Mathematics selected response constructed response and technology enhanced items
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Mathematics Selected Response, Constructed Response, and Technology-Enhanced Items . Learning Outcomes. Understand the purpose of selected response, constructed response, and technology-enhanced items

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Mathematics selected response constructed response and technology enhanced items

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


Learning outcomes

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 limitations of selected response 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 of selected response items

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

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


Non traditional selected response item

Non-Traditional Selected Response Item

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)


Non traditional selected response item1

Non-Traditional Selected Response Item

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.


Non traditional selected response item2

Non-Traditional Selected Response Item

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

STEM

1a.

1b.

MULTIPLE PARTS

OPTIONS

1c.

1d.


Non traditional selected response item3

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 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.


Non traditional selected response item4

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 item5

Non-Traditional Selected Response Item


Purpose of constructed response items

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 of constructed response items

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


Components of a constructed response item

Components of aConstructed Response Item

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


Components of a constructed response item1

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.

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


Qualities of a 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

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

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 items1

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

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

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


Examples of poorly written items1

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 items2

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

Selected Response and Constructed Response Item Module

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

Essential Elements

Benefits and Limitations

Flawed and Exemplary Items


Capitalize on technology

Capitalize on Technology

Technology-Enabled items

Technology-Enhanced items


Technology enabled items

Technology-Enabled Items

  • Digital Media

    • Video

    • Animation

    • Sound

    • Interactive tools

  • Response Types

    • Selected

    • Constructed


Example of technology enabled item

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

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 items1

Technology-Enhanced Items

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


Key components of a technology enhanced item

Key Components of a Technology-Enhanced Item

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


Key components of a technology enhanced item1

Key Components of a Technology-Enhanced Item

Draw a line of symmetry throughthe figure below.


Key components of a technology enhanced item2

Key Components of a Technology-Enhanced Item

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

Scoring Rule

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.


Scoring rule1

Scoring Rule

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 variables

Boolean Variables

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.


Comparing technology enabled and technology enhanced items

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

Technology-Enhanced Item Template

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


Technology enhanced items2

Technology-Enhanced Items

Essential Elements

Steps required to write an item

Type of item templates


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