Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 11
Mary [email protected]
OSPI MathematicsAssessment Update
for Grades 3-5
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 22
AgendaAgendaAssessment Tools and Resources
- Assessment OF and FOR Learning- Lessons Learned - Released Items Document
Assessment Update- Assessment 2009
- Assessment 2010
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 33
Looking at Student WorkLooking at Student Work
http://mathnexus.wwu.edu/Howlers Out of the Mouths of Actual Math
Students--Part IV- The commutative law of addition is when you
add a column of figures from bottom to top and top to bottom and get two different answers.
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 44
An average is a thing that hens lay their eggs on--for example, "My hens lay four eggs a week on the average."
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 55
Balanced AssessmentBalanced Assessment
Assessment Crisis: The Absence of Assessment FOR Learning
by Richard J. Stiggins, Phi Delta Kappan, June 2002
“Assessment of Learning” versus “Assessment for Learning”
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 66
Assessment Assessment of of LearningLearning“…assessment in the United States..has led to
the strongly held view that school improvement requires:
- the articulation of higher achievement standards- transformation of expectations into
rigorous assessments, and- accountability for student
achievement…”
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 77
Assessment Assessment for for LearningLearning
“There is another way in which assessment can contribute to the development of effective schools…..assessments for learning serve to help students learn more.”
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 88
The Mathemtics Washington The Mathemtics Washington Assessment of Student Learning Assessment of Student Learning
(WASL) (WASL)
Purpose: Assessment of Student Learning (Summative Assessment)
Lessons Learned/Released Items: Assessment for Student Learning
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 99
Assessment Assessment forfor Learning Learning
Understanding and articulating in advance of teaching achievement targets
Informing students about learning goals, in terms they understand, from the beginning
Becoming assessment literate and able to transform expectations into assessment exercises and scoring procedures that accurately reflect student achievement
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 1010
Assessment Assessment forfor Learning cont. Learning cont.
Using classroom assessments to build students’ confidence in themselves as learners and help them take responsibility for their own learning
Translating classroom assessment results into frequent descriptive feedback for students, providing them with specific insights as to how to improve
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
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December 2008December 2008
Slide Slide 1111
Assessment Assessment forfor Learning cont. Learning cont.
Continuously adjusting instruction based on results of classroom assessments
Engaging students in regular self-assessment, with standards held constant
Actively involving students in communicating with their teacher and their families about their achievement status and improvement
Mathematics AssessmentMathematics Assessment
Office of Superintendent
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December 2008December 2008
Slide Slide 1212
Lessons LearnedLessons Learned
Students misrepresent what they know and understand.
Students can improve their scores by following guidelines in Lessons Learned.
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 1313
Lessons LearnedLessons Learned
Format- Actions students could take for
improvement of scores- General guidelines for all grades- Grade level bands
Read Grades 3-5 first column
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December 2008December 2008
Slide Slide 1414
3-5 Number Sense3-5 Number SenseGrade 4 2002 RIDs Grade 4 2002 RIDs
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 1515
3-5 Number Sense3-5 Number Sense
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 1616
Partitive and Quotative DivisionPartitive and Quotative Division
Quotative – Measurement186 pencils in packages of six. How many packages?
Partitive—Fair Sharing186 pencils distributed to six tables. How many pencils at each table?
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 1717
More Partitive and Quotative Division ExamplesMore Partitive and Quotative Division Examples
I have $12. If socks cost $3 a pair, how many pairs can I buy?
Quotative
Socks are on sale at 3 pairs for $12. How much is this per pair?
Partitive
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 1818
More Partitive and Quotative Division ExamplesMore Partitive and Quotative Division Examples
There are 240 rooms on 24 floors of a hotel. How many rooms are there per floor?
Partitive
There are 240 rooms with 24 rooms per floor. How many floors?
Quotative
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 1919
Grades 3-5 MeasurementGrades 3-5 Measurement
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 2020
Mislabels everywhere. . . . . .Mislabels everywhere. . . . . .
