Preparing for the PARCC and the Common Core: 

PARCC and Common Core Mathematics Updates

www.parccmann.pbworks.com Dr. Bob Mann

Mathematics, Western Illinois Universityrr-mann@wiu.edu

www.ictm.org to access full slide show from Heather Brown of ISBE

What Is PARCC?

The Partnership for Assessment of Readiness for College and Careers: Made up of 19 states + DC and US Virgin Islands

KY and PA are participating states Developing common, high-quality math and English

language arts (ELA) tests for grades 3–11Computer-based and linked to what students need to            

                            know for college and careersFor use starting in the 2014–15 school year

AssessmentsELA/Literacy and Mathematics, Grades 3–11

Beginning of School Year

End of School Year

DiagnosticAssessment

Mid-Year Assessment

Performance-Based

Assessment

End-of-Year Assessment

Speaking and Listening

Assessment

Optional Required

Key:

Flexible administration

• PARCC states first developed the Model Content Frameworks to provide guidance to key elements of excellent instruction aligned with the Standards.

• The Model Content Frameworks were then used to provide guidance in the content emphasis for the mathematics assessment.

So, for the first time. . .

• PARCC is communicating in the same voice to teachers as it is to assessment developers! 

• PARCC is designing the assessments around exactly the same SHIFTS the standards expect of teachers and students.

What is Different About PARCC’s Development Process?

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Model Content Frameworks

• Final version in November of 2012• Look at these to see exactly which standards 

should be covered in each grade or course

Pathways

• Traditional (Algebra, Geometry, Algebra II)• Integrated (Math 1, 2, 3)• For grades 9-12, PARCC is making tests for 

both pathways• High Schools in Illinois can choose which form 

they would like to use• By the end of grade 11, the standards covered 

would be the same

• Focus: PARCC assessments will focus strongly on where the Standards focus.  Students will have more time to master concepts at a deeper level.

• Problems worth doing: Multi-step problems, conceptual questions, applications, and substantial procedures will be common, as in an excellent classroom.

• Better Standards Demand Better Questions: Instead of reusing existing items, PARCC will develop custom items to the Standards.

• Fidelity to the Standards: PARCC Evidence Statements are rooted in the language of the Standards so that expectations remain the same in both instructional and assessment settings.

PARCC’s Core Commitments to Mathematics Assessment Quality 

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What Are the Shifts at the Heart of PARCC’s Design?

1. Focus: The PARCC assessment will focus strongly where the Standards focus.

2. Coherence: Think across grades and link to major topics within grades.

3. Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application.

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College and Career Ready Determination (CCRD)

• Students who achieve a College and Career Ready Determination on the high school assessment will be able to enter directly into certain entry-level, credit-bearing courses in college, without having to take placement tests.

What’s new?

• PARCC Performance Level Descriptors (PLDs)• PARCC Evidence Tables and test blueprints• PARCC Sample test items and prototypes: • ISBE Mathematics Model Curriculum• Abundance of resources at PARCC, ISBE, and 

other sites

What are Performance Level Descriptors?

Performance Level Descriptors or PLDs describe what students at each performance level know and can do relative to grade-level or course content standards assessed.

Performance Level Descriptor Language

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Level 5: Students performing at this level demonstrate a distinguished command of the knowledge, skills, and practices embodied by the Common Core State Standards assessed at their grade level.Level 4: … strong command …Level 3: … moderate command …Level 2: … partial command …Level 1: … minimal command …

Evidence-Centered Design (ECD) for the PARCC Assessments

ClaimsDesign begins with the inferences (claims) we want to make about students

Evidence

In order to support claims, we must gather evidence

Tasks

Tasks are designed to elicit specific evidence from students in support of claims

ECD is a deliberate and systematic approach to assessment development that will help to establish the validity of the assessments, increase the

comparability of year-to year results, and increase efficiencies/reduce costs.

