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Mathematics Content Specifications,
Item Specifications, and Depth of
Knowledge Training Module
Dawn Sparks
Adrianna DiGregorio
Agenda
Blue Print of a CCSS Mathematics Summative
Assessment
Drill Deeper to Consider “Sample” Grade Level
Assessment
Development of Assessment Items based on Claims,
Targets and Task Models
Sample & Practice Test Review
Goals
I can …
Understand a blue print for Summative Assessment
Name the four claims
Navigate to targets for each claim
Write sample test items that reflect task models
for specific claims and targets.
If I look at a blueprint of a summative
grade level test…
What would I need more
information about?
Let’s go a bit deeper
How is the sample 3rd grade test map connected to
the test blueprint?
What new information might you need?
4 Claims for Mathematics
“Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency.”
Concepts and Procedures
“Students can frame and solve a range of complex problems in pure and applied mathematics.”
Problem Solving
“Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.”
Communicating Reasoning
“Students can analyze complex, real-world scenarios and can use mathematical models to interpret and solve problems.”
Data Analysis and Modeling
(a/o Round 1 – released 8/29/11)
Smarter Balanced Assessment Consortium
Mathematics Content Specifications
Structure of the Smarter Balanced Assessment
Consortium Mathematics Content Specifications
Introduction and Background
• Claims and Assessment Targets
• Rationale and Evidence for Each Claim
• Cognitive Rigor Matrix / Depth of Knowledge
• General Considerations
Mathematics Claim #1
Concepts and Procedures
“This claim addresses procedural skills and the
conceptual understanding on which developing skills
depend.”
Selected Response
Short Constructed Response
Highly Scaffolded Tasks
Extended Response
Cluster Headings are the Assessment Targets
Structure of the Common Core State
Standards for Mathematics
STANDARD
CLUSTER
DOMAIN 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 x 80, 5 x 60) using strategies on place and properties of
operations..
Claim #2
Problem Solving
“Assessment items and task focused on this claim
include well-posed problems in pure mathematics and
problems set in context.”
Single Step/Multistep Problems
Balanced types of problems that could include…
Problems in Pure Math
Design Problems
Planning Problems
Claim #2
Problem Solving
Relevant verbs include:
Understand
Solve
Apply
Describe
Illustrate
Interpret
Analyze
Draw from knowledge
and skills within many
standards
May draw on
knowledge and skills
from lower grades
Provide evidence for
many assessment
targets
Targets for Claim 2 – Problem Solving
Target A: Apply mathematics to solve well-
posed problems in pure mathematics and arising
in everyday life, society, and the workplace.
Target B: Select and use appropriate tools
strategically.
Target C: Interpret results in the context of a
situation.
Target D: Identify important quantities in a
practical situation and map their relationships
(e.g., using diagrams, two-way tables, graphs,
flowcharts, or formulas).
Claim #3
Communicating Reasoning
“This claim refers to a recurring theme in the CCSSM
content and practice standards: the ability to construct
and present a clear, logical convincing argument.”
Claim #3
Communicating Reasoning
Derived from Content
Standards (Pg. 67)
Relevant Verbs Include:
Understand
Explain
Justify
Prove
Derive
Assess
Illustrate
Analyze
Targets for Claim 3 - Communicating
Reasoning
Target A: Test propositions or conjectures with specific examples.
Target B: Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures.
Target C: State logical assumptions being used.
Target D: Use the technique of breaking an argument into cases.
Target E: Distinguish correct logic or reasoning from that which is flawed and – if there is a flaw in the argument – explain what it is.
Target F: Base arguments on concrete referents such as objects, drawings, diagrams, and actions.
Claim 4
Modeling and Data Analysis
“Modeling is the process of choosing and using
appropriate mathematics and statistics to analyze
empirical situations, to understand them better, and
to improve decision-making.”
Claim #4
Modeling and Data Analysis
Relevant Verbs Include:
Model
Construct
Compare
Investigate
Build
Interpret
Estimate
Analyze
Summarize
Represent
Solve
Evaluate
Extend
Apply
Targets for Claim 4 – Modeling and
Data Analysis
Target A: Apply mathematics to solve problems
arising in everyday life, society, and the
workplace.
Target B: Construct, autonomously, chains of
reasoning to justify mathematical models used,
interpretations made, and solutions proposed for
a complex problem.
Target C: State logical assumptions being used.
Target D: Interpret results in the context of a
situation.
Targets for Claim 4 – Modeling and
Data Analysis
Target E: Analyze the adequacy of and make
improvements to an existing model or develop a
mathematical model of a real phenomenon.
Target F: Identify important quantities in a
practical situation and map their relationships.
Target G: Identify, analyze, and synthesize
relevant external resources to pose or solve
problems.
Math Practices in the Claims
Claim 1 – MP 5, 6, 7, 8
Claim 2 – MP 1, 5, 7, 8
Claim 3 – MP 3, 6
Claim 4 – MP 2, 4, 5
Assessing your understanding of the
Mathematical Claims and DOK
Work in Small Groups or Partners
Choose a grade band of Sample Test Items
Decide on a Mathematical Claim for the Sample
Item
Decide on the DOK for the Sample Item
Provide evidence for your answers
Foundations for Test Items
Assessment Items
Task Models
Assessment Targets
Mathematical Claims
Common Core Standard
Assessment
Targets
Claim 1
Concepts and Procedures
3rd Grade Operations and Algebraic Thinking
Target A [m]: Represent and solve problems involving multiplication and division.6 (DOK 1)
Items/tasks for this target require students to use multiplication and division within 100 to solve straightforward, one-step contextual word problems in situations involving equal groups, arrays, and measurement quantities such as length, liquid volume, and masses/weights of objects. These problems should be of the equal-groups and arrays-situation types, but can include more difficult measurement quantity situations. All of these items/tasks will code straightforwardly to standard 3.OA.3. Few of these tasks coding to this standard will make the method of solution a separate target of assessment. Other tasks associated with this target will probe student understanding of the meanings of multiplication and division (3.OA.1,2).7
Claim 1
Concepts and Procedures
Grade 4
Operations and Algebraic Thinking
Target A [m]: Use the four operations with whole numbers to solve problems. (DOK 1, 2)
Tasks for this target will require students to use the four operations to solve straightforward,
one-step contextual word problems in situations involving equal groups, arrays, and finding an
unknown number, including problems where the remainder must be interpreted. Some of these
tasks will draw on contexts in 4.MD Target I using measurement quantities such as time, liquid
volume, and masses/weights of objects, and money (with decimal representations limited to
those described in standards 4.NF.6 and 4.NF.7).
Claims 2, 3, and 4
Assessment Targets for Claims
2, 3, and 4 are not divided into a
grade-by-grade description.
A general set of assessment targets
applicable across grade levels.
Structure of Item Specification Table
Task Models for 3rd Grade Target E
Task Model 1
Task Model 2 a-b
Task Model 2 c-f
Task Model 3 a
Task Model 3 b
With a partner look at each of the different task models.
Develop an example task for each task model. (Three total)
Be ready to share your tasks in a gallery walk.
How would this process help inform
classroom instruction?
Discuss with your group how you could use this
information.
Be prepared to share your groups ideas.
Lunch: 11:30-12:30
Little Bites…
Practice Tests
Online Resources-PDF Formats
CAT Tests
Performance Tests
Online Training Tests
Sign in as a Guest
Select a Grade
Training Test
Practice Test
Performance Test
Evaluation Survey
January 26, 2015
ESD 105
Other - SBAC Overview
6 Hours
http://tinyurl.com/nhd67u6
Break-Meet Back in the Ahtanum Room
