Preparing for the Common Core State Standards Mathematics Assessment
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Preparing for the Common Core State Standards Mathematics Assessment October 30, 2012
description
Preparing for the Common Core State Standards Mathematics Assessment. October 30, 2012. Today’s Goals . Participants will have the opportunity to: e xplore the design of the SBAC assessment system c onsider the design of a balanced assessment system for your districts. Today’s Agenda. - PowerPoint PPT Presentation
Transcript of Preparing for the Common Core State Standards Mathematics Assessment
Preparing for the Common Core State Standards Mathematics Assessment
October 30, 2012
Today’s Goals
Participants will have the opportunity to:
• explore the design of the SBAC assessment system
• consider the design of a balanced assessment system for your districts
Today’s Agenda• Welcome, Context, and Introductions • Opening Comments - Dr. Burkhardt• Explore SBAC Content Specifications and Items
– SBAC Basics– Summative Assessment Target Tables– SBAC Tasks– Computer Adapted Test Design– AM Summary & Reflections - Dr. Burkhardt
Lunch & District Debrief• A Balanced Classroom and District Assessment System
– Introduction to Formative Assessment – Dr. Burkhardt– MAPS Tasks
• Closing Remarks - Dr. Burkhardt• District Debrief & End of Day Reflections
CCSS States and the Smarter Balanced Assessment Consortium
Balanced States
CCSSM States
SBAC - A Balanced System
Assessment Principles
1. Assessments are grounded in a thoughtful, standards-based curriculum and are managed as part of an integrated system.
2. Assessments include evidence of student performance.
3. Teachers are integrally involved in the development and scoring of assessments.
4. Assessments are structured to continuously improve teaching and learning.
5. Assessment, reporting, and accountability systems provide useful information on multiple measures.
Hugh Burkhardt, Ph.D. Shell Center for
Mathematics Education
Mathematics Assessment Resources Project (MARS)
Mathematics Assessment Project (MAP)
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Key Elements of the CCSSM Connected to Issues of Assessment
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CCSS Learning Progressions Within grades Across Grades
www.TurnonCCMath.net
http://ime.math.arizona.edu/progressions/
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William McCallum
Standards for Mathematical PracticeTucson, April 2011
Reasoning andexplaining
Modeling andUsing tools
Seeing structureand generalizing
Key Elements of the CCSSM Connected to Issues of Assessment
Standards for Mathematical Practice
Smarter Balanced Assessment Consortium Mathematics Content Specifications
Beginning with the basics! Claims DOK Cluster Headings Targets Item Types
SBAC Basics - A Balanced System
SBAC Basics: Foundational Beliefs
Assessments should be structured to continuously improve teaching and learning
■ Assess around learning progressions■ Using Computer Adaptive Testing Technology■ Creating opportunities for students and teachers to get
actionable feedback on student learning throughout the year
■ Provide curriculum-embedded assessments that offer models of good curriculum and assessment practices
■ Allowing close examination of student work and moderated teacher scoring as professional development
SBAC Basics: Reporting Categories
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“Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.”
Claim 1: Concepts and
Procedures, ≈ 40%
“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 2: Problem Solving
≈ 20%
“Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.”
Claim 3: Communicating
Reasoning ≈ 20%
“Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.”
Claim 4:Data Analysis and
Modeling ≈ 20%
“Each claim is a summary statement about the knowledge and skill students will be expected to demonstrate on the assessment related to a particular aspect of the CCSS for mathematics.”
Same Target, Different Claims
For each task consider:
Which claim or claims do you see the task supporting? Why?
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SBAC Basics: Depth of Knowledge (DOK) Measure of Cognitive RigorThe level of task complexity.
Level 1: Recall and Reproduction Requires eliciting information such as a fact, definition, term,
or a simple procedure, as well as performing a simple algorithm or applying a formula.
Level 2: Basic Skills and Concepts Requires the engagement of some mental processing beyond
a recall of information.Level 3: Strategic Thinking and Reasoning
Requires reasoning, planning, using evidence, and explanations of thinking.
