Test Information Guide

Field 68: Elementary Mathematics
Sample Open-Response Item

The following materials contain:

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.

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 0014
Prepare an organized, developed analysis on a topic related to one or more of the following: measurement; data; geometry.

Use the information in the exhibit to complete the assignment that follows.

Use your knowledge of mathematics to develop a response of approximately 150–300 words, or 1–2 pages, in which you:

Problem

A teacher tells a student that sunrise occurred at 6:25 a.m. and that sunset is expected to occur at 7:30 p.m. The student is asked to determine the total amount of sunlight for that day.

Student Response

a circle on a graph

A student work sample is shown. The top of the work sample shows a number line that is marked with the times 6:25, 7:00, 12:00, 7:00, and 7:30. 4 curved lines symbolizing jumps along the number line are also shown. The jump from 6:25 to 7:00 is labeled 75 m. The jump from 7:00 to 12:00 is labeled 5 h. The jump from 12:00 to 7:00 is labeled 7 h. The jump from 7:00 to 7:30 is labeled 30 m. Two sums are shown at the bottom left. The first reads 7 h plus 5 h equals 12 h. The second reads 75 m plus 30 m equals 105 m. These sums are added at the bottom right, where 12 h plus 105 m is shown above a box of text reading 13 h 5 m.

Sample Strong Response to the Open-Response Item

The student appears to understand adding whole hours, since they have correctly added the hours from 7 A M to 7 P M, and that a half-hour is 30 minutes, since they correctly identify 7:00 to 7:30 as 30 minutes. The student’s misconception is that an hour has 100 minutes because they believe there are 75 minutes between 6:25 and 7:00. They repeat this error when adding 12h + 105 minutes; they change 105 minutes into 1 hour and 5 minutes to get 13h and 5m.

The correct solution is 13 hours and 5 minutes (which the student arrived at with incorrect thinking). I calculated that 7 A M to 7 P M equals 12 hours, plus the two half-hours (6:30to7:00 and 7:00to7:30), plus the five minutes from 6:25 to 6:30.

Instead of using a number line, use a clock face. First, orient the student to the clock by having them advance the minute hand through an hour. This provides a visual and kinetic representation that there are 30 minutes in a half-hour and 60 minutes in an hour. Then, to solve the problem, put the hands at 6:25 and move them to 6:30, noting down that five minutes have passed. Then, move the hands to 7:00, noting that 30 minutes have passed. This demonstrates that 6:25 to 7:00 is 30 minutes + 5 minutes = 35 minutes, not 75 minutes. Count the hours that pass until you get from 7 A M to 7:00 P M -- that is, 12 hours, which the student understands, but the movement of the minute hand will reinforce that there are 60 minutes in one hour. Count off the 30 minutes to 7:30. Now the student should be able to group the two 30-minute intervals into an hour to add to the 12 hours. Then they just add the additional 5 minutes to get 13h 5m.

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.