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### Oklahoma Mathematics Educator Workshop

### What Makes a Good Multiple-Choice Item?

September 28-October 2, 2009

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Who’s Who?

Teachers of Grades 3 through 8

Oklahoma State Department of Education

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Goals

- Provide educators with an overview of how mathematics test items are developed and aligned to the PASS standards.
- Increase understanding and use of the Mathematics Test and Item Specification documents.
- Work collaboratively with educators to create and discuss aligned test items.
- Inform educators about various resources for their classrooms.

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OCCT Test Development Cycle

Writing of Item

Build Test Oper. & Field

Test and Item Specs

Content & Bias Review

Scoring & Reporting

Review Item Pool

TESTING

Data Review

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Walkthrough of the Guiding Documents

PASS Mathematics Standards/Objectives

Alignment and validity

Mathematics Test Blueprints

Percent emphasis of content

Mathematics Test and Item Specifications

New combined document

Clarifies assessment limits, guides item development, and provides sample items

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Mathematics Test and Item Specifications

- Provide parameters and guidelines for item writers and DRC mathematics assessment specialists to design the PASS Math items.
- Provide Oklahoma educators and SDE staff with guidance to judge whether or not items are appropriate for field testing.

Mathematics Test and Item Specifications

- Components
- Emphasis
- Assessment Limits
- Format for Items
- Distractor Domains
- Sampling of Items

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Parts of an Item

- Multiple-choice items
- Stem
- Response Options
- Correct Answer
- Distractors
- Graphics/Artwork (if applicable)

Oklahoma Mathematics Educator Workshop

September 28-October 2, 2009

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Is there clear primary standard alignment?

John earned $37.50 for 5 hours of babysitting. At this rate, how much will he earn for 8 hours of babysitting?

This item addresses the primary standard of solving a proportion and the non-primary standard of using multiplication and division.

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Is there clear primary standard alignment?

John earned $37.50 for 5 hours of babysitting. At this rate, how much will he earn for 8 hours of babysitting?

A $1.07 (5/37.50 = x/8)

B $23.44 (5/8 = x/37.50)

C $40.50 (5+3=8 so 37.50+3)

D $60.00 (correct)

Answer options must only reflect errors related to the standard being tested.

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Is there clear primary standard alignment?

Ryan’s garden is 3 feet long and 2 feet wide. What is the area of Ryan’s garden in square inches?

This item tests two standards: calculating area and converting units. It should test only one standard.

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Is the stem context-based?

Use this figure to answer the question.

What is the area of the square?

11 feet

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Melissa wants to carpet the floor of a

square-shaped room.

How many square feet of carpet are needed to cover the floor of Melissa’s room?

Is the stem context-based?11 feet

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Is the item written as an interrogative?

Declarative Form

This table shows the number of points Jim scored in 5 games.

Find the mean number of points Jim scored.

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Is the item written as an interrogative?

Interrogative Form

This table shows the number of points Jim scored in 5 games.

What is the mean number of points Jim scored?

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Is there one and only one correct response?

Leticia drew a triangle with two sides of equal length. What type of triangle did Leticia draw?

A scalene

B isosceles

C equilateral

D right

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Is there one and only one correct response?

Leticia drew a triangle with exactly two sides of equal length. What type of triangle did Leticia draw?

A scalene

B isosceles

C equilateral

D equiangular

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Do items that require estimation contain qualifiers?

What is the approximate value of ?

A 5

B 7

C 8

D 10

“Approximate” is too vague.

(rounded to nearest 5)

(rounded to nearest 1)

(rounded up to nearest 1)

(rounded up to nearest 5)

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Do items that require estimation contain qualifiers?

Which is closest to the value of ?

A 5

B 7

C 8

D 10

closest

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Do the distractors reflect plausible errors?

A rectangular garden is shown.

What is the perimeter of the garden?

A. 7 feet C. 15 feet

B. 8 feet D. 46 feet

8 feet

15 feet

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Do the distractors reflect plausible errors?

A rectangular garden is shown.

What is the perimeter of the garden?

A. 23 feet C. 60 feet

B. 46 feet D. 120 feet

(½ area)

(area)

(½ per.)

(correct)

8 feet

15 feet

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Can authentic data and information be used?

What is the mode of the data shown?

5, 13, 20, 8, 9, 15, 13, 17

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The normal high temperatures, in ºF, each month in Oklahoma are shown.

47, 54, 62, 71, 79, 87,

93, 93, 84, 74, 60, 50

What is the mode of the temperatures?

Can authentic data and information be used?Data Recognition Corporation Copyright 2009

Is the item teaching the student?

A board foot is defined as the volume of a piece of square-cut lumber with a top surface area of 1 ft2 and a thickness of 1 in. A lumber company sells pine lumber for $1.25 per board foot. What is the cost of a pine board that is 8 ft. long, 1 ft. wide, and ¾ in. thick?

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Is the item the specified complexity?

Complexity of an item is relative to the grade and developmental levels of the students.

Do not confuse difficulty and complexity.

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Can the item be completed in the time specified?

All multiple-choice items must be written so a typical student can complete each item in 1½ minutes or less.

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Is the item grammatically and structurally correct?

Watch for:

Tense

Number style

Plural/singular

Third person

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Is the item testing mathematics or reading?

To minimize the influence of student reading ability:

Be concise

Be direct

Maintain linguistic simplicity

Use appropriate vocabulary

Use simple sentences

Write in a positive sense

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Is the item testing mathematics or reading?