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 2121
Grades 3-8 Geometric SenseGrades 3-8 Geometric SenseUse geometric attributes/mathematical
vocabulary to identify, describe, compare, classify figures such as: number of sides, angle measures, number of lines of symmetry, parallel and/or perpendicular line segments, etc.
Some figures belong to more than one category: e.g. a square is a rectangle, rhombus, and parallelogram.
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
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December 2008December 2008
Slide Slide 2222
Grades 3-8 Geometric SenseGrades 3-8 Geometric Sense
Examples of descriptions that do NOT use geometric vocabulary and/or mathematical language:- They are the same shape.- They are shaped like flags (or houses).- They have sharp edges. - They have letters in them.
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 2323
QuestionsQuestions
Read Algebraic Sense through Problem Solving.
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 2424
Grade 3-5 Algebraic SenseGrade 3-5 Algebraic SenseGrade 4 2007 RIDsGrade 4 2007 RIDs
Connect operations in equations to situations:
Mathematics AssessmentMathematics Assessment
Office of Superintendent
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December 2008December 2008
Slide Slide 2525
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 2626
Questions Grades 3-5Questions Grades 3-5
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 2727
Lessons LearnedLessons LearnedAssessment FOR Learning: Translating classroom assessment results into
frequent descriptive feedback for students, providing them with specific insights as to how to improve
http://www.k12.wa.us/assessment/WASL/Mathematics/resources.aspx
-2008 Lessons Learned (ppt) (pdf) -2007 Lessons Learned (Word) -2006 Lessons Learned (ppt) (Word) (pdf)
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
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December 2008December 2008
Slide Slide 2828
Released Items Released Items Eighth annual release of operational itemsThree multiple-choice items, three short-
answer items & Student Examples (Grades 3-5) Three multiple-choice items, two short-
answer items, one extended-response item & Student Examples (Grades 6-8)
Resources- CD – Grades 3-8- Extra Data
Mathematics AssessmentMathematics Assessment
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of Public Instruction
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December 2008December 2008
Slide Slide 2929
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 3030
Scoring RubricScoring RubricA 2-point response:
- shows relationship between 2 feet and 24 inches by using 12 or 24 in the supporting work-writes 8
A 1-point response: (one of the following)- shows relationship between 2 feet and 24
inches by using 12 or 24 in the supporting work- writes 8- makes a computational error and the answer
given is a result of that error.
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
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December 2008December 2008
Slide Slide 3131
2008 Released Items Data2008 Released Items DataGrade 5, Problem 5Grade 5, Problem 5
Options LEVEL 1 LEVEL 2 LEVEL 3 LEVEL 4 Total
0 84.7% 52.8% 19.8% 3.5% 32.8%
1 8.5% 17.8% 15.7% 7.0% 12.2%
2 4.4% 28.8% 64.2% 89.4% 54.3%
B 2.3% 0.7% 0.4% 0.1% 0.7%
Total 0.18 0.76 1.45 1.86 1.22
Mathematics AssessmentMathematics Assessment
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of Public Instruction
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December 2008December 2008
Slide Slide 3232
2008 Released Items Data2008 Released Items DataGrade 4, Problem 2Grade 4, Problem 2
Mathematics AssessmentMathematics Assessment
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of Public Instruction
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December 2008December 2008
Slide Slide 3333
2008 Released Items Data2008 Released Items DataGrade 4, Problem 2Grade 4, Problem 2
Options
LEVEL 1 LEVEL 2
LEVEL 3 LEVEL 4 TOTAL
A (1) 40.1% 38.4% 30.2% 16.9%54.5%B (2)
28.2% 17.2% 11.0% 5.1%
*C (3) 31.0% 44.2% 58.6% 77.9%
Blank 0.6% 0.2% 0.2% 0.1%
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
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December 2008December 2008
Slide Slide 3434
Released ItemsReleased ItemsAssessment FOR Learning - Able to transform expectations into
assessment exercises and scoring procedures that accurately reflect student achievement
- Engaging students in regular self-assessment, with standards held constant
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
WERAWERA
December 2008December 2008
Slide Slide 3535
Released Items, continuedReleased Items, continued
http://www.k12.wa.us/assessment/WASL/Mathematics/ resources.aspxReleased Item Documents (RIDs) view description
- 2008- 2007- 2006- 2004- 2003- 2002- 2001
Mathematics AssessmentMathematics Assessment
Office of Superintendent
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December 2008December 2008
Slide Slide 3636
2009 Assessment Update2009 Assessment Update