Sub-claim A:  Students solve problems involving the major content for their grade level 

with connections to practices 

Sub-Claim B:  Students solve problems involving the

additional and supporting content for their grade level with connections to practices

Sub-claim C:  Students express mathematical reasoning by constructing mathematical arguments and critiques

Sub-Claim D:  Students solve real world problems engaging particularly in the modeling

practice

Sub-Claim E:  Student demonstrate fluency in areas set forth in the Standards for 

Content in grades 3-6 

Claims for Mathematics

Master Claim: Students are on-track or ready for college and careers 

Evidence-Centered Design (ECD) for the PARCC Assessments

Claims

Design begins with the inferences (claims) we want to make about students

EvidenceIn order to support claims, we must gather evidence

Tasks

Tasks are designed to elicit specific evidence from students in support of claims

ECD is a deliberate and systematic approach to assessment development that will help to establish the validity of the assessments, increase the

comparability of year-to year results, and increase efficiencies/reduce costs.

Several types of evidence statements are being used to describe what a task should be assessing, including:1. Those using exact standards language2. Those transparently derived from exact standards language, 

e.g., by splitting a content standard3. Integrative evidence statements that express plausible direct 

implications of the standards without going beyond the standards to create new requirements

4. Sub-claim C & D evidence statements, which put MP.3, 4, 6 as primary with connections to content 

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Evidence Statement Tables:Types of Evidence Statements

Evidence-Centered Design (ECD) for the PARCC Assessments

Claims

Design begins with the inferences (claims) we want to make about students

Evidence

In order to support claims, we must gather evidence

TasksTasks are designed to elicit specific evidence from students in support of claims

ECD is a deliberate and systematic approach to assessment development that will help to establish the validity of the assessments, increase the

comparability of year-to year results, and increase efficiencies/reduce costs.

• The PARCC assessments for mathematics will involve three primary types of tasks: Type I, II, and III. 

• Each task type is described on the basis of several factors, principally the purpose of the task in generating evidence for certain sub claims.

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Overview of Task Types

Source: Appendix D of the PARCC Task Development ITN on page 17

Overview of PARCC Mathematics Task Types

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Task Type Description of Task Type

I. Tasks assessing concepts, skills and procedures

• Balance of conceptual understanding, fluency, and application• Can involve any or all mathematical practice standards• Machine scorable including innovative, computer-based formats• Will appear on the End of Year and Performance Based Assessment components• Sub-claims A, B and E

II. Tasks assessing expressing mathematical reasoning

• Each task calls for written arguments / justifications, critique of reasoning, or precision in mathematical statements (MP.3, 6). 

• Can involve other mathematical practice standards• May include a mix of machine scored and hand scored responses• Included on the Performance Based Assessment component• Sub-claim C

III. Tasks assessing modeling / applications

• Each task calls for modeling/application in a real-world context or scenario (MP.4) • Can involve other mathematical practice standards• May include a mix of machine scored and hand scored responses• Included on the Performance Based Assessment component• Sub-claim D

For more information see PARCC Task Development ITN Appendix D.

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Type II

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Type III

Algebra II/Math III Sample Task

Algebra II/Math III Sample Task

Algebra II/Math III Sample Task

Master Claim: On-Track for college and career readiness. The degree to which a student is college and career ready (or “on-track” to being ready) in mathematics. 

Sub-Claim A: Major Content1

with Connections to PracticesSub-Claim B: Additional & Supporting Content2 with Connections to Practices

Sub-Claim E: Fluency in applicable grades (3-6)

    Claims Structure: Mathematics

Sub-Claim C: Highlighted Practices MP.3,6 with Connections to

Content3 (expressing mathematical reasoning)

. 

Sub-Claim D: Highlighted Practice MP.4 with Connections to Content (modeling/application)

Total Exam Score Points: 

82 (Grades 3-8), 97 or 107(HS)

12 pts (3-8),18 pts (HS)

6 pts (Alg II/Math 3 CCR)

~37 pts (3-8),~42 pts (HS)

~14 pts (3-8),~23 pts (HS)

14 pts (3-8),14 pts (HS)

4 pts (Alg II/Math 3 CCR)

7-9 pts (3-6)

What’s Important?

• The content itself has not changed that much• The way it is packaged and delivered should 

be different• The way it will be assessed should be different• The expectations are higher throughout• The Mathematical Practices must not be 

forgotten

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the

reasoning of others.4. Model with mathematics. 5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated

reasoning.

