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The Essential Skill of Mathematics

The Essential Skill of Mathematics. Using the New Math Scoring Guide: An Introduction for High School Math Teachers. Goals for this workshop. 1 . Review Oregon’s Math Problem Solving Scoring Guide Classroom uses of the Math Scoring Guide

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The Essential Skill of Mathematics

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  1. The Essential Skillof Mathematics Using the New Math Scoring Guide: An Introduction for High School Math Teachers

  2. Goals for this workshop 1. Review • Oregon’s Math Problem Solving Scoring Guide • Classroom uses of the Math Scoring Guide • Supporting colleagues in using math work samples in content classes 2. Understand • Options for Demonstrating Proficiency in the Essential Skill of Mathematics for the Oregon Diploma 3. Score student papers and calibrate to scoring standards 4. Set the stage for follow-up training

  3. OAR: 581-22-0615 For students first enrolled in grade 9 during the 2010-2011 school year [and subsequent years], school districts and public charter schools shall require students to demonstrate proficiency in the Essential Skills listed • (A) Read and comprehend a variety of text; and • (B) Write clearly and accurately • (C) Apply mathematics

  4. Essential SkillDefinition Apply Mathematics in a variety of settings • Interpret a situation and apply workable mathematical concepts and strategies, using appropriate technologies where applicable. • Produce evidence, such as graphs, data, or mathematical models, to obtain and verify a solution. • Communicate and defend the verified process

  5. The Common Core State Standards For Mathematics describe varieties of expertise... that rest on important “processes and proficiencies” …[including the] NCTM process standards of • problem solving • reasoning and proof • communication • representation • and connections

  6. Make sense of problems and persevere in solving them “Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution….

  7. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.”

  8. Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. From Common Core State Standards for Mathematics

  9. Essential Skill Proficiency Three options for diploma requirement • OAKS Statewide Mathematics Assessment • Score of 236 or higher • Other approved standardized assessments

  10. Option 3Math Work Samples • Mathematics Work Sample scored using Official State Scoring Guide • Two Mathematics Work Samples Required: algebra, geometry, statistics • Students must earn • a score of 4or higher • in each dimension • for each work sample

  11. Level of Rigor • Work samples must meet the level of rigor required on the OAKS assessment. • Work samples provide an optional means to demonstrate proficiency notaneasier means.

  12. Let’s Review the scoring guide !

  13. The Math Problem Solving Scoring Guide Background • In use since 1988 (minor revisions in 2000) • 2009-2010 new version based on Oregon Mathematics Content Standards • 2010-11 aligned to the Common Core State Standards • Adopted by Oregon State Board of Education May 2011

  14. Mathematics Problem Solving Scoring Guide

  15. Making sense of the problem Interpret the concepts of the task and translate them into mathematics

  16. Representing and solvingthe problem Use models, pictures, diagrams, and/or symbols to represent the problem and select an effective strategy to solve the problem.

  17. Communicating Reasoning Communicate mathematical reasoning coherently and clearly use the language of mathematics.

  18. Accuracy Clearly identify and support the solution.

  19. Reflecting and Evaluating • State the solution in the context of the problem. • Defend the process. Evaluate and interpret the reasonableness of the solution

  20. Simplified Mathematics Scoring Guide Exemplary 6 Strong 5 Proficient 4 Developing 3 Emerging 2 1 Beginning

  21. Another way to look at scores 6 −Enhanced or connected to other mathematics 5 – Thoroughly developed 4 – Work is proficient (not perfect) 3 – Work is partially effective or partially complete 2 – Work is underdeveloped or sketchy 1 – Work is ineffective, minimal, or not-evident

  22. What does a Math Work Sample look like?

  23. Mathematics Problem Solving Work Samples Present complex, multi-step tasks Are designed to judge student abilities to apply specific knowledge & skills Allow a variety of problem-solving approaches May simulate real-word mathematics problems

  24. Farmer John The Task: Farmer John has a rectangular holding pen that measures 10 yards long and 5 yards wide to contain his cattle. He is acquiring more cattle from the neighboring farmer and wants to add the same amount of fencing to each side to create a new holding pen that encloses 176 square yards. How much should Farmer John add on to each side of his existing holding pen to achieve his goal?

  25. Share your solution Share your solution!

  26. Scoring the First Anchor Paper This anchor paper met the achievement standard in each trait. Why did this paper earn these scores?

  27. Scoring the 2nd Anchor Paper This anchor paper did not meet the achievement standard. What scores did this paper earn?

  28. Scoring Within the Traits . . .What differentiates a 3 and a 4?

  29. Scoring Papers 3, 4, & 5 Use the scoring guide to rate each paper. What scores did these papers earn?

  30. Bike Rental A local bicycle rental company charges $12 to rent a bicycle. They normally have 300 rentals per month. The company owner has determined that each increase in price of $2 will decrease the number of rentals by 15. What price will maximize the revenue?

  31. Share your solution!

  32. Scoring the First Anchor Paper for Bike Rental This anchor paper met the achievement standard in each trait. Why did this paper earn these scores?

  33. Scoring the 2nd Anchor Paper For Bike Rental This anchor paper also met the achievement standard. What scores did this paper earn?

  34. Scoring Papers 8, 9, & 10 Use the scoring guide to rate each paper. What scores did these papers earn?

  35. The Mathematics Scoring Guide Purposes • Instructional Tool • Formative Assessment • Summative Assessment • Demonstrate Proficiency in the Essential Skill of Apply Math to earn an Oregon Diploma

  36. Building Consensus on Definitions of Assessments

  37. Multiple Uses for the Scoring Guide • Instructional Tool • Makes targets explicit to students • Opportunities to show students models from website or other examples • Screening Tool • Help determine likelihood of reaching proficiency – on target, need assistance, at risk • Help determine which students need additional instruction and coaching

  38. Building Consensus on Definitions of Assessments

  39. Multiple Uses for the Scoring Guide • Formative & Interim Assessments • Inform instructional strategies • Provide data on student progress • Classroom/ Summative Assessment • End of unit, course, etc. or Essential Skills

  40. Formative Assessment • The Scoring Guide can help to identify math strengths and weaknesses. • Students learn where to focus to improve math skills. • Teachers learn where additional instruction is needed.

  41. 2 work samples − • Algebra, geometry, or statistics • Score of 4 or higher in all dimensions on Official Scoring Guide Requirements for Essential Skill Proficiency Using Math Work Samples

  42. Work Sample Design • Math Problem Solving Tasks must be carefully designed to provide opportunities for students to demonstrate skills in all dimensions of the scoring guide. • Math tasks must be at the appropriate difficulty level and address high school content standards.

  43. Work Sample Implementation Administration • Work samples must be the product of an individual • Work samples must be supervised by an authorized adult; • Students may not work on work samples outside a supervised setting.

  44. Work Sample Implementation Scoring • All work samples must be scored using Oregon’s Official Math Scoring Guide. • All raters must have been trained to use the Scoring Guide. • Only one set of scores is required for a work sample. (Districts may want more than one rater for borderline papers.)

  45. Work Sample Implementation Feedback and Revision FEEDBACK: Only 2 options • Oregon’s Official Scoring Form • Oregon’s Scoring Guide (highlight/underline) STUDENT REVISION: • Students are allowed to revise and resubmit their work samples following scoring/feedback. • Most papers should be revised only once.

  46. Resources & Coming Attractions • ODE Website: www.ode.state.or.us/go/worksamples • OCTM Website: http://www.octm.org/ • Follow-up workshops (List any scheduled) • Contact information (List your information here)

  47. A Parting Thought It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts. - Paul Halmos

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