Grade Level Expectations (GLEs)Two sessions : Grades 3-8Shortened Test
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
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December 2008December 2008
Slide Slide 3737
Mathematics Assessment WASL Mathematics Assessment WASL Redesign: Redesign:
Grades
2008
MC
2008
SA
2008
ER
2009
MC
2009
SA
2009
ER3 23 12* 0 22 8 0
4 - 5 21 11 3 22 8 0
6 - 8 27 11 4 26 8 2High
School27 11 4 No
change
No chang
e
No chang
e
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
WERAWERA
December 2008December 2008
Slide Slide 3838
2010 Assessment Update2010 Assessment Update
Testing CycleAs of now:
- Washington K-8 Mathematics Standards, adopted April 28, 2008
- Clarifications: fluency; algorithms- Test and Item Specs
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
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December 2008December 2008
Slide Slide 3939
Assessment TimelineAssessment TimelineApril 2008
- New Grade 3-8 Math Standards approved- Draft Test and Items Specifications
May - November 2008- Align or revise items in existing test items to new grade-level standards- Write new items to fill in gaps, Content Review, Bias and Fairness October – January 2009- Laser Rounds – edit items for 2008 Spring WASL - Review, edit, and place pilot items
April-May 2009- Last year of current Grade 3-8 math WASL- Pilot new and rewritten items
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
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December 2008December 2008
Slide Slide 4040
Assessment Timeline cont.Assessment Timeline cont.
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
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
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December 2008December 2008
Slide Slide 4141
The term The term fluencyfluency . . . . . . . .
A student is considered fluent when the procedure can be performed immediately and accurately.
Also, when fluent, the student knows when it is appropriate to use a particular procedure in a problem or situation.
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 4242
AlgorithmsAlgorithms
Understand and use the standard algorithms generally seen in the United States to add, subtract, multiply, and divide whole numbers.
Some teachers may find value in students learning other algorithms to enhance understanding.
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
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December 2008December 2008
Slide Slide 4343
On the WASL, the standard algorithms and other possible algorithms, step-by-step mathematical procedures that, if followed correctly, always produce a correct solution or answer will be given credit.
Mathematics AssessmentMathematics Assessment
Office of Superintendent
of Public Instruction
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December 2008December 2008
Slide Slide 4444
Item SpecsItem SpecsGoals:Retain clarity and specificity of Standards Document.Identify which Performance Expectations to assess on WASL.
Mathematics AssessmentMathematics Assessment
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of Public Instruction
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December 2008December 2008
Slide Slide 4545
GoalGoalIdentify restrictions, if any, forVocabulary- “Vocabulary First Used in Assessment Items”- “Measurement Vocabulary”Computation- Number of addends- Denominators- Decimal placesMeasurements
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 4646
GoalGoal
For each Performance Expectation Identify:
Cognitive Complexity (Webb’s model)Item Type (MC or SA)Contextual Situation or not“Tools” or “No-Tools” day
Mathematics Mathematics AssessmentAssessment
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December 2008December 2008
Slide Slide 4747
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
Mathematics Mathematics AssessmentAssessment
Office of Superintendent
of Public Instruction
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December 2008December 2008
Slide Slide 4848
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
Mathematics Mathematics AssessmentAssessment
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December 2008December 2008
Slide Slide 4949
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
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 5050
Standards
Assess-ment
Assessment
Standards
StandardsAssessment
Assessment Items
Standards
Adapted from Norman Webb, 2005
AlignmentAlignment
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 5151
Performance Expectation InformationPerformance Expectation InformationGrades 3-8Grades 3-8
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
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 5252
Instruction
Standards
Assessment
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
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Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 5454
Instruction
Standards
Assessment
Mathematics AssessmentMathematics Assessment
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December 2008December 2008
Slide Slide 5555
Questions Questions