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The University of the State of New York
THE STATE EDUCATION DEPARTMENT
Albany, New York 12234
information booklet for administering and scoring
the component retests in mathematics a
The general procedures to be followed in administering component retests are provided in the publication Directions for Administering and Scoring Component Retests (DET 241). This document is available on the Department’s web site, http://www.emsc.nysed.gov/osa/component.html. Questions about general administration procedures for component retests should be directed to the Office of State Assessment at 518-474-8220 or 518-474-5902. For information about the rating of the Component Retests in Mathematics A, contact the Office of State Assessment at 518-474-5900.
School administrators should photocopy this information booklet and distribute copies to school personnel who will be involved in the administration and scoring of the component retests.
There are component retests for four mathematics key ideas from The
Learning Standards for Mathematics, Science, and Technology (1996): key
ideas 4, 5, 6, and 7. Each component retest has two modules administered on
two successive dates. Each module consists of six multiple-choice and
three 4-point open-ended questions. For each session, each student is to be
given the appropriate test booklet for the date and session. Students are to
answer all questions; no choice is permitted. All work should be written in
pen except for graphs and drawings, which should be done in pencil. Students
are to be allowed a maximum of 50 minutes in which to complete each module.
Part I of each module comprises six multiple-choice questions, for which the student is to select the correct answer from among the four choices given. Answers to Part I questions are to be recorded on the detachable answer sheet, which is the last page of the test booklet. Each Part I question is worth two credits, for a maximum Part I raw score of 12 credits.
Part II of each module consists of three open-ended questions. Answers to Part II questions are to be recorded in the test booklet. Students must clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Each Part II question is worth four credits, for a maximum Part II raw score of 12 credits.
The maximum total raw score for each module is 24 credits. The maximum total raw score for each component retest is 48 credits.
Scrap paper is not permitted. Students may use the blank spaces in the test booklet and the page of graph paper at the end of the booklet as scrap paper. Schools should have a supply of graph paper available for students who request it in the event that they need to change their work on graphs.
A straightedge (ruler) and a compass must be available for the exclusive use
of each student while taking the component retests. In addition, each
student taking the Component Retests in
Mathematics A must have a scientific calculator available for his or her
exclusive use during the entire scheduled time for the examination. Since
students are not permitted to use printed trigonometric and
logarithmic reference tables during this examination, scientific calculators
must have these features. Graphing calculators without symbol
manipulation are permitted but not required. When students enter the testing
room, clear, reset, or disable the memory of any calculator with programming
capability.
If the memory of a student’s calculator is password-protected and cannot be cleared, the calculator must not be used. Remove or disable any applications that have been added to graphing calculators. Students may not use calculators that are capable of symbol manipulation or that can communicate with other calculators through infrared sensors, nor may students use operating manuals, instruction or formula cards, or other information concerning the operation of calculators during the examination.
The Component Retest in Mathematics A is to be scored by committees of mathematics teachers. No one teacher is to score all the questions on a student’s paper. The committee membership must be comprised of at least three teachers. Each of these teachers is responsible for scoring a selected number of the open-ended questions. The more teachers who serve on a committee, the fewer questions each teacher will need to score. This process yields consistent and reliable scores and allows scoring to proceed quickly.
On or about May 22, 2006, rating materials for all of the component retests will be posted on the Department’s web site, http://www.emsc.nysed.gov/osa/component.html; paper copies of the rating materials will not be sent to schools. Schools must print sufficient copies of these materials to provide them to each rater.
Each component retest booklet includes a detachable answer sheet for student responses to the multiple-choice questions contained within that test booklet. The student’s raw score for Part I should be entered in the box labeled “Score” on the front of the answer sheet. The back of each answer sheet includes a table for recording the credits earned for Part I, the credits earned for each of the three questions in Part II, and the “Total Raw Score” for Parts I and II of that module.
Unlike the scores earned on Regents Examinations, final scores for the component retests will not be on a 0–100 scale. The student’s final result will be designated as one of three possible score ranges:
· Score range 65 and above
A component retest result of score range 65 and above is equivalent to a score of 65 on a Regents Examination and satisfies the State testing requirement for a local or a Regents diploma. Students who are required to take retests in two components in Mathematics A must achieve a component retest result of score range 65 and above on both components to achieve the equivalent of 65 on the Regents Examination in Mathematics A.
· Score range 55–64
A component retest result of score range 55–64 is equivalent to a score between 55 and 64 on the corresponding Regents Examination. In schools that have designated 55 as the passing score on a Regents Examination in mathematics for the awarding of a local diploma, achieving a component retest result of score range 55–64 satisfies the State testing requirement for the local diploma. Students who are required to take retests in two components of Mathematics A must achieve a component retest result of score range 55–64 (or higher) on both components to earn the equivalent of a score from 55 to 64 on the Regents Examination in Mathematics A.
· Score range below 55
A component retest result of score range below 55 is equivalent to a score below 55 on the Regents Examination in Mathematics A. Such a result does not satisfy the State testing requirement for a local or a Regents diploma.
A table similar to the one at the right
appears on the back of the Module 2 answer
sheet. In this table, enter the student’s scores
for Modules 1 and 2. Add the student’s scores
for Modules 1 and 2 and record the total score.
To determine the
student’s final score
range, use the conversion chart provided with
the scoring materials for that component.
