high-stake state mathematics assessment: crs and bcrs…the secrets revealed

This material is based upon work supported by the National Science Foundation Grant No. 0314898.

High-Stake State Mathematics Assessment:

CRs and BCRs…The Secrets RevealedNational Council for Teachers of Mathematics (NCTM)

St. Louis, April 2006

Beth Schefelker, Teaching SpecialistMilwaukee Public [email protected]

Laura Moranchek, NAEP CoordinatorWI Department of Public [email protected]


NCTM Principles & Standards Communication

Standard• Organize and consolidate their mathematical

thinking through communication;

• Communicate their mathematical thinking coherently and clearly to peers, teachers, and others;

• Analyze and evaluate the mathematical thinking and strategies of others;

• Use the language of mathematics to express mathematical ideas precisely.


Standards Required by No Child Left Behind

(NCLB):• Content Standards: what students know

and should be able to do at specified grade levels

• Performance Standards: how students show that they meet content standards

• Proficiency Standards: how well students must perform


Wisconsin Model Academic Standard for Mathematics – A. Mathematical

ProcessesGrade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 10

Use reasoning and logic to:

_ perceive patterns _ identify

relationships _ formulate questions

_ pose problems _ make conjectures

_ justify strategies _ test reasonableness

of results






of results


_ perc eive patterns _ identify




of results




_ pose problems _ make conjectu res


of results






of results






of results




_ pose problems _ make conj ectures


of results

Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways e.g., using words, numbers, symbols, pictures, charts, tables, diagrams, graphs, and models.


Communicate mathematical ideas and reasoning using the vocabu lary of mathematics in a variety of ways e.g., using words, numbers, symbols, pictures, charts, tables, diagrams, graphs, and models.




Communicate mathematical ideas and reasoning usin g the vocabulary of mathematics in a variety of ways e.g., using words, numbers, symbols, pictures, charts, tables, diagrams, graphs, and models.

Connect mathematics to the real world, as well as within mathematics.





Connect mathem atics to the real world, as well as within mathematics.


Create and use representations to organize, record, and communicate mathematical ideas.

Create and use representations to organi ze, record, and communicate mathematical ideas.



Create and use representations t o organize, record, and communicate mathematical ideas.



A. Mathematical Processes

Students will effectively use mathematical knowledge, skills and strategies related to

reasoning,

communication, connections, representation and problem solving.

Solve and analyze rout ine and non -routine problems.

Solve and analyze routine and non -routine problems.







"Make this the golden rule, the equivalent of the

Hippocratic oath: Everything we ask a child to do should be worth doing."

—Philip Pullman, ISIS speech, April 1, 2003


Alarming Data….

WKCE Data Analysis Constructed Response Milwaukee Public Schools

2003-04 Black

2004-05 Red 4th Grade 8th Grade

Wisconsin Model Academic Standards Blank "0" Points Blank "0" Points

Mathematical Process

6%2%

62%62%

16%6%

58%56%

Algebraic Relationships

6%2%

68%69%

22%14%

47%56%

Measurement5%2%

28%31%

14%6%

66%56%


Score Points Constructed Response

(CR’s)• Grades 3 – 8

– Three Points• One Point – Content• Two Points – Process

• Grade 10– Two Points - Brief Constructed Response

• One Point – Content• One Point – Process

– Four Points - Extended Constructed Response


Changing the Status Quo!

• How do we get educators to value the importance of being able to communicate mathematically?

• What changes need to be made in everyday classroom practice to support students’ ability to effectively communicate?


Session Goals

• To inform participants of the development of CR items.

• To engage participants in the process used to score CR items.


Who Scores the Items?

• All scorers have a 4-year degree.

• Scorers work 7 hour shifts.

• Each scorer scores approximately 150-300 papers/day.

• Scorers are trained on every item and subject to frequent accuracy checks.


Directions for aSimulated Scoring

Session• Complete the question independently.

• Compare responses to the rubric.

• Practicing on a series of student work samples.

• Benchmark examples

• Student Anchor papers

• Qualifying – Round 1 and 2


Patrick spins a spinner that has three colors. He spins it 10 times and records his results in a table below.

Patrick’s Spinner ResultsColor Frequency

Blue 5

Red 2

Yellow 3Step A

Next Patrick will spin the spinner 50 times. Based on the results in the table, how many times is Patrick’s spinner likely to land on red?

Answer:_____________ times

Step B

Use math to explain why your prediction is valid. Use words and/or numbers in your explanation. Include a description of what Patrick’s spinner probably looks like.____________________________________________________________________________________________________


Scoring Rubric• Three Points Possible:

Step A – Mathematical Content:• 1 point – Correct• 0 points – Incorrect

Step B – Mathematical Process:• 2 points – Demonstrates a thorough understanding, uses

appropriate mathematical procedures or concepts to explain or justify the response to Step A

• 1 point – Demonstrates only partial understanding, lacks an essential understanding of the underlying mathematical concepts used to provide the response to Step A

• 0 points – Provides a completely incorrect explanation or justification or one that cannot be interpreted, or no response at all


WKCE-CRT CRs Simulated Scoring Practice

Benchmark Papers: Anchor Papers:B1________ A1__________B2________ A2__________B3________ A3__________B4________ A4__________B5________ A5__________B6________ A6__________

A7__________ A8__________

A9__________ A10_________


WKCE-CRT CRs Simulated Scoring Practice

Benchmark Papers: Anchor Papers:B1__1/2__ A1___1/1_____B2__1/1___ A2___1/1_____B3__0/2__ A3___1/2_____B4__1/0__ A4___1/2_____B5__0/0__ A5___0/0_____B6__0/0___ A6___0/0_____

A7___1/1_____ A8___1/0____

A9___0/0_____ A10__0/1_____


WKCE-CRT ConstructedResponse

Simulated Scoring Practice

Qualifying Round 1: Qualifying Round 2:Q1-1__________ Q2-1__________Q1-2__________ Q2-2__________Q1-3__________ Q2-3__________Q1-4__________ Q2-4__________Q1-5__________ Q2-5__________Q1-6__________ Q2-6__________Q1-7__________ Q2-7__________Q1-8__________ Q2-8__________Q1-9__________ Q2-9__________Q1-10_________ Q2-10__________________% accurate ___________% accurate


Things to Ponder…

• In what way can we assist students to build clear coherent mathematical communication?

• How can we support growth and development of others in their understanding of the Communication Standard?


Questions and Contact Information

National Council for Teachers of Mathematics (NCTM)St. Louis, April 2006

Beth Schefelker, Teaching SpecialistMilwaukee Public [email protected]

Laura Moranchek, NAEP CoordinatorWI Dept of Public [email protected]

high-stake state mathematics assessment: crs and bcrs…the secrets revealed

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