1. Mathematics Assessment Office of Superintendent of Public Instruction 1 OSPI Mathematics Assessment Update for Grades 3-8 and High School Karen Hall 2008 WERA

2. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction RCW 28A.305.215(3) “…The recommendations [for revised EALRs and GLEs in mathematics] shall be based on: (a) Considerations of clarity, rigor, content, depth, coherence from grade to grade, specificity, accessibility, and measurability.” 2

3. Mathematics Assessment Office of Superintendent of Public Instruction StandardsCurriculum Assessment 3

4. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction  April 2008: New Grade 3-8 Math Standards approved  May - November 2008 ◦ Develop Item Specifications for new grade-level standards ◦ Align or revise items in existing test items to new grade-level standards ◦ Write new items to fill in gaps  April-May 2009 ◦ Last year of current Grade 3-8 math WASL ◦ Pilot new and rewritten items  April-May 2010: First administration of new Grade 3-8 math WASL  July 2010: State Board adopts new performance standards on Gr. 3-8 math tests 4

5. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction  August 2008: New High School Mathematics Standards approved  November 2008 –August 2009 ◦ Align existing assessment items to new grade-level standards ◦ Write new items to fill in gaps  2009 and 2010: Pilot new and rewritten items  2011: First administration of new HS End of Course Assessments  July 2011: State Board adopts new performance standards on High School End of Course Assessments 5

6. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction Develop Item Specifications for Grades 3-8 while retaining clarity and specificity of Standards Document. 6

7. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction  5.3. Core Content: Triangles and quadrilaterals (Geometry/Measurement, Algebra)  Students focus on triangles and quadrilaterals to formalize and extend their understanding of these geometric shapes. They classify different types of triangles and quadrilaterals and develop formulas for their areas. In working with these formulas, students reinforce an important connection between algebra and geometry. They explore symmetry of these figures and use what they learn about triangles and quadrilaterals to solve a variety of problems in geometric contexts. 7

8. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction Grade LevelArea of EmphasisExpectation 5.3.D 8

9. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction  Identify which Performance Expectations to assess on WASL. 9

10. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction  Identify restrictions, if any, for ◦ Vocabulary  “Vocabulary First Used in Assessment Items”  “Measurement Vocabulary” ◦ Computation  Number of addends  Denominators  Decimal places ◦ Measurements 10

11. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction  For each Performance Expectation Identify: ◦ Cognitive Complexity (Webb’s model) ◦ Item Type (MC or SA) ◦ Contextual Situation or not ◦ “Tools” or “No-Tools” day 11

12. Items may ask students to:C.C.FormatSitToo l 5.3.A Classify quadrilaterals.2MC,SANI 5.3.B Identify, sketch, and measure acute, right, and obtuse angles.1MC,SANI 5.3.C Identify, describe, and classify triangles by angle measure and number of co ngruent sides. 1,2MC,SANI 5.3.D Determine the formula for the area of a parallelogram by relating it to the are a of a rectangle. NA 5.3.EDetermine the formula for the area of a triangle by relating it to the area of a parallelogram. NA 5.3.F Determine the perimeters and areas of triangles and parallelograms.1MCNI 5.3.G Draw quadrilaterals and triangles from given information about sides and a ngles. 2SAII 5.3.HDetermine the number and location of lines of symmetry in triangles and q uadrilaterals. 1MCNI 5.3.I Solve single- and multi-step word problems about the perimeters and areas of quadrilaterals and triangles and verify the solutions. 2MC,SAYI 12

13.  Use Item Development Guidelines at the beginning of this document.  Answer choices will be stated in terms of the same system of measurement.  Items will not require students to convert between U.S. customary and metric units.  Exponents will not be used to express square units.  Items may tell students to use a straight edge or a protractor.  Items will not require use of a particular strategy to determine a derived measurement.  Grids may be provided in items that require students to draw angles or figures. Stimulus, Stem, and Prompt Rules 13

14.  Items assessing 5.3.A may include parallelograms, kites, squares, rhombi, trapezoids, and rectangles.  Items assessing 5.3.C may require triangles to be classified by angles as acute, right obtuse or by sides as scalene, isosceles, or equilateral.  Items assessing 5.3.F may include side measures or may require students to measure sides of figures. Stimulus, Stem, and Prompt Rules 14

15. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction OSPI Mathematics Assessment Team Yoonsun Lee, Ph.D Draft 1 Review by Teachers and Coaches Mathematics Assessment Leadership Team (MALT) Draft 2 Review by Testing Experts Review by OSPI & other interested educators Draft 3 15

16. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction  Summer Item Writing ◦ 120 Item writers, ~900 items for grades 3-8 ◦ Excellent feedback on item specifications  Content Review of New Items ◦ 5 committees ◦ 2 weeks Draft #8 16

17. Mathematics Assessment Office of Superintendent of Public Instruction Test Experts Recommendation : Assign Cognitive Complexity to each Performance Expectation 17

18. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction 18  No Child Left Behind (NCLB) requires assessments to “measure the depth and breadth of the state academic content standards for a given grade level” (U.S. Department of Education, 2003, p. 12)

19. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction 19  Mechanism to ensure that the intent of the standard and the level of student demonstration required by that standard matches the assessment items (required under NCLB)  Provides cognitive processing ceiling for item development

20. Mathematics Assessment Office of Superintendent of Public Instruction Alignment Standards Assess- ment Assessment Standards Assessment Assessment Items Standards Adapted from Norman Webb, 2005 20

21. Mathematics Assessment Office of Superintendent of Public Instruction Develop assessment items to align with cognitive complexity of Performance Expectation 21

22. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction 22 The demand on thinking the items requires: Low Complexity Relies heavily on the recall and recognition of previously learned concepts and principles. Moderate Complexity Involves more flexibility of thinking and choice among alternatives than do those in the low-complexity category. High Complexity Places heavy demands on students, who must engage in more abstract reasoning, planning, analysis, judgment, and creative thought.