Level 4: Extended Thinking Requires complex reasoning, planning, developing, and
thinking most likely over an extended period of time.
DOK Level 1 Example - Grade 8
Select all of the expressions that have a value between 0 and 1. 87 ∙ 8–12
74
7–3
13
2
∙ 13
9
(–5)6
(–5)10
DOK Level 2 Example - Grade 8
A cylindrical tank has a height of 10 feet and a radius of 4 feet. Jane fills this tank with water at a rate of 8 cubic feet per minute. How many minutes will it take Jane to completely fill the tank without overflowing at this rate? Round your answer to the nearest minute.
DOK Level 3 Example - Grade 8
The total cost for an order of shirts from a company consists of the cost for each shirt plus a one-time design fee. The cost for each shirt is the same no matter how many shirts are ordered.
The company provides the following examples to customers to help them estimate the total cost for an order of shirts.
• 50 shirts cost $349.50• 500 shirts cost $2370
Part A: Using the examples provided, what is the cost for each shirt, not including the one-time design fee? Explain how you found your answer. Part B: What is the cost of the one-time design fee? Explain how you found your answer.
DOK Level 4 Example - Grade 8
During the task, the student assumes the role of an architect who is responsible for designing the best plan for a park with area and financial restraints. The student completes tasks in which he/she compares the costs of different bids, determines what facilities should be given priority in the park, and then develops a scale drawing of the best design for the park and an explanation of the choices made. This investigation is done in class using a calculator, an applet to construct the scale drawing, and a spreadsheet.
Cognitive Rigor Matrix
Structure of the CCSSM
STANDARD
Number and Operations in Base Ten 4.NBT
Generalize place value understanding for multi-digit whole numbers.
1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
3. Use place value understanding to round multi-digit whole numbers to any place.
DOMAIN
CLUSTER
SBAC Basics: Large Scale Assessment Constraints
On the large scale summative assessment not everything in the CCSSM can have equal priority given time limitations. Cluster headings at each grade level are categorized as Major (m), or as Additional/Supporting (a/s).
About 75% - 80% of the items should come from Major clusters for Claim 1
About 20% - 25% of the items should come from Additional/Supporting clusters for Claim 1
SBAC Basics: Large Scale Assessment Constraints
Identifying some standards within “major” clusters and others within “additional/supporting” clusters is not to say that anything in the standards can be neglected. To do so would leave gaps in student preparation for later mathematics. In other words, all content is eligible for and should be encompassed in the assessment. (p.29)
SBAC Basics: Large Scale Assessment Constraints
Working at the cluster level helps to avoid obscuring the big ideas and getting lost in the details of specific standards (which are individually important, but impossible to measure in their entirety within the bounds of reasonable testing time). p.29
SBAC Mathematics
Content Specifications
Content Specifications for the Summative Assessment of CCSSM Details of the
Assessment Specifications are organized around the four Claims that will be used as reporting categories
Claim 1: Concepts and
Procedures, ≈ 40%
Claim 2: Problem Solving
≈ 20%
Claim 3: Communicating
Reasoning ≈ 20%
Claim 4:Data Analysis and
Modeling ≈ 20%
Summative Assessment Target TablesCurrently under development by SBAC
Indicates Targets for the summative portion of the Smarter Balanced assessment
Suggests what is taken as evidence of student proficiency for a particular target
Articulates Content (cluster heading and related standards) Depth of Knowledge task assignments Assessment method/Task types
Summative Assessment Target Tables
The cluster headings can be viewed as the most effective means of communicating the focus and coherence of the standards. Therefore,
Claim 1: Concepts and
Procedures, ≈ 40%
this content specifications document uses the cluster headings as the targets of assessment for generating evidence for Claim #1. (p.29)
Structure of the CCSSM
STANDARD
Number and Operations in Base Ten 4.NBT
Generalize place value understanding for multi-digit whole numbers.
