Test Information Guide

Field 53: Elementary Mathematics
Sample Open-Response Item

The following materials contain:

• Sample test directions for the open-response item
• A sample open-response item
• An example of a strong response to the open-response item
• The scoring rubric

Sample Test Directions for Open-Response Items

This section of the test consists of two open-response item assignments. You will be asked to prepare a written response of approximately 150–300 words, or 1–2 pages, for each assignment.

Read the assignments carefully before you begin your responses. Think about how you will organize your responses. You may use the erasable sheet(s) to make notes, write an outline, or otherwise prepare your responses. However, your final response to each assignment must be either:

1. typed into the on-screen response box,
2. written on a response sheet and scanned using the scanner provided at your workstation, or
3. provided using both the on-screen response box (for typed text) and a response sheet (for calculations or drawings) that you will scan using the scanner provided at your workstation.

Instructions for scanning your response sheet(s) are available by clicking the "Scanning Help" button at the top of the screen.

As a whole, your response to each assignment must demonstrate an understanding of the knowledge of the field. In your response to each assignment, you are expected to demonstrate the depth of your understanding of the subject area by applying your knowledge rather than by merely reciting factual information.

Your responses to the assignments will be evaluated based on the following criteria.

• PURPOSE: the extent to which the response achieves the purpose of the assignment
• SUBJECT KNOWLEDGE: appropriateness and accuracy in the application of subject knowledge
• SUPPORT: quality and relevance of supporting evidence
• RATIONALE: soundness of argument and degree of understanding of the subject area

The open-response item assignments are intended to assess subject knowledge. Your responses must be communicated clearly enough to permit valid judgment of the evaluation criteria by scorers. Your responses should be written for an audience of educators in this field. The final version of each response should conform to the conventions of edited American English. Your responses should be your original work, written in your own words, and not copied or paraphrased from some other work.

Be sure to write about the assigned topics. Remember to review your work and make any changes you think will improve your responses.

Any time spent responding to an assignment, including scanning the response sheet(s), is part of your testing time. Monitor your time carefully. When your testing time expires, a pop-up message will appear on-screen indicating the conclusion of your test session. Only response sheets that are scanned before you end your test or before time has expired will be scored. Any response sheet that is not scanned before testing ends will NOT be scored.

Sample Open-Response Item

Objective 0016
Prepare an organized, developed analysis on a topic related to one or more of the following: number sense, operations, and data analysis; patterns, relations, and algebra; and geometry and measurement.

Use the diagram below to complete the exercise that follows.

Net of an unfolded prism. There are three parts to this net at the top we have a half circle with a radii of r the curved side is connected to the next part at the center of the width of a rectangle with a height of h the third part is connected to the rectangle in the center of its width the third part is a half circle that has a long skinny rectangle with a height of h connected to the flat part below it.

A "net" is a two-dimensional diagram that can be cut along its edges and folded into a three-dimensional figure. Use your knowledge of measurement and geometry to analyze the characteristics of the three-dimensional figure that the net above represents. In your response, you should:

• draw a sketch of the figure with the dimensions labeled as in the diagram, and identify the figure;
• using the dimensions as labeled in the diagram, derive an equation for the volume of the figure; and
• using the dimensions as labeled in the diagram, derive an equation for the surface area of the figure.

Sample Strong Response to the Open-Response Item

The sample response below reflects a strong knowledge and understanding of the subject matter.

1) This is 1/2 of a half right circular cylinder.

1) This is one half of a right circular cylinder. that has a height of h and a radii of r

2) A circle has the area of π r². There are 2 half circles. The height of the cylinder excluding the 2 half circles is represented by h. However, there is only 1/2 of a cylinder.

 Volume equals 1/2 π r²h
   V = volume
   π = 3.14
   r = radius
   h = height

3) As a result of analyzing the above: surface area = the areas of the 2 bases (2 x 1/2 π r²) AND the curved surface of the cylinder (1/2 x 2 π rh) AND the area of the rectangular surface (2rh).

Hence the equation for the surface area = π r² + π rh + 2 rh.

Scoring Rubric

Performance Characteristics

The following characteristics guide the scoring of responses to the open-response item(s).

Performance Characteristics

Purpose	The extent to which the response achieves the purpose of the assignment.
Subject Matter Knowledge	Accuracy and appropriateness in the application of subject matter knowledge.
Support	Quality and relevance of supporting details.
Rationale	Soundness of argument and degree of understanding of the subject matter.

Scoring Scale

The scoring scale below, which is related to the performance characteristics for the tests, is used by scorers in assigning scores to responses to the open-response item(s).

Score Scale with description for each score point.

Score Point	Score Point Description
4	The "4" response reflects a thorough knowledge and understanding of the subject matter. The purpose of the assignment is fully achieved. There is substantial, accurate, and appropriate application of subject matter knowledge. The supporting evidence is sound; there are high-quality, relevant examples. The response reflects an ably reasoned, comprehensive understanding of the topic.
3	The "3" response reflects an adequate knowledge and understanding of the subject matter. The purpose of the assignment is largely achieved. There is a generally accurate and appropriate application of subject matter knowledge. The supporting evidence is adequate; there are some acceptable, relevant examples. The response reflects an adequately reasoned understanding of the topic.
2	The "2" response reflects a limited knowledge and understanding of the subject matter. The purpose of the assignment is partially achieved. There is a limited, possibly inaccurate or inappropriate, application of subject matter knowledge. The supporting evidence is limited; there are few relevant examples. The response reflects a limited, poorly reasoned understanding of the topic.
1	The "1" response reflects a weak knowledge and understanding of the subject matter. The purpose of the assignment is not achieved. There is little or no appropriate or accurate application of subject matter knowledge. The supporting evidence, if present, is weak; there are few or no relevant examples. The response reflects little or no reasoning about or understanding of the topic.
U	The response is unrelated to the assigned topic, illegible, primarily in a language other than English, not of sufficient length to score, or merely a repetition of the assignment.
B	There is no response to the assignment.

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