Mathematics Selected Response, Constructed Response, and

Technology-Enhanced Items

Learning Outcomes

• Understand the purpose of selected response, constructed response, and technology-enhanced items

• Describe the components of selected response, constructed response, and technology-enhanced items

• Understand the essential requirements of quality items

• Apply general guidelines for writing selected response, constructed response, and technology-enhanced items

• Identify exemplary and flawed items

Benefits and Limitationsof Selected Response Items

• Benefits– Answered quickly– Assess a broad range of

content in one test– Inexpensive and

objectively scored– Results collected quickly

• Limitations– Limited ability to reveal

a student’s reasoning process

– Difficult to assess higher-order thinking skills

Formats and Components ofSelected Response Items

• Traditional Selected Response Item

• Key and Distractor Analysis

Which number is both a factor of 100 and a multiple of 5?

A. 4

B. 40

C. 50

D. 500

A. 4

B. 40

C. 50

D. 500

OPTIONS: Possible answers the students must select from

Which number is both a factor of 100 and a multiple of 5?

STEMStatement ofthe question

A. Did not consider criteria of “multiple of 5”

B. Did not consider criteria of “factor of 100”

C. Correct

D. Multiplied 100 and 5

KEY

RATIONALE

DISTRACTOR

Non-Traditional Selected Response Item

A multiplication problem is shown below. 17 × 12Which model(s) below could represent the solution to this problem? Select all that apply.

A.

(1×1)+(1×7)+(1×2)+(2×7)

C.

(17×2)+(17×1) E. F.

Which model(s) below could represent the solution to this problem? Select all that apply.

STEM

B.

D.

STIMULUS

17 × 12

Non-Traditional Selected Response Item

Key and Distractor Analysis: A. Does not understand how to model

multiplication of two two-digit numbers using area models.

B. Correct C. Did not account for the values

of the digits in the tens places. D. Correct E. Did not understand that the 1 represents 10 in the multiplication problem F. Showed multiplication of 17 and (1 + 2) instead of 17 and 12 Responses to this item will receive 0–2 points, based on the following: 2 points: B, D 1 point: Either B or D 0 points: Any other combination of selections.

Non-Traditional Selected Response Item

For numbers 1a – 1d, state whether or not each figure has ⅖ of its whole shaded.

1a.

1b.

1c.

1d.

STEM

MULTIPLE PARTS OPTIONS

Non-Traditional Selected Response Item

Scoring Rubric: Responses to this item will receive 0–2 points, based upon the following: • 2 points: YNYN The student has a solid

understanding of ⅖ as well as the equivalent form of ⅖. • 1 point: YNNN, YYNN, YYYN The student has

only a basic understanding of ⅖. Either the student doesn‘t recognize an equivalent fraction for ⅖ or doesn‘t understand that all 5 parts must be equal-sized in figure 1b. • 0 points: YYYY, YNNY, NNNN, NNYY, NYYN, NYNN, NYYY, NYNN, NNNN, NYNY,

NNYN, NNNY. The student demonstrates inconsistent understanding of ⅖ or answers “Y” to figure 1d, clearly showing a misunderstanding of what ⅖ means. Figure 1d is considered a “disqualifier “and an answer of “Y” to this part of the item would cancel out any other correct responses as “guesses” on the part of the student.

Non-Traditional Selected Response Item

Match each shape below to its name. Scoring Rule:

Students who properly match the four shapes to their name will receive two points.

Students who make two or three correct matches will receive partial credit of one point

All other connections will receive a score of 0.

Non-Traditional Selected Response Item

Purpose of Constructed Response Items

• Constructed Response items – Address assessment targets and claims that

are of greater complexity – Require more analytical thinking and reasoning

Administration ofConstructed Response Items

• Administered during the computer-adaptive component

• Scored using artificial intelligence

• Most constructed response items take between 1 and 5 minutes to complete

• Some more complex items may take up to 10 minutes to complete

A teacher asked her students to use estimation to decide if the sum of the problem below is closer to 4,000 or 5,000.

496 + 1,404 + 2,605 + 489 =

One student replied that she thinks the sum is closer to 4,000. She used the estimation shown below to support her reasoning.

Is the student’s reasoning correct? In the space below, use numbers and words to explain why or why not. If the student’s reasoning is not correct, explain how she should have estimated.

