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

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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

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Benefits and Limitations of 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 students reasoning process – Difficult to assess higher- order thinking skills

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Formats and Components of Selected 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 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? STEM Statement of the 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

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

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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.

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Non-Traditional Selected Response Item For numbers 1a – 1d, state whether or not each figure has of its whole shaded. 1a. 1b. 1c. 1d. STEM MULTIPLE PARTS OPTIONS

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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 as well as the equivalent form of. 1 point: YNNN, YYNN, YYYN The student has only a basic understanding of. Either the student doesnt recognize an equivalent fraction for or doesnt 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 or answers Y to figure 1d, clearly showing a misunderstanding of what 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.

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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.

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Non-Traditional Selected Response Item

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

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Administration of Constructed 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

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A teacher asked her students to use estimation to decide if the sum of the problem below is closer to 4,000 or 5, , , = 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 students reasoning correct? In the space below, use numbers and words to explain why or why not. If the students reasoning is not correct, explain how she should have estimated. A teacher asked her students to use estimation to decide if the sum of the problem below is closer to 4,000 or 5, , , = 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 students reasoning correct? In the space below, use numbers and words to explain why or why not. If the students reasoning is not correct, explain how she should have estimated. Components of a Constructed Response Item STEM STIMULI

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Components of a Constructed Response Item Sample Top-Score Response: The students 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 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

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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

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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

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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

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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

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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 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 VehicleWeight (in pounds) Car4,050 Motorcycle497 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, , 107, , 95, 107 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, , 107, , 95, 107 StudentNumber of Apples Bobby107 Carlos95 Jenna121

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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.

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Examples of Poorly Written Items Look at the rectangle below. What is the area, in square feet, of the rectangle? Look at the rectangle below. What is the area, in square feet, of the rectangle? feet 6 feet

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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.

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Capitalize on Technology Technology-Enabled items Technology-Enhanced items

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Technology-Enabled Items Digital Media – Video – Animation – Sound – Interactive tools Response Types – Selected – Constructed

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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? 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?

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

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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. 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 whether it contains at least one pair of parallel sides.

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INTERACTION SPACE 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.

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Draw a line of symmetry through the figure below. Key Components of a Technology-Enhanced Item

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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 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.

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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 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.

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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

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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 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.

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Comparing Technology-Enabled and Technology-Enhanced Items Draw a line of symmetry through the 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? 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

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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 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 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

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Technology-Enhanced Items Essential Elements Steps required to write an item Type of item templates

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