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

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

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

  2. 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

  3. 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

  4. 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

  5. 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)

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. Non-Traditional Selected Response Item

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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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.

  21. 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

  22. 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

  23. Capitalize on Technology Technology-Enabled items Technology-Enhanced items

  24. Technology-Enabled Items • Digital Media • Video • Animation • Sound • Interactive tools • Response Types • Selected • Constructed

  25. 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?

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

  27. 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

  28. 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

  29. Key Components of a Technology-Enhanced Item Draw a line of symmetry throughthe figure below.

  30. 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.

  31. 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.

  32. 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

  33. 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.

  34. 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

  35. 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

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

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