High-Stake State Mathematics Assessment: CRs and BCRs…The Secrets Revealed

1. High-Stake State Mathematics Assessment:CRs and BCRs…The Secrets Revealed National Council for Teachers of Mathematics (NCTM)St. Louis, April 2006 Beth Schefelker, Teaching SpecialistMilwaukee Public Schoolsschefeba@mail.milwaukee.k12.wi.us Laura Moranchek, NAEP CoordinatorWI Department of Public Instructionlaura.moranchek@dpi.state.wi.us

2. 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.

3. 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

4. Wisconsin Model Academic Standard for Mathematics – A. Mathematical Processes

6. "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

7. Alarming Data…. WKCE Data Analysis Constructed Response Milwaukee Public Schools

8. 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

9. 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?

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

11. 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.

12. 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

13. Patrick spins a spinner that has three colors. He spins it 10 times and records his results in a table below. Patrick’s Spinner Results Step 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. ____________________________________________________________________________________________________

14. 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

15. 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_________

16. 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_____

17. 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

18. 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?

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