HighStake State Mathematics

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High-Stake State Mathematics AssessmentCRs and
BCRsThe Secrets Revealed
National Council for Teachers of Mathematics
(NCTM)St. Louis, April 2006
Beth Schefelker, Teaching SpecialistMilwaukee
Public Schoolsschefeba_at_mail.milwaukee.k12.wi.us
Laura Moranchek, NAEP CoordinatorWI Department
of Public Instructionlaura.moranchek_at_dpi.state.wi
.us
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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.

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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

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Wisconsin Model Academic Standard for Mathematics
A. Mathematical Processes
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(No Transcript)
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"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
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Alarming Data.

• WKCE Data Analysis Constructed Response
• Milwaukee Public Schools

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Score Points Constructed Response (CRs)

• 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

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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?

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Session Goals

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

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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.

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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

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Patrick spins a spinner that has three colors.
He spins it 10 times and records his results in
a table below. Patricks
Spinner Results
Step A Next Patrick will spin the spinner 50
times. Based on the results in the table, how
many times is Patricks 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 Patricks spinner
probably looks like. _____________________________
__________________________________________________
_____________________
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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

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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_________
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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_____
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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

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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?

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Questions and Contact Information
Beth Schefelker, Teaching SpecialistMilwaukee
Public Schoolsschefeba_at_mail.milwaukee.k12.wi.us
Laura Moranchek, NAEP CoordinatorWI Dept of
Public Instructionlaura.moranchek_at_dpi.state.wi.us
National Council for Teachers of Mathematics
(NCTM)St. Louis, April 2006