Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction 1
Karen Hall2008 WERA
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics 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
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Standards Curriculum
Assessment
3
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics 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
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics 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
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Develop Item Specifications for Grades 3-8 while retaining clarity and specificity of Standards Document.
6
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics 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
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction 8
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Identify which Performance Expectations to assess on WASL.
9
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics 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
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics 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
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
12
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
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
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction 15
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics 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
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Test Experts Recommendation:
Assign Cognitive Complexityto each Performance Expectation
17
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics 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)
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics 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
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Alignment
Standards
Assess-ment
Assessment
Standards
StandardsAssessment
Assessment Items
Standards
Adapted from Norman Webb, 2005 20
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Develop assessment items to align with
cognitive complexity of Performance Expectation
21
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction 22
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.
23
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics 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
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics 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.
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics 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
Mathematics AssessmentMathematics 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.
Mathematics AssessmentMathematics 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.
Mathematics AssessmentMathematics 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.
Mathematics AssessmentMathematics 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.
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction 31
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
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction 32
• 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
33
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction 34
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics 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
Grades 3-5 Grades 6-8
38 Points Total 24 Multiple-Choice 7 Short-Answer
50 Points Total 30 Multiple-Choice 10 Short-Answer
36
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
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
37
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics 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
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Survey results Paragraphs in Standards Document Performance Expectations
39
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
40
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
Mathematics AssessmentMathematics 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
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
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
42