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24. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction 24  Adapted from the model used by Norman Webb, University of Wisconsin, to align standards with assessments  Used by the Council of Chief State School Officers (CCSSO) for assessment alignment in more than ten states

25. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction 25  The Depth of Knowledge is NOT determined by the verb, but the context in which the verb is used and the depth of thinking required.

26. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction  Level 1 (Low) Recall  Level 2 (Moderate) Skill/Concept  Level 3 (High) Strategic Thinking  Level 4 Extended Thinking NOTE: Definitions with examples of skills at each level. 26

27. Mathematics Assessment Office of Superintendent of Public Instruction 27 DOK 1 requires recall of information, such as a fact, definition, term, or performance of a simple process or procedure. Answering a Level 1 item can involve following a simple, well-known procedure or formula. Simple skills and abilities or recall characterize DOK 1.

28. Mathematics Assessment Office of Superintendent of Public Instruction 28 DOK 2 includes the engagement of some mental processing beyond recalling or reproducing a response. Items require students to make some decisions as to how to approach the question or problem. These actions imply more than one mental or cognitive process/step.

29. Mathematics Assessment Office of Superintendent of Public Instruction 29 DOK 3 requires deep understanding as exhibited through planning, using evidence, and more demanding cognitive reasoning. The cognitive demands at Level 3 are complex and abstract. An assessment item that has more than one possible answer and requires students to justify the response they give would most likely be a Level 3.

30. Mathematics Assessment Office of Superintendent of Public Instruction 30 DOK 4 requires high cognitive demand and is very complex. Students are expected to make connections and relate ideas within the content or among content areas—and have to select or devise one approach among many alternatives on how the situation can be solved. Due to the complexity of cognitive demand, DOK 4 often requires an extended period of time.

31. Mathematics Assessment Office of Superintendent of Public Instruction 31 However, extended time alone is not the distinguishing factor. TaskThinking Collecting data samples over several months Recall Organizing the data in a chartSkills/ concepts Using this chart to make and justify predictions Strategic Thinking Developing a generalized model from this data and applying it to a new situation Extending Thinking

32. Mathematics Assessment Office of Superintendent of Public Instruction 32 Remember… Depth of Knowledge (DOK) is a scale of cognitive demand. DOK requires looking at the assessment item/standard order to determine the level. DOK is about the item/standard-not the student. The context of the assessment item/standard must be considered to determine the DOK-not just a look at which verb was used.

33.  Read example items and discuss cognitive complexity of each item 33

34. Mathematics Assessment Office of Superintendent of Public Instruction 34 Develop Grades 3-8 Test Maps

35. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction  Total Number of points  Total Number of Multiple-Choice Items  Total Number of Short-Answer Items  Distribution of Points by Area of Emphasis  Distribution of Points by Cog. Complexity 35

36. Grades 3-5Grades 6-8  38 Points Total  24 Multiple-Choice  7 Short-Answer  50 Points Total  30 Multiple-Choice  10 Short-Answer 36

37. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction Areas of Empha sis MCSATotal PointsPoints Level 1 Points Level 2 Points Level 3 5.1 5.2 5.3 5.4 5.5 5.6 Total Number of Items 247 Total Number of Points 241438 37

38. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction  Surveyed ~150 teachers, coaches and mathematics coordinators  Workgroup to distribute test points among areas of emphasis ◦ Cathy Seeley, Dana Center ◦ George Bright, OSPI, Mathematics Special Assistant ◦ OSPI Teaching and Learning Mathematics ◦ OSPI Mathematics Assessment  Test Map Review Committee ◦ Standards Revision Team ◦ Teachers, Coaches, Administrators 38

39. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction  Survey results  Paragraphs in Standards Document  Performance Expectations 39

40. 34 BOLD text Performance Expectations 31 test questions 38 total points. Items may ask students to:C.C.FormatSitToo l 5.3.A Classify quadrilaterals.2MC,SANI 5.3.B Identify, sketch, and measure acute, right, and obtuse angles.1MC,SANI 5.3.C Identify, describe, and classify triangles by angle measure and number of co ngruent sides. 1,2MC,SANI 5.3.D Determine the formula for the area of a parallelogram by relating it to the are a of a rectangle. NA 5.3.EDetermine the formula for the area of a triangle by relating it to the area of a parallelogram. NA 5.3.F Determine the perimeters and areas of triangles and parallelograms.1MCNI 5.3.G Draw quadrilaterals and triangles from given information about sides and a ngles. 2SAII 5.3.HDetermine the number and location of lines of symmetry in triangles and q uadrilaterals. 1MCNI 5.3.I Solve single- and multi-step word problems about the perimeters and areas of quadrilaterals and triangles and verify the solutions. 2MC,SAYI 40

41. Mathematics Assessment Office of Superintendent of Public Instruction Mathematics Assessment Office of Superintendent of Public Instruction  Use results of test map review to finalize test maps for grades 3-8  Submit test maps for approval to National Technical Advisory Committee on January 11, 2009  Post Grades 3-8 Test and Item Specification Document on OSPI website.  Review and feedback of assessment restrictions for high school performance expectations – January Conference  Write items to assess high school PEs 41

42. Mathematics Assessment Office of Superintendent of Public Instruction GRADETotal PE’sPE’s Assessed# of items Assessed 2010 3373231 4433731 5403331 6393540 7353240 8333140 42