Components of aConstructed Response Item

STEM

STIMULI

Components of aConstructed Response Item

Sample Top-Score Response:

The student’s reasoning is incorrect. She was rounding to the thousands place. She had 2 numbers that were less than 500, and she decided to round these numbers to 0. This is like saying these numbers were not in the problem at all. She needs to account for these two numbers. Together, they have a sum that is very close to 1,000. I think adding 1,000 + 1,000 + 3,000 is a better strategy. This means the sum is closer to 5,000 than to 4,000.

TOP-SCORE

Scoring Rubric: Responses to this item will receive 0–2 points, based on the following:

2 points: Student has thorough understanding of how to estimate and how improper estimation can lead to flawed reasoning. Student states that the student in the scenario used reasoning that is incorrect and provides reasoning that shows a better estimation strategy.

1 point: Student has partial understanding of how to estimate and how improper estimation can lead to flawed reasoning. Student states that the student in the scenario used reasoning that is incorrect, but alternate estimation strategy is also flawed.

0 points: Student has little or no understanding of how to estimate and how improper estimation can lead to flawed reasoning. Student states that the student in the scenario used reasoning that is correct.

SCORING RUBRIC

Qualities of a Rubric

• Focus on the essence of the primary claim and sometimes secondary claim

• Address the requirements of the specific assessment targets

• Distinguish between different levels of understanding and/or performance

• Contain relevant information, details, and numbers that support different levels of competency related to the item or task

Essential Requirements of Selected Response and Constructed Response Items

• Aligned to claims and assessment targets

• Mathematical accuracy

• Clarity, readability, and accessibility

• Free from bias issues

• More complex constructed response items may include scaffolding

• Selected response items must have appropriate distractors

General Guidelines for Developing Selected Response and Constructed Response Items

• Each item should be written to assess a primary claim

• Secondary content claims are also possible

General Guidelines for Developing Selected Response and Constructed Response Items

• May include mathematical concepts detailed in the Common Core State Standards for lower grades

• Central focus

• Clearly stated to ensure that students understand the task

• Clearly elicit the desired evidence

• Appropriate grade-level difficulty, cognitive complexity, and reading level

• Depth of Knowledge considered

• Grades 3–5: items do not require a calculator

Examples of Poorly Written Items

The table below shows the weights of three vehicles.

Which list shows the vehicles in order from lightest to heaviest? ☐ car, motorcycle, truck☐ motorcycle, car, truck☐ truck, car, motorcycle☐ truck, motorcycle, car

Vehicle Weight (in pounds)

Car 4,050

Motorcycle 497

Truck12,159

The table below shows the number of apples three students picked.

Which list shows the number of apples picked in order from greatest to the least?

☐ 95, 107, 121☐ 95, 121, 107☐ 121, 107, 95☐ 121, 95, 107

Student Number of Apples

Bobby 107

Carlos 95

Jenna 121

Examples of Poorly Written Items

Mercedes received 32 pieces of candy on Halloween. She ate ¼ of the candy. How many pieces of candy did Mercedes have left? Show or explain how you found your answer.

Examples of Poorly Written Items

Look at the rectangle below.

What is the area, in square feet, of the rectangle?☐ 3☐ 15☐ 18☐ 63

3 feet

6 feet

Selected Response and Constructed Response Item Module

• Essential Elements

• Benefits and Limitations

• Flawed and Exemplary Items

Continue with this module to learn about technology-enhanced items.

Capitalize on Technology

• Technology-Enabled items

• Technology-Enhanced items

Technology-Enabled Items

• Digital Media– Video– Animation– Sound– Interactive tools

• Response Types– Selected– Constructed

Example of Technology-Enabled Item

Gregory is installing tile on a rectangular floor. • He is using congruent square tiles that each have a side length of ½ foot • The area of the floor is 22 square feet. • The width of the floor is 4 feet. Use the grid and the tile below to model the floor.

What is the length, in feet, of the floor?

Technology-Enhanced Items

• Specialized interaction

• May have digital media for stimulus

• Same requirements as selected and constructed response items

• Students manipulate information

• Defined responses

Technology-Enhanced ItemsDraw a line of symmetry throughthe figure below.

