Transcript Goals - Smarter Balanced Assessment Consortium

Mathematics Selected Response,
Constructed Response, and
Technology-Enhanced Items
Learning Outcomes
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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
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Benefits
– Answered quickly
– Assess a broad range of
content in one test
– Inexpensive and
objectively scored
– Results collected quickly
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Limitations
– Limited ability to reveal
a student’s reasoning
process
– Difficult to assess higherorder thinking skills
Formats and Components of
Selected Response Items
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Traditional Selected
Response Item
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Key and Distractor
Analysis
Which number is both a factor
of 100 and a multiple of 5?
A. Did not consider criteria
of “multiple of 5”
A. 4
B. Did not consider criteria
of “factor of 100”
STEM
B. 40
Statement of
the question
C. 50
D. 500
DISTRACTOR
OPTIONS: Possible answers the
students must select from
C. Correct
D. Multiplied 100 and 5
RATIONALE
KEY
Non-Traditional Selected Response Item
STIMULUS
A multiplication problem is shown below.
STEM
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 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.
STEM
1a.
1b.
MULTIPLE
PARTS
OPTIONS
1c.
1d.
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
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Constructed Response items
– Address assessment targets and claims that
are of greater complexity
– Require more analytical thinking and reasoning
Administration of
Constructed Response Items
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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
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 =
STIMULI
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.
STEM
Components of a
Constructed 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
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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
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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
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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
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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.
Vehicle
Car
Motorcycle
Truck
Weight (in pounds)
The table below shows the number of
apples three students picked.
Student
Number of Apples
4,050
Bobby
107
497
Carlos
95
12,159
Jenna
121
Which list shows the vehicles in order
from lightest to heaviest?
Which list shows the number of apples
picked in order from greatest to the least?
☐
☐
☐
☐
☐
☐
☐
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car, motorcycle, truck
motorcycle, car, truck
truck, car, motorcycle
truck, motorcycle, car
95, 107, 121
95, 121, 107
121, 107, 95
121, 95, 107
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.
3 feet
6 feet
What is the area, in square feet, of the rectangle?
☐ 3
☐ 15
☐ 18
☐ 63
Selected Response and Constructed Response
Item Module
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Essential Elements
Benefits and Limitations
Flawed and Exemplary Items
Continue with this module to learn about
technology-enhanced items.
Capitalize on Technology
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Technology-Enabled items
Technology-Enhanced items
Technology-Enabled Items
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Digital Media
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Video
Animation
Sound
Interactive tools
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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
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Specialized interaction
May have digital media for stimulus
Same requirements as selected and
constructed response items
Students manipulate information
Defined responses
Technology-Enhanced Items
Draw a line of symmetry through
the figure below.
The graph on the right
shows a triangle. Draw the
triangle after it is reflected
over the y-axis.
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
Draw a line of symmetry through
the figure below.
Classify each shape below based on whether it contains at
least one pair of parallel sides.
INTERACTION
SPACE
Key Components of a Technology-Enhanced Item
Draw a line of symmetry through
the figure below.
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 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
Scoring Rule
Scoring Rule: Logic used to score student response
Which number is both a factor of
100 and a multiple of 5?
Scoring Rule:
A. 4
If student response = C, then correct
B. 40
Otherwise, incorrect
C. 50
D. 500
Classify each shape below based on whether
it contains at least one pair of parallel sides.
Scoring Rule:
If object 1 = B, 2 = A, 3 = B, 4 = A,
5 = A, then correct
Otherwise, incorrect
Scoring Rule
Draw a line of symmetry through
the 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: A variable that has a value of True or False
Draw a line of symmetry through the figure below.
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
Comparing Technology-Enabled
and Technology-Enhanced Items
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.
Technology-Enhanced Item Template
1) Select Type of Interaction
Draw a line of symmetry through the figure below.
2) Enter Content for Item
3) 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
4) 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
Technology-Enhanced Items
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Essential Elements
Steps required to write an item
Type of item templates