Locate the student’s final score down the left
side of the chart. The score range to the right of
the student’s final score is the student’s final
score range. Enter an X or check mark in the
appropriate box to indicate the score range
(65 and above, 55–64, or below 55)
on the answer sheet.
Because the score ranges corresponding to raw scores in the conversion chart vary for each component and change from one component retest administration to another, it is crucial that for each administration the conversion chart provided with the scoring materials for that component’s administration be used to determine the student’s final score range. Extreme care should be taken in recording the student’s scores on each part of the test, in adding these scores to determine the total score for each module and for the two modules combined, and in using the conversion chart to obtain the final score range.
Rescoring Student Answer Papers
All student answer papers with a total component retest score that is two or fewer credits below the total score required to achieve score range 65 and above or score range 55–64 must be scored a second time. For the second scoring, a different committee of teachers may score the student’s paper or the original committee may score the paper, but no teacher may score the same open-ended questions that he or she scored in the first rating of the paper. It is the responsibility of the school principal to ensure that the student’s final test score is based on a fair, accurate, and reliable scoring of the student’s answer paper.
Use the Specific Information for Scoring the Regents Examination in Mathematics A on the following pages as a guideline for scoring Component Retests in Mathematics A.
______________________
*The procedure for determining the student’s score range is the same for Components 5, 6, and 7 except that the school must use the conversion charts provided with the scoring materials for those components.
Specific Information for Scoring the
Regents Examination in Mathematics A
The information below refers to the scoring of open-ended questions on the Mathematics A Examination and is intended as a supplement to the Guide for Rating Regents Examinations in Mathematics.
The open-ended questions (Parts II, III, and IV) on the Mathematics A Examination should be scored in accordance with these guidelines:
· If the student gives one legible response, even if it is crossed out, teachers should score the response.
· If there are two or more responses with some crossed out, teachers should score only the response not crossed out.
· If there are one or more partial responses and one complete response, teachers should score the complete response. No credit is deducted for incorrect start-ups.
· If there are two or more complete responses, teachers should score each one. Credit will be allocated in the following way:
If one response is completely correct and the others are completely incorrect,
teachers should award 50% credit and round down (2 credits for a 4-credit
question, 1 credit for
a 2-credit question, and 1 credit for a 3-credit question).
If each response warrants more than 50%, the lesser of the responses is awarded credit. (For example, if a 4-credit question is done two ways, one of which is worth 4 credits and the other worth 3 credits, the student should be awarded 3 credits for the question.)
· If the question requires the student to include units of measure, full credit may not be awarded if the student omits the unit. Students may include the appropriate unit of measure even if it is not required.
Examples:
If the question asks for the number of feet in the length of a figure, no unit is required in the answer.
If the question asks for the dimensions of a figure, the proper unit of measure is required in the answer in order to receive full credit.
The rubric will specify how much credit is awarded if units are not used when required.
· If a student gives only a correct numerical answer to a problem but does not show how he or she arrived at the answer, the student will be awarded only 1 credit. All constructed-response questions require the student to show work. If the question has only one part, this rule is straightforward, but this rule needs some clarification for multiple-part questions.
A fully correct answer for a multiple-part question requires correct responses for all parts of the question. For example, if a 3-credit question has three parts, the correct response to one or two parts of the question that required work to be shown is not considered a fully correct response with no work shown and would receive 0 credits.
The rubric of a multiple-part question will specify credit for various amounts of work shown.
· Students should receive 0 credits if the solution is completely incorrect, irrelevant, or incoherent or if a correct response was arrived at using an obviously incorrect procedure.
This last statement is illustrated by a student who is asked to find one leg of
a right
triangle if the hypotenuse is 5 and the other leg is 3, and gives a correct
response of 4 by showing that 4 is the average of 3 and 5.
The method of solution must be obviously incorrect to warrant a score of 0.
In some cases, the rubric will specifically state which responses should receive a score of 0.
· Students who use trial and error to solve a problem must show their method. Merely showing that the answer checks or is correct is not considered a complete response for full credit. Most rubrics will address this issue directly. For more detail, teachers are encouraged to consult the Guide for Rating Regents Examinations in Mathematics.
Sample Question – Mathematics A
Solve the following system of equations algebraically.
y = x2 + 4x – 2
y = 2x + 1
Rubric
[ 4 ] (–3,–5), (1,3), and appropriate algebraic work is shown.
[ 3 ] Appropriate algebraic work is shown, but x = –3 and x = 1 are given as the solution.
[ 2 ] (–3,–5), (1,3), but a graphic solution is shown.
or
[ 2 ] Correct substitution and an algebraic equation set equal to zero are shown, but the result is not factored, such as x2 + 2x – 3 = 0.
[ 1 ] Any correct substitution is shown, such as 2x + 1 = x2 + 4x – 2.
or
[ 1 ] (–3,–5), (1,3), but no algebraic work is shown.
[ 0 ] A zero response is completely incorrect, irrelevant, or incoherent, or is a correct response that was obtained by an obviously incorrect procedure.
Student Response
Comment
Score: 0
The student’s response shows major misunderstanding of the problem.
Student Response
Comment
Score: 1
The student correctly substituted for y, but has shown no further correct work.
Student Response
Comment
Score: 2
The student has put the equation in standard form (set equal to zero) but has shown no further correct work.
Student Response
Comment
Score: 3
The student has shown appropriate algebraic work but has given only part of the correct solution.
Student Response
Comment
Score: 4
The student has a complete and correct answer.