Study Guide

Field 082: Elementary Mathematics Specialist 
Sample Constructed-Response Assignment

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Test Directions for the Constructed-Response Assignment

This section of the test consists of one constructed-response assignment. You are to prepare a written response of approximately 300–600 words on the assigned topic. You should use your time to plan, write, review, and edit your response to the assignment.

Read the assignment carefully before you begin to write. Think about how you will organize your response.

As a whole, your response must demonstrate an understanding of the knowledge and skills of the field. In your response to the assignment, you are expected to demonstrate the depth of your understanding of the content area through your ability to apply your knowledge and skills rather than merely to recite factual information.

Your response to the assignment will be evaluated on the basis of the following criteria:

 start bold PURPOSE: end bold  the extent to which the response achieves the purpose of the assignment
 start bold SUBJECT MATTER KNOWLEDGE: end bold  accuracy and appropriateness in the application of subject matter knowledge
 start bold SUPPORT: end bold  quality and relevance of supporting details
 start bold RATIONALE: end bold  soundness of argument and degree of understanding of the subject matter

The constructed-response assignment is intended to assess subject matter knowledge and skills, not writing ability. However, your response must be communicated clearly enough to permit valid judgment of the scoring criteria. Your response should be written for an audience of educators in this field. The final version of your response should conform to the conventions of edited American English. Your written response must 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 topic. Remember to review what you have written and make any changes you think will improve your response.

Sample Constructed-Response Assignment

Competency 0011 
Prepare an organized analysis of student work and a response to this work.

 start bold Use the information below to complete the assignment that follows.  end bold 

A second-grade student writes down the following attempt at the standard subtraction algorithm:

   

The student has written the subtraction in vertical format, with 100 on the top line, minus 36 on the next line, an underscore, and 74 below the underscore. The rightmost 0 of the 100 has been struck through and 10 written above it. The 0 to the left of it has also been struck through and 10 written above it. The 1 has been struck through and 0 written above it.



When asked to show the process using base-ten blocks, the student takes out 4 ones cubes and 6 ones cubes, saying, "See, 4 and 6 make 10," and then takes out 7 tens rods and 3 tens rods, saying, "… and 3 plus 7 is also 10."

Using your knowledge of pedagogy and mathematics, prepare a response in which you:

Sample Strong Response to the Constructed-Response Assignment

 start bold Please note: The sample response provided below is for review purposes only and should not be used in a response on an operational exam. Use of the exact words and phrases presented in this sample response will result in a score of "U" (Unscorable) due to lack of original work. end bold 

The student knows that regrouping is needed in order to do this subtraction and shows this using the notation of regrouping. The student does not understand the relationship of the place values or that in order to have 10 ones, there will be one fewer group of ten in the tens place (this is shown by the tens the student wrote in each of the tens and ones places). Similarly, the student does not regroup when checking the answer by adding, keeping ten ones rather than equating the ten ones to one ten.

A lesson that would remedy the place value misconception would use the base ten blocks to focus only on trading so that the student consistently trades ten ones for one ten and ten tens for one hundred. The trading practice should require various combinations of trades in both directions, involving trades where only one regrouping is required and as well as trades where two regroupings are needed. Attention should be paid to the order in which multiple regroupings need to be made by pointing out the need, for example, of having tens blocks to “borrow” from in order to trade for ones. The student should be asked to write the notation for each of the trades in the order that they are done. These activities will strengthen place value and regrouping concepts which can then be extended to any decimal numbers.

Performance Characteristics

The following characteristics guide the scoring of responses to the constructed-response assignment.

Characteristics that guide the scoring of responses
Purpose The extent to which the response achieves the purpose of the assignment
Subject Matter Knowledge The accuracy and appropriateness in the application of subject matter knowledge
Support The quality and relevance of supporting details
Rationale The soundness of argument and degree of understanding of the subject matter

Scoring Scale

Scores will be assigned to each response to the constructed-response assignment according to the following scoring scale.

Score Scale with description for each score point.
Score Point Score Point Description
4  start bold The "4" response reflects a thorough knowledge and understanding of the subject matter. end bold 
  • The purpose of the assignment is fully achieved.
  • There is a 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  start bold The "3" response reflects a general knowledge and understanding of the subject matter. end bold 
  • The purpose of the assignment is largely achieved.
  • There is a generally accurate and appropriate application of subject matter knowledge.
  • The supporting evidence generally supports the discussion; there are some relevant examples.
  • The response reflects a general understanding of the topic.
2  start bold The "2" response reflects a partial knowledge and understanding of the subject matter. end bold 
  • 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  start bold The "1" response reflects little or no knowledge and understanding of the subject matter. end bold 
  • 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 unscorable because it is illegible, not written to the assigned topic, written in a language other than English, or lacking a sufficient amount of original work to score.
B There is no response to the assignment.