Pat is baking cupcakes for the Hyland Elementary School annual fundraiser. Pat’s recipe calls for 2½ cups of flour to make 2 dozen cupcakes. Pat will double the recipe. How many cups of flour does Pat need to make 48 cupcakes?

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Is the item testing mathematics or reading?

Pat is baking cupcakes. The recipe calls for 2½ cups of flour to make 24 cupcakes. How many cups of flour does Pat need to make 48 cupcakes?

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Is the item bias-free?

Bias is

the existence of some characteristic of an item and/or test that could result in two individuals of the same ability but from different subgroups performing differently.

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Is the item bias-free?

Types of Bias

Stereotyping

Gender Bias

Regional or Geographic Bias

Ethnic Bias

Cultural Bias

Religious Bias

Socioeconomic Bias

Age Bias

Bias Against Persons with Disabilities

Experiential Bias

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Is the item bias-free?

The number of yards rushed each game by Adrian Peterson during the 2008 regular season is shown.

103, 160, 77, 101, 32, 111,

121, 139, 192, 85, 80, 103

What was Peterson’s average number of rushing yards per game for the 2008 regular season?

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Is the item bias-free?

Mrs. Rogers bought a new car for $45,000. She will make car payments of $700 every month. At this rate, how many months will it take Mrs. Rogers to pay for her car?

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Are response options such as “none of the above” used?

NO!

Use of phrases like

- “none of the above”
- “all of the above”
- “A and C”

are not necessary and tend to decrease the validity of an item.

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Questions?

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Grade 3, Objective 2.2aCompare and order whole numbers up to 4 digits.

The heights of four mountains are shown in the table.

What is the order of the heights from least to greatest?

A 12,970 1,300 2,420 29,030 (ordered by first 2 digits)

B 29,030 1,300 2,420 12,970 (ordered by last 3 digits)

C 1,300 2,420 12,970 29,030 (correct)

D 12,970 1,300 2,420 29,030 (ordered 1st, then 2nd digit)

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Grade 6, Objective 2.1Multiply and divide fractions and mixed numbers to solve problems using a variety of methods.

Simone needs 2½ cups of flour for one recipe and 1¾ cups for another. She will double both recipes. How many cups of flour does Simone need in all?

A 2 8/17 cups (error converting 17/2)

B 3 1/2 cups (converted 4¼ to 9/4)

C 7 2/3 cups (adding error)

D 8 1/2 cups (correct)

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Grade 4, Objective 4.3a: Describe the effects on two- and three-dimensional objects when they slide (translate), flip (reflect), and turn (rotate).

Fred made a design by reflecting the letter F over a line. Which shows a reflection of the letter F over a line?

A

B

C

D

F

F

F

F

F

F

F

F

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Grade 7, Objective 1.1Identify and apply the commutative, associative, distributive, inverse, and identity properties.

Which shows a use of the commutative property?

A (3 + 2) + 4 = 3 + (2 + 4)

B (3 + 2) x 4 = 3 x 4 + 2 x 4

C 3 + 2 + 4 = 3 + 4 + 2

D 3 + 2 + 4 = 2 + 3 + 4

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Grade 5, Objective 3.2b: Multiply and divide whole numbers and decimal numbers with 1- or 2-digit multipliers or divisors to solve problems.

Loren and four friends decided to go out for pizza to celebrate the end of the school year. They bought three large pizzas and five pops. The total cost was $35.60. The 5 friends split the bill evenly. How much did each friend pay?

A $0.71

B $7.01

C $7.12

D $712

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Grade 5, Objective 3.2b: Multiply and divide whole numbers and decimal numbers with 1- or 2-digit multipliers or divisors to solve problems.

Loren and his friends bought pizzas and pop. The total cost was $35.60. The 5 friends divided the cost evenly. How much did each friend pay?

A $0.71

B $7.01

C $7.12

D $712

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Grade 8, Objective 1.1aModel, write, and solve 2-step linear equations using a variety of methods.

Marti has a dog-walking business called Marti’s Marching Mutts. She walks dogs one hour a day, five days a week. She gets paid $7 per hour for each dog. Plus, she gets a $3 bonus each week. Which equation can be used to find the number of weeks, w, it will take Marti to earn $100?

A 35w + 3 = 100

B 3w + 35 = 100

C 35w – 3 = 100

D 3w – 35 = 100

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Grade 8, Objective 1.1aModel, write, and solve 2-step linear equations using a variety of methods.

Marti has $4 and earns $32 a week raking leaves. Which equation can be used to find the number of weeks, w, it will take Marti to have a total of $100?

A 32w + 4 = 100

B 4w + 32 = 100

C 32w – 4 = 100

D 4w – 32 = 100

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Questions?

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Universal Design

Item Review Committee

- Summer 2010
- Oklahoma educators are involved.
- Committees composed of classroom teachers, curriculum specialists, administrators, and other educational stakeholders.
- Committees represent the state geographically, ethnically, by gender, and by type and size of school district.
- Ask your superintendent, principal, or district test coordinator to recommend you for these committees if you are interested.

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Workshop Wrap Up

- What did you learn?
- How will you use what you learned?
- What do you still need to know?

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SDE Contact Information

- Michael Reid

Mathematics Assessment Specialist

<Michael_Reid@sde.state.ok.us>

(405) 521-3341

- www.sde.state.ok.us
- Accountability and Assessments

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