Example 27 uses pictures to illustrate important information in the text.
Example 27 Source: 1996 NAEP 4M #22 (rev)
Grade 4 Moderate Complexity
Number Properties and Operations
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A fourth-grade class needs 5 leaves each day to feed its 2 caterpillars.
How many leaves do they need each day for 12 caterpillars?
Answer: _______________________
Use drawings, words, or numbers to show how you got your answer.
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Using Contextual Information Appropriately
Often, items will be designed so that they measure mathematics in context. Contextual information includes problem scenarios, explanations, more thorough directions, and background text. Using contextual information judiciously can place mathematical concepts in fuller, often more realistic, conditions, measure students’ ability to apply mathematical concepts, and provide necessary background information. However, the contextual information should not interfere with the mathematics being assessed or become a barrier to a student’s ability to demonstrate his or her mathematical knowledge. The context should be the minimum necessary to set up the problem. Guidelines for using contextual information appropriately include the following:
Use contexts that are meaningful to the mathematics being assessed.
Use contexts that are appropriate for the grade level assessed.
Use realistic contexts.
Use familiar contexts; avoid contexts that may confuse or be unfamiliar to some students taking the assessment.
Examples 27 (above) and 28 show the use of contexts that are appropriate for the grade level. The contexts are likely to be familiar to students in 4th and 12th grade, respectively.
EXAMPLE 28 Source: 1996 NAEP 12M12 #10
Grade 12 Moderate Complexity
Data Analysis, Statistics and Probability
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The table below shows the daily attendance at two movie theaters for 5 days and the mean (average) and the median attendance.
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Theater A
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Theater B
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Day 1
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100
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72
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Day 2
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87
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97
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Day 3
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90
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70
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Day 4
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10
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71
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Day 5
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91
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100
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Mean (average)
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75.6
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82
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Median
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90
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72
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(a) Which statistic, the mean or the median, would you use to describe the typical daily attendance for the 5 days at Theater A? Justify your answer.
(b) Which statistic, the mean or the median, would you use to describe the typical daily attendance for the 5 days at Theater B? Justify your answer.
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Writing Items with Multiple Access Points
Students vary in their abilities to access information and respond to tasks through visual, spatial, auditory, kinesthetic, and tactile pathways. When possible, items should be designed to allow students to approach and respond to the item in different ways. Incorporating multiple pathways appropriately in both constructed-response and multiple-choice items can increase the ability of the assessment to elicit responses from students across the range of achievement without affecting the mathematical content being assessed.
a) Multiple access in how items are written or presented to the students
Use visuals to accompany and explain the text when appropriate.
Write both multiple-choice and constructed-response items that allow for various approaches to determining the solution.
Use manipulatives.
Use a brief activity when appropriate to address students with auditory, kinesthetic, or tactile strengths.
b) Multiple response opportunities
Write constructed-response items that allow for multiple response formats. For example, students might be allowed to show their answers through illustrations, diagrams, or formulas.
When possible, write constructed-response items and scoring rubrics that measure the mathematical knowledge and skills of students with a range of achievement.
Example 27 (shown earlier) allows for a variety of response formats. Students can give verbal explanations, draw, or construct charts, for example.
Example 29 provides access through the use of dialogue, personalizing the mathematics. The item uses dialogue in a grade-appropriate way.
EXAMPLE 29 Source: 1996 NAEP 4M10 #6
Grade 4 Moderate Complexity
Measurement
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The following shapes were provided to students. (Shapes were larger than shown.)
Who was correct? _______________________________
Use pictures and words to explain why.
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Example 30 provides access through the use of manipulatives, which allow students to use both tactile and kinesthetic pathways.
EXAMPLE 30 Source: 2005 NAEP 4M4 #11
Grade 4 Moderate Complexity
Number Properties and Operations
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This question refers to the number tiles. Please remove the 10 number tiles and the paper strip from your packet and put them on your desk.
Audrey used only the number tiles with the digits 2, 3, 4, 6, and 9. She placed one tile in each box below so the difference was 921.
Write the numbers in the boxes below to show where Audrey placed the tiles.
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