August 2011 28

Practices?

Engagement

Tasks and Talk

Work and Words

·       When students transform expressions purposefully, they are looking for and making use of structure (MP.7).·       When modeling a situation, students often can get started by working repetitively with numerical examples and then look for and express regularity in that repeated reasoning by writing equations or functions (MP.8).·       Throughout high school, students construct viable arguments and critique the reasoning of others (MP.3). As in geometry, important questions in advanced algebra cannot be answered definitively by checking evidence. Results about all objects of a certain type — the factor theorem for polynomials, for example — require general arguments. And deciding whether two functions are equal on an infinite set cannot be settled by looking at tables or graphs; it requires a deeper argument.

Questions

Illinois State Board of Education

Mathematics Performance-based Assessment and End-of-Year Assessment

PARCC Subclaim

Percentage of Items on High School Assessments

Task Types

A: Solve problems with major content 39%

• Balance of conceptual understanding, fluency, and application

• Can involve any or all mathematical practice standards

B: Solve problems with additional and supporting content 21%

• Balance of conceptual understanding, fluency, and application

• Can involve any or all mathematical practice standards

C: Express mathematical reasoning

17%• Each task calls for written arguments / justifications, critique 

of reasoning, or precision in mathematical statements • Can involve other mathematical practice standards

D: Solve real-world problems engaging in modeling 22%

• Each task calls for modeling/application in a real-world context or scenario 

• Can involve other mathematical practice standards

Illinois State Board of Education

• Approximately 50% of the items on the ACT Mathematics Test involve knowledge and skills

• Approximately 30%  of items involve direct application

• Approximately 20% of the items involve understanding concepts/integrated conceptual understanding

Prairie State Achievement Exam

PARCC Comprehensive Accessibility Policies

Accessibility Features for All Students

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Accessibility Features for All StudentsAudio Amplification

Blank Paper (provided by test administrator)

Eliminate Answer ChoicesFlag Items for Review

General Administration Directions Clarified (by test administrator)

General Administration Directions Read Aloud and Repeated (by test administrator)

Highlight ToolHeadphones

Magnification/Enlargement DeviceNotePad

Pop-Up GlossaryRedirect Student to Test (by test administrator)

Spell CheckerWriting Tools

Accessibility Features Identified in Advance

• Available to all students (i.e., not limited to students with IEPs, 504 plans, or English learners), but will be selected and “turned on” by school-based educators prior to the assessment, based on each student’s Personal Needs Profile (PNP). 

• Based on each student’s individual needs, a PNP is created for the student to ensure that he or she receives appropriate access without the distraction of other tools and features that are not required by the student. 

• Although school-based educators will enable specific accessibility features for students, the student will decide whether or not to use the feature.  These accessibility features will be readily available on the computer-delivered testing platform. 

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Accessibility Features Identified in Advance

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Accessibility Features Identified in Advance 

Answer Masking

Background/Font Color (Color Contrast)

General Masking

Line Reader Tool

Text-to-Speech for the Mathematics Assessments

Administrative Considerations for All Students

• Detailed guidelines on the administration of the PARCC assessments will be included in the PARCC Test Administration Manual.

• Principals may determine that any student may require one or more of the following test administration considerations, regardless of the student’s status as a student with a disability or who is an English learner: – Small group testing – Frequent breaks – Time of day – Separate or alternate location – Specified area or seating – Adaptive and specialized equipment or furniture 

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PARCC Information Release

 July 2013 Summative assessment cost estimates  Final English Language Learners policy  Final accommodations manual for students with disabilities  Final performance level descriptors for all grades/courses in 

ELA/literacy and mathematics August 2013 Additional sample items  Specific information about windows for traditional and block 

scheduling, when assessment components will be available within the window, models of what PARCC will look like in schools, and proctor requirements 

Heather Brown – hedi0201@me.comJennie Winters – jwinters@lake.k12.il.us 

For “End-of-Course” Questions, email Rachel Jachino, rjachino@isbe.net  

Any publicly released assessment policies, item prototypes, PARCC Model Content Frameworks, and other valuable resources can be found at www.PARCConline.org

www.facebook.com/ilmathcommoncore

Contact

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