The Essential Skill of Mathematics

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

2. Goals for this workshop 1. Introduce • Oregon’s Math Problem Solving Scoring Guide • Principles of math instruction and assessment in content area classes • Classroom uses of the Math Scoring Guide 2. Examine • Essential Skill of Mathematics requirements • Student work samples 3. 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 Skill Definition 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. Essential Skill Proficiency • Three options for diploma requirement • OAKS Statewide Mathematics Assessment • Score of 236 or higher • Other approved standardized assessments

6. 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 4 or higher in each dimension for each work sample

7. 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.

8. Let’s Look at the scoring guide !

9. 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

10. Mathematics Problem Solving Scoring Guide

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

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

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

14. Accuracy Clearly identify and support the solution.

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

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

17. 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

18. What does a Math Work Sample look like?

19. Mathematics Problem SolvingWork Samples • Present complex, often multi-step tasks that could not be presented in a multiple choice test format • Designed to judge student abilities to apply specific knowledge & skills • Allow a variety of problem-solving approaches • May simulate real-word mathematics problems

20. Mr. Gerard’s Oil Tank Mr. Gerard bought a house that contained an empty heating oil tank with the dimensions shown in the drawing. The left and right arcs of the tank are perfect semi-circles. If heating oil costs $3.50 per gallon, how much would it cost Mr. Gerard to fill this tank? (There are 231 cubic inches in a gallon.)

21. Share your solution!

22. Scoring the First Anchor Paper This anchor paper met the achievement standard in each dimension of the scoring guide. Why did this paper earn these scores?

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

24. Scoring Within the Dimensions . . .What differentiates a 3 from a 4?

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

26. Roof Vents How many roof vents will it take to properly vent an attic with a span of 32 feet, a length of 62 feet, and an 8/12 roof pitch? Industry standards determine that one vent is needed for every 660 cubic feet of air space.

27. Share your solution!

28. Scoring the First Anchor Paper This anchor paper almost met the achievement standard. Why did this paper earn these scores?

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

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

31. 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

32. Multiple Uses for the Scoring Guide • Instructional Tool • Makes targets explicit to students • Opportunities to show students models from website or other examples

33. 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

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

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

36. 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.

37. 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.

38. 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.)

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

40. 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)

41. A Parting Thought The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move nor think.  This is the hog-tie, and it is what Euclid did to geometry. ~Eric Bell, The Search for Truth