mathematics assessment office of superintendent of public instructionwera december 2008 slide 1 mary...

Mathematics AssessmentMathematics Assessment

Office of Superintendent

of Public Instruction

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December 2008December 2008

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Mary [email protected]

OSPI MathematicsAssessment Update

for Grades 3-5




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AgendaAgendaAssessment Tools and Resources

- Assessment OF and FOR Learning- Lessons Learned - Released Items Document

Assessment Update- Assessment 2009

- Assessment 2010




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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.




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An average is a thing that hens lay their eggs on--for example, "My hens lay four eggs a week on the average."




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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”




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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…”




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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.”




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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




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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




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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




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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




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Lessons LearnedLessons Learned

Students misrepresent what they know and understand.

Students can improve their scores by following guidelines in Lessons Learned.




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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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3-5 Number Sense3-5 Number SenseGrade 4 2002 RIDs Grade 4 2002 RIDs




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3-5 Number Sense3-5 Number Sense




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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?




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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




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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




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Grades 3-5 MeasurementGrades 3-5 Measurement




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Mislabels everywhere. . . . . .Mislabels everywhere. . . . . .




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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.




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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.




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QuestionsQuestions

Read Algebraic Sense through Problem Solving.




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Grade 3-5 Algebraic SenseGrade 3-5 Algebraic SenseGrade 4 2007 RIDsGrade 4 2007 RIDs

Connect operations in equations to situations:




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Questions Grades 3-5Questions Grades 3-5




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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)




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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




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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.




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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




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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%




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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




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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




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2009 Assessment Update2009 Assessment Update

Grade Level Expectations (GLEs)Two sessions : Grades 3-8Shortened Test




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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




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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




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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




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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




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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.




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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.




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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.




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Item SpecsItem SpecsGoals:Retain clarity and specificity of Standards Document.Identify which Performance Expectations to assess on WASL.




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GoalGoalIdentify restrictions, if any, forVocabulary- “Vocabulary First Used in Assessment Items”- “Measurement Vocabulary”Computation- Number of addends- Denominators- Decimal placesMeasurements




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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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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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Standards

Assess-ment

Assessment

Standards

StandardsAssessment

Assessment Items

Standards

Adapted from Norman Webb, 2005

AlignmentAlignment




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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




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Instruction

Standards

Assessment




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Instruction

Standards

Assessment




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Questions Questions




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Thank you for all you do

for the students of Washington!

mathematics assessment office of superintendent of public instructionwera december 2008 slide 1 mary...

Documents

absence of assessment

resources assessment

assessment literate

assessment exercises

student learning slide

agenda assessment tools

student achievement

public instructionwera