mathematics assessment office of superintendent of public instruction 1 ospi mathematics assessment...

Mathematics AssessmentMathematics Assessment

Office of Superintendent

of Public Instruction 1

Karen Hall2008 WERA



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.”

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Standards Curriculum

Assessment

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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

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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

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Develop Item Specifications for Grades 3-8 while retaining clarity and specificity of Standards Document.

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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.

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Identify which Performance Expectations to assess on WASL.

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Identify restrictions, if any, for◦Vocabulary “Vocabulary First Used in Assessment Items” “Measurement Vocabulary”

◦Computation Number of addends Denominators Decimal places

◦Measurements

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For each Performance Expectation Identify:◦Cognitive Complexity (Webb’s model)◦Item Type (MC or SA)◦Contextual Situation or not◦“Tools” or “No-Tools” day

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Items may ask students to: C.C. Format Sit Tool

5.3.A Classify quadrilaterals. 2 MC,SA N I

5.3.B Identify, sketch, and measure acute, right, and obtuse angles. 1 MC,SA N I

5.3.C Identify, describe, and classify triangles by angle measure and number of congruent sides.

1,2 MC,SA N I

5.3.D Determine the formula for the area of a parallelogram by relating it to the area of a rectangle.

NA NA NA NA

5.3.E Determine the formula for the area of a triangle by relating it to the area of a parallelogram.

NA NA NA NA

5.3.F Determine the perimeters and areas of triangles and parallelograms. 1 MC N I

5.3.G Draw quadrilaterals and triangles from given information about sides and angles.

2 SA I I

5.3.H Determine the number and location of lines of symmetry in triangles and quadrilaterals.

1 MC N I

5.3.I Solve single- and multi-step word problems about the perimeters and areas of quadrilaterals and triangles and verify the solutions.

2 MC,SA Y I

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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

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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

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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

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Test Experts Recommendation:

Assign Cognitive Complexityto each Performance Expectation

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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)







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




Alignment

Standards

Assess-ment

Assessment

Standards

StandardsAssessment

Assessment Items

Standards

Adapted from Norman Webb, 2005 20




Develop assessment items to align with

cognitive complexity of Performance Expectation

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The demand on thinking the items requires:

Low ComplexityRelies heavily on the recall and recognition of previously learned concepts and principles.

Moderate ComplexityInvolves more flexibility of thinking and choice among alternatives than do those in the low-complexity category.

High ComplexityPlaces heavy demands on students, who must engage in more abstract reasoning, planning, analysis, judgment, and creative thought.







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







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.







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.

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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.




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.




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.




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.




However, extended time alone is not the distinguishing factor.

Task Thinking

Collecting data samples over several months

Recall

Organizing the data in a chart Skills/concepts

Using this chart to make and justify predictions

StrategicThinking

Developing a generalized model from this data and applying it to a new situation

ExtendingThinking




• 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.

Read example items and discuss cognitive complexity of each item

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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

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Grades 3-5 Grades 6-8

38 Points Total 24 Multiple-Choice 7 Short-Answer

50 Points Total 30 Multiple-Choice 10 Short-Answer

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Areas of Emphasis

MC SA Total Points PointsLevel 1

PointsLevel 2

PointsLevel 3

5.1

5.2

5.3

5.4

5.5

5.6

Total Number of Items

24 7

Total Number of Points

24 14 38

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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

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Survey results Paragraphs in Standards Document Performance Expectations

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34 BOLD text Performance Expectations31 test questions

38 total points.

Items may ask students to: C.C. Format Sit Tool

5.3.A Classify quadrilaterals. 2 MC,SA N I

5.3.B Identify, sketch, and measure acute, right, and obtuse angles. 1 MC,SA N I

5.3.C Identify, describe, and classify triangles by angle measure and number of congruent sides.

1,2 MC,SA N I

5.3.D Determine the formula for the area of a parallelogram by relating it to the area of a rectangle.

NA NA NA NA

5.3.E Determine the formula for the area of a triangle by relating it to the area of a parallelogram.

NA NA NA NA

5.3.F Determine the perimeters and areas of triangles and parallelograms. 1 MC N I

5.3.G Draw quadrilaterals and triangles from given information about sides and angles.

2 SA I I

5.3.H Determine the number and location of lines of symmetry in triangles and quadrilaterals.

1 MC N I

5.3.I Solve single- and multi-step word problems about the perimeters and areas of quadrilaterals and triangles and verify the solutions.

2 MC,SA Y I

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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

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GRADE Total PE’s PE’s Assessed # of items Assessed 2010

3 37 32 31

4 43 37 31

5 40 33 31

6 39 35 40

7 35 32 40

8 33 31 40

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mathematics assessment office of superintendent of public instruction 1 ospi mathematics assessment...

Documents

public instruction rcw

new items

existing assessment

new gradelevel standards

administration of new

new performance standards

math standards

wera slide