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Mathematics Selected Response, Constructed Response, and Technology-Enhanced Items

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Mathematics Selected Response, Constructed Response, and Technology-Enhanced Items

- 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
- 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

- 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

Did not consider criteria of “multiple of 5”

Did not consider criteria of “factor of 100”

Correct

Multiplied 100 and 5

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

RATIONALE

A. 4

B. 40

C. 50

D. 500

STEM

Statement ofthe question

KEY

DISTRACTOR

OPTIONS: Possible answers the students must select from

STIMULUS

STEM

A multiplication problem is shown below.

17 × 12

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

17 × 12

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

A.

B.

C.

(1×1)+(1×7)+(1×2)+(2×7)

D.

E.

F.

(17×2)+(17×1)

Key and DistractorAnalysis:

Does not understand how to modelmultiplication of two two-digitnumbers using area models.

Correct

Did not account for the valuesof the digits in the tens places.

Correct

Did not understand that the 1 represents 10 in the multiplication problem

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.

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

STEM

1a.

1b.

MULTIPLE PARTS

OPTIONS

1c.

1d.

Scoring Rubric:

Responses to this item will receive 0–2 points,based upon the following:

2 points: YNYN The student has a solidunderstanding of ⅖ as well as the equivalentform of ⅖.

1 point: YNNN, YYNN, YYYN The student hasonly 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 beequal-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.

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.

- Constructed Response items
- Address assessment targets and claims that are of greater complexity
- Require more analytical thinking and reasoning

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.

STIMULI

STEM

- 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.

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.

TOP-SCORE

SCORING 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

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

Each item should be written to assess a primary claim

Secondary content claims are also possible

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

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

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

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.

Look at the rectangle below.

What is the area, in square feet, of the rectangle?

☐3

☐15

☐18

☐63

3 feet

6 feet

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

Essential Elements

Benefits and Limitations

Flawed and Exemplary Items

Technology-Enabled items

Technology-Enhanced items

- Digital Media
- Video
- Animation
- Sound
- Interactive tools

- Response Types
- Selected
- Constructed

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?

- Specialized interaction
- May have digital media for stimulus
- Same requirements as selected and constructed response items
- Students manipulate information
- Defined responses

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

Draw a line of symmetry throughthe figure below.

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

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

3/5

3/4

2/6

1/2

2/3

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

Draw a line of symmetry throughthe figure below.

INTERACTION SPACE

Draw a line of symmetry throughthe figure below.

Parameter: A variable provides input to a computer program

Interaction Space Parameters

Default Coordinates: False

Coordinates for corners: (1,1), (13,13)

Grid Visible: True

Labels: False

Snap: True

Object Displayed: True

Object 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.

Interaction Space Parameters

Default Coordinates: False

Coordinates for corners: (1,1), (13,13)

Grid Visible: False

Labels: False

Snap: True

Object Displayed: True

Object Coordinates: (4,10), (10,10), (4,20), (10,20)

Points Connected: True

Draw a line of symmetry through the figure below.

Scoring 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.

Draw a line of symmetry throughthe figure below.

Scoring Rule:

Start Point: Do not consider

End Point: Do not consider

x-Intercept: Consider, 0, .5

y-Intercept: Consider, 0, .5

Slope: Consider, -1, .25

Alternate Scoring Rule:

Start Point: Do not consider

End Point: Do not consider

x-Intercept: Consider, 0, 0

y-Intercept: Consider, 0, 0

Slope: Consider, -1, 0

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

Interaction Space Parameters

Default Coordinates: False

Coordinates for corners: (1,1), (13,13)

Grid Visible: True

Labels: False

Snap: True

Object Displayed: True

Object 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.

Interaction Space Parameters

Default Coordinates: False

Coordinates for corners: (1,1), (13,13)

Grid Visible: FALSE

Labels: False

Snap: True

Object Displayed: True

Object 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.

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

Draw a line of symmetry through the figure below.

- Enter Content for Item

- Define Parameter Values

Interaction Space Parameters

Default Coordinates: False

Coordinates for corners: (1,1), (13,13)

Grid Visible: True

Labels: False

Snap: True

Object Displayed: True

Object Coordinates: (4,10), (7,11), (10,10), (9,8), (10,4), (6,5), (4,4), (3,7), (4,10)

Points Connected: True

- Specify Scoring Information

Scoring Rule:

Start Point: Do not consider

End Point: Do not consider

x-Intercept: Consider, 0, .5

y-Intercept: Consider, 0, .5

Slope: Consider, -1, .25

Select Type of Interaction

Essential Elements

Steps required to write an item

Type of item templates