lessons, or units to meet the rigor of the ICS and make sure you have balance.
- Visit the websites provided to view sample lesson plans and formative assessment activities.
- Complete the post-webinar recording and activity.

This presentation can be found at…

http://www.sde.idaho.gov/site/common/commonCorePD.htm

Evaluation

- Please complete a survey on your experience in participating in Connecting the ICS-M and Smarter Balanced Assessment, Implications for InstructionWorkshop
- Your feedback is greatly appreciated and is used to make adjustments in future trainings!
- To access the survey, please visit, https://www.surveymonkey.com/s/>>>>
- Thank you for taking time out of your busy schedule to participate in today’s workshop!

Contact Information

Nancy Thomas Price, Formative and Interim Assessment Coordinator

208-332-6988

Nichole Hall, Assessment Coordinator

208-332-6933

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