PK-5 Math Forum

PK-5 MATH FORUMOctober 4, 2012

I need exactly 4 quarts of water to make a punch for the class party. I have a 5 qt. bucket and a 3 qt. bucket. How can I measure exactly 4 qt. of water using just these two buckets?

How would you model this problem to help you think it through?

How would you record your steps to communicate what you did?

How many different solutions?

http://e2math.weebly.com/• Explain “why”

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Advances in the PARCC Mathematics Assessment

August 2012

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http://parcconline.org/samples/item-task-prototypes

http://parcconline.org/samples/item-task-prototypes

PARCC is designed to reward quality instruction aligned to the Standards, so the assessment is worthy of preparation rather than a distraction from good work.

PARCC’s Fundamental Advance

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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 (now in Teacher’s hands): PARCC evidences 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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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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What Are the Shifts in the Math Standards at the Heart of PARCC 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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Advances in Assessment

Specific advances in the PARCC mathematics assessments demanded by the three shifts…

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Advances in Assessment Demanded by the Shifts

Shift #1 – Focus: The PARCC assessments will focus strongly where the Standards focus

Advance: PARCC assessments will focus strongly where the Standards focus (70% or more on the major work in grades 3-8). Focus allows for a variety of problem types to get at

concept in multiple ways. Students will have more time to master concepts at a

deeper level.

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Shift #2 - Coherence: Think across grades, and link to major topics within grades

Advance: The assessment design is informed by multi-grade progressions in the Standards and the Model Content Frameworks. Key beginnings are stressed (e.g., ratio concepts in grade

6), as are key endpoints and takeaway skills (e.g., fluency with the multiplication table in grade 3).

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Shift #2 - Coherence: Think across grades, and link to major topics within grades

Advance: Integrative tasks draw on multiple standards to ensure students are making important connections. The Standards are not treated as a checklist.

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Advances in assessment demanded by the shifts

Shift #3 - Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application

Advance: PARCC assessments will reach the rigor in the Standards through innovations in technology and item design…

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Using Technology to Advance Assessment and the Shifts

• Technology enhancements supporting accessibility (e.g., the ability to hover over a word to see and/or hear its definition, etc.)

• Transformative formats making possible what can not be done with traditional paper-pencil assessments (e.g., simulations to improve a model, game-like environments, drawing/constructing diagrams or visual models, etc.)

• Getting beyond the bubble and avoiding drawbacks of traditional selected response such as guessing or choice elimination.

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Using Technology to Advance Assessment and the Shifts

• Capturing complex student responses through a device interface (e.g., using drawing tools, symbol palettes, etc.)

• Machine scorable multi-step tasks are more efficient to administer and score.

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Sample Items Illustrating the Advances in Assessment

The next section of this presentation is comprised of sample items that illustrate some of the advances called for by the three shifts.

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Overview of Mathematics Task Types

PARCC mathematics assessments will include three types of tasks.

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Task Type Description of Task TypeI. 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

componentsII. 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

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

For more information see PARCC Item Development ITN Appendix D.

FLUENCYTo support mathematical thinking

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Erin Wheeler, IES Erie 2 BOCES, 8-26-2012

Counting Fluency PK- K 1-2 3 4-5

1-3

1-5

1-10

Up to 100

“math way”1 ten 2, 1 ten 3,

Whisper/ speak

Roller coaster

1’s (pennies)

5’s (nickels)

10’s (dimes)

23, 33, 43, etc.

Up to 120

Whisper odd, speak evens

Repeated + or subtraction

Multiples of whole numbers

Unit fractions (beyond 1- keep as improper fractions)

Multiples of unit fractions/ whole numbers

Decimals


Sprints

Bill Davidson http://www.youtube.com/watch?v=G_y9gGnd68M


ApplicationProblem solving requires studentsto apply the 8 Mathematical Practices

Bill McCallum – “Structuring the Mathematical Practices” http://commoncoretools.me

http://commoncoretools.me/




Table I and 2

Making the Connection

Concrete

Pictorial

Abstract


9 + 6 = 15

Multipurpose Models• Number path• Number stairs• Number bond• Place Value Models

• Ten frames, bundles, base ten blocks, money, number disks• Bar Model• Area Model• Number line• Array

• Rekenrek- physical model of an array


Second Grade8 children are swimming in the pool. 5 more

children jump in. How many children are in the pool now?


?

8 children5 more

8 + 5 = 13 13 children are in the pool.

Marcus has 12 pencils. Sergio has 3 more pencils than Marcus. How many pencils does Sergio have?


Jerry has 12 eggs. He gave 3 to Kevin. How many eggs does Jerry have now?


PK-5 Math Forum

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