The graph on the right shows a triangle. Draw the triangle after it is reflected over the y-axis.

Reorder the fractions below so that they are ordered from smallest to largest.

3/53/42/61/22/3

Classify each shape below based whether it contains at least one pair of parallel sides.

INTERACTION SPACE

Key Components of a Technology-Enhanced Item

Draw a line of symmetry throughthe figure below.

Classify each shape below based on whether it contains at least one pair of parallel sides.

Draw a line of symmetry throughthe figure below.

Key Components of a Technology-Enhanced Item

Key Components of a Technology-Enhanced Item Parameter: A variable provides input to a computer program

Draw a line of symmetry through the figure below. Interaction Space ParametersDefault Coordinates: FalseCoordinates for corners: (1,1), (13,13)Grid Visible: TrueLabels: FalseSnap: TrueObject Displayed: TrueObject Coordinates: (4,10), (7,11), (10,10), (9,8), (10,4), (6,5), (4,4), (3,7), (4,10)Points Connected: True

Interaction Space ParametersDefault Coordinates: FalseCoordinates for corners: (1,1), (13,13)Grid Visible: FalseLabels: FalseSnap: TrueObject Displayed: TrueObject Coordinates: (4,10), (10,10), (4,20), (10,20)Points Connected: True

Draw a line of symmetry through the figure below.

Scoring RuleScoring Rule: Logic used to score student response

Which number is both a factor of 100 and a multiple of 5?

A. 4

B. 40

C. 50

D. 500

Scoring Rule:

If student response = C, then correct

Otherwise, incorrect

Scoring Rule:

If object 1 = B, 2 = A, 3 = B, 4 = A, 5 = A, then correct

Otherwise, incorrect

Classify each shape below based on whether it contains at least one pair of parallel sides.

Scoring Rule

Draw a line of symmetry throughthe figure below.

Scoring Rule: Start Point: Do not considerEnd Point: Do not considerx-Intercept: Consider, 0, .5y-Intercept: Consider, 0, .5Slope: Consider, -1, .25

Alternate Scoring Rule: Start Point: Do not considerEnd Point: Do not considerx-Intercept: Consider, 0, 0y-Intercept: Consider, 0, 0Slope: Consider, -1, 0

Boolean VariablesBoolean: A variable that has a value of True or False

Draw a line of symmetry through the figure below. Interaction Space ParametersDefault Coordinates: FalseCoordinates for corners: (1,1), (13,13)Grid Visible: TrueLabels: FalseSnap: TrueObject Displayed: TrueObject Coordinates: (4,10), (7,11), (10,10), (9,8), (10,4), (6,5), (4,4), (3,7), (4,10)Points Connected: True

Interaction Space ParametersDefault Coordinates: FalseCoordinates for corners: (1,1), (13,13)Grid Visible: FALSELabels: FalseSnap: TrueObject Displayed: TrueObject Coordinates: (4,10), (7,11), (10,10), (9,8), (10,4), (6,5), (4,4), (3,7), (4,10)Points Connected: True

Draw a line of symmetry through the figure below.

Comparing Technology-Enabled and Technology-Enhanced Items

Draw a line of symmetry throughthe figure below.

Gregory is installing tile on a rectangular floor. • He is using congruent square tiles that each have a side length of ½ foot. • The area of the floor is 22 square feet. • The width of the floor is 4 feet. Use the grid and the tile below to model the floor.

What is the length, in feet, of the floor?

5.5 feet

Technology-Enhanced Item Template

1) Select Type of Interaction Draw a line of symmetry through the figure below.

2) Enter Content for Item

4) Specify Scoring Information

3) Define Parameter ValuesInteraction Space ParametersDefault Coordinates: FalseCoordinates for corners: (1,1), (13,13)Grid Visible: TrueLabels: FalseSnap: TrueObject Displayed: TrueObject Coordinates: (4,10), (7,11), (10,10), (9,8), (10,4), (6,5), (4,4), (3,7), (4,10)Points Connected: True

Scoring Rule:Start Point: Do not considerEnd Point: Do not considerx-Intercept: Consider, 0, .5y-Intercept: Consider, 0, .5Slope: Consider, -1, .25

Technology-Enhanced Items

• Essential Elements

• Steps required to write an item

• Type of item templates