1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
3. Use place value understanding to round multi-digit whole numbers to any place.
DOMAIN
CLUSTER
Summative Assessment Target DClaim 1 - Concepts and Procedures
Grade 4Operations and Algebraic Thinking
Target D [m]: Generalize place value understanding for multi-digit whole numbers. (DOK 1, 2) Tasks for this target will require students to compare multi-digit numbers using >, =, and <. Tasks should tap into students’ understanding of place value (e.g., by asking students to give a possible digit for the empty box in 4357 < 43☐9 that would make the inequality true). A smaller number of these tasks will incorporate student understanding of rounding (e.g., explaining why rounding to a certain place would change the symbol < or > to =). In claims 2-4, students should see contextual problems associated with this target that highlight issues with precision, including problems in Claim 3 that ask students to explain how improper estimation can create unacceptable levels of precision and/or lead to flawed reasoning. (pg. 34 - 35)
Cluster Headings RULE!
In the CCSSM the cluster headings usually serve to communicate the larger intent of a group of standards. For example, a cluster heading in Grade 4 reads: “Generalize understanding of place value for multi-digit numbers.”
Individual standards in this cluster pinpoint some signs of success in the endeavor, but the important endeavor itself is stated directly in the cluster heading. In addition, the word generalize signals that there is a multi-grade progression in grades K-3 leading up to this group of standards. (p.28)
Summative Assessment TargetsClaim 1 - Concepts and Procedures
Grade 4
Operations and Algebraic Thinking A. Use the four operations with whole numbers to solve problems. B. Gain familiarity with factors and multiples. C. Generate and analyze patterns. D. Generalize place value understanding for multi-digit whole numbers. E. Use place value understanding and properties of operations to perform
multi-digit arithmetic.
Number and Operations – FractionsF. Extend understanding of fraction equivalence and ordering.G. Build fractions from unit fractions by applying and extending previous
understandings of operations on whole numbers. H. Understand decimal notation for fractions, and compare
decimal fractions.
Summative Assessment TargetsClaim 1 - Concepts and Procedures
Grade 4 continued
Measurement and DataI. Solve problems involving measurement and conversion of
measurements from a larger unit to a smaller unit. J. Represent and interpret data.K. Geometric measurement: understand concepts of angle and
measure angles.
GeometryL. Draw and identify lines and angles, and classify shapes by
properties of their lines and angles.
Claim 1- Concepts and ProceduresStudents can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.
Grade LevelNumber of
Assessment Targets
3 11
4 12
5 11
6 10
7 9
8 10
11 16
Summative Assessment Target Tables for Claims 2, 3, and 4 (≈ 60%)
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.
Claim 2: Problem Solving
≈ 20%
Claim 3: Communicating
Reasoning ≈ 20%
Claim 4:Data Analysis and
Modeling ≈ 20%
Pages 59 - 68
Summative Assessment TargetsClaim 2 – Problem Solving
A. Apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace
B. Select and use tools strategically
C. Interpret results in the context of the situation
D. Identify important quantities in a practical situation and map their relationships.
Claim 2: Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.
Summative Assessment TargetsClaim 3 – Communicating Reason
A. Test propositions or conjectures with specific examples.B. Construct, autonomously, chains of reasoning that justify or refute
propositions or conjectures.C. State logical assumptions being used.D. Use the technique of breaking an argument into cases.E. Distinguish correct logic or reasoning from that which is flawed,
and—if there is a flaw in the argument—explain what it is.F. Base arguments on concrete referents such as objects, drawings,
diagrams, and actions.G. Determine conditions under which an argument does and
does not apply.
Claim 3: Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.
Summative Assessment TargetsClaim 4 – Modeling and Data Analysis
A. Apply mathematics to solve problems arising in everyday life, society, and the workplace.
B. Construct, autonomously, chains of reasoning to justify mathematical models used, interpretations made, and solutions proposed for a complex problem.
C. State logical assumptions being used.D. Interpret results in the context of a situation.E. Analyze the adequacy of and make improvement to an existing model
or develop a mathematical model of a real phenomenon.F. Identify important quantities in a practical situation and map their
relationships.G. Identify, analyze, and synthesize relevant external resources to pose
or solve problems.
Claim 4: Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.
