1. 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 Revealed National Council for Teachers of Mathematics (NCTM) St. Louis, April 2006 Beth Schefelker, Teaching Specialist Milwaukee Public Schools schefeba@mail.milwaukee.k12.wi.us Laura Moranchek, NAEP Coordinator WI Department of Public Instruction laura.moranchek@dpi.state.wi.us

2. This material is based upon work supported by the National Science Foundation Grant No. 0314898. 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. This material is based upon work supported by the National Science Foundation Grant No. 0314898. 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. This material is based upon work supported by the National Science Foundation Grant No. 0314898. Wisconsin Model Academic Standard for Mathematics – A. Mathematical Processes

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

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. This material is based upon work supported by the National Science Foundation Grant No. 0314898. Alarming Data…. WKCE Data Analysis Constructed Response Milwaukee Public Schools 2003-04 Black 2004-05 Red4th Grade8th Grade Wisconsin Model Academic Standards Blank"0" PointsBlank"0" Points Mathematical Process 6% 2% 62% 16% 6% 58% 56% Algebraic Relationships 6% 2% 68% 69% 22% 14% 47% 56% Measurement 5% 2% 28% 31% 14% 6% 66% 56%

8. This material is based upon work supported by the National Science Foundation Grant No. 0314898. 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. This material is based upon work supported by the National Science Foundation Grant No. 0314898. 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. This material is based upon work supported by the National Science Foundation Grant No. 0314898. Session Goals To inform participants of the development of CR items. To engage participants in the process used to score CR items.

11. This material is based upon work supported by the National Science Foundation Grant No. 0314898. 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. This material is based upon work supported by the National Science Foundation Grant No. 0314898. Directions for a Simulated 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. This material is based upon work supported by the National Science Foundation Grant No. 0314898. 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 ColorFrequency Blue5 Red2 Yellow3 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. This material is based upon work supported by the National Science Foundation Grant No. 0314898. 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. This material is based upon work supported by the National Science Foundation Grant No. 0314898. 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. This material is based upon work supported by the National Science Foundation Grant No. 0314898. 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. This material is based upon work supported by the National Science Foundation Grant No. 0314898. WKCE-CRT Constructed Response 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. This material is based upon work supported by the National Science Foundation Grant No. 0314898. 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. This material is based upon work supported by the National Science Foundation Grant No. 0314898. Questions and Contact Information National Council for Teachers of Mathematics (NCTM) St. Louis, April 2006 Beth Schefelker, Teaching Specialist Milwaukee Public Schools schefeba@mail.milwaukee.k12.wi.us Laura Moranchek, NAEP Coordinator WI Dept of Public Instruction laura.moranchek@dpi.state.wi.us