Summative Assessment Targets Tables
Orient yourself to the grade levelCluster headings with
standardsDOKRelated requirements in
Claims 2 – 4
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As a table group select a grade level and skim through the corresponding Targets for Claim 1.
Read one assessment target and explore related targets in Claims 2 – 4.
Share a feature that may suggest changes at the system and/or classroom level.
SBAC Related Assessment Resources
Where can I go for instructional and assessment tasks that reflect the types of thinking students will need to be able to demonstrate on the SBA?
SBAC Sample Math Tasks
Explore the SBAC collection www.tinyurl.com/SBsamples
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Be sure to push forward to explore a variety of task types (Selected-response, Technology-enhanced, Constructed-response, Performance)
Check out the two right tabs along the top bar for a number of items.
SBAC Website Resourceshttp://www.smarterbalanced.org/smarter-balanced-assessments/
Content Specifications (with some items at the end) Item/Task Specifications (with more sample tasks) Technology Enhanced Items (still more sample tasks) Performance Tasks (you guessed it, more sample tasks!) Guidelines
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Click Here
SBAC Website Resourceshttp://www.smarterbalanced.org/smarter-balanced-assessments/
Item and Task Types Accessibility and Accommodations For more information: Visit the support for under-represented students webpage Download the Accessibility and Accommodations Factsheet
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Click Here
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Oakland CCSS Initiative Resources
The Common Core State Standards Initiative (CCSSI) Oakland provide support and direction for educators as they move toward full implementation:
CCSS aligned curriculum and coherent units of study to highlight needed shifts in content related and pedagogical practices
Highlight Lessons Formative Assessment Resources (video, sample student work,
rubrics, instructional websites, etc.)
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Atlas Curriculum Mapping Units, lessons, formative assessments, and
other resources available in Atlas by Rubicon.
http://oaklandk12.rubiconatlas.org/public
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Online CCSS Curriculum Resources
Units of Study Lesson resources Assessment resources Professional resources
Video Sample student work And more
Classroom and Systems Implications
As a group discuss implications for your particular roles instruction assessments teacher evaluation student subgroups classroom materials such as
textbooks, computers, etc. Be prepared to share your
thinking with the whole group.
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An Introduction to Computer Adaptive Tests (CATs)
Not to be Confused with Computer Administered Tests (CATs)! :-O
Computer Adaptive Tests…
Place student ability and test question difficulty on the same scale
Modify the test based on student responses Can assess student ability more efficiently
than “fixed-form” tests Can be used to measure “growth” Have a set of inherent challenges all of their
own.
Ability /Difficulty
Less/ Easier
More/ HarderQ1
Q2
Q3Q4
Test Scale Score
Student 1
Ability /Difficulty
Less/ Easier
More/ HarderQ1
Q2*
Q3*
Q4*
Test Scale Score
Student 2
Things to Notice
Different students will get different items Students aren’t presented with (many) items
that are far from their estimated ability Since items are “targeted” to ability, the tests
can be shorter than fixed-form tests. Potential for (real) Claim-level scores The exact algorithm for selecting the next
item and when to stop is still under development
CATs and Measurement Error
ALL Measurement involves error CAT is no different
As tests get longer, our estimates get better, both in terms of Location (ability) Error (precision)
Perhaps another graph will help
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Morning Wrap-up & Questions
Dr. Burkhardt
What questions do you have?
Lunch
We will
reconvene
at 12:30.
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Afternoon Wrap-up & Questions
Dr. Burkhardt
What questions do you have?
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End of Day Reflections
1.Pick an idea that came up today and that you found particularly interesting. What is your current thinking about this idea? What questions do you still have?
2.What is your reaction to the work we did today? What seems promising and/or challenging at this point?
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SB-CEU’s
SB-CEU sign-out is available in the lobby.
Don’t forget to Sign-Out!
Contact us!
Mary Bouck [email protected] Hugh Burkhardt [email protected] Geraldine Devine [email protected] Jonathan Flukes [email protected] Dana Gosen [email protected] Jim Gullen [email protected] Valerie L. Mills [email protected] Carrie Zielinski [email protected]
