Rubric
M
Information Booklet for Scoring
the Regents Examinations in
Mathematics A and Mathematics B
(Including a supplement to the Guide for Rating Regents Examinations in
Mathematics)
The general procedures to be followed in administering Regents Examinations
are provided in the publications Directions for Administering Regents Examinations (DET
541), and Regents Examinations, Regents Competency Tests, and Proficiency
Examinations: School Administrator’s Manual, 2001
Edition. Copies of the Directions are shipped to schools prior
to each Regents Examination period and may also be accessed on the Department’s
web site at: http://www.emsc.nysed.gov/osa/hsgen.html.
The School Administrator’s Manual may be accessed on the Department’s
web site at: http://www.emsc.nysed.gov/osa/hsinfogen/hsinfogenarch/sam2001.pdf.
Questions about general administration procedures for Regents
Examinations should be directed to the Office of State Assessment at 518-474-8220
or 518-474-5902. For information about the rating of the Mathematics
A or Mathematics B Examination, contact the Office of State Assessment at 518-474-5900
or the Office of Curriculum, Instruction and Instructional Technology at 518-474-5922.
School administrators should print or photocopy this information booklet and
distribute copies to all school personnel who will be scoring these examinations.
The Regents Examinations in Mathematics A and Mathematics B are to be scored
by committees of mathematics teachers. No one teacher is to score all the questions
on a student’s paper. The committee must consist of at least three teachers.
Each of these teachers is responsible for scoring a selected number of the
open-ended questions. The more teachers serving on a committee, the fewer questions
each teacher scores. This process yields consistent and reliable scores and
allows scoring to proceed quickly.
Each examination is accompanied by a scoring key that includes the answers
to the Part I multiple-choice questions and rubrics for scoring each of the
open-ended questions. Teachers must become thoroughly familiar with the rubrics
for the questions they are scoring before beginning to score student responses
to examination questions.
The detachable answer sheet contains a table with spaces for recording the
Part I score; the score for each question in Parts II, III, and IV; the total-test
raw score; and the scaled score.
Multiple-choice questions may be either hand scored or machine scored. When hand scoring, indicate by means of a check mark each incorrect or omitted answer to multiple-choice questions on the designated answer sheet. Do not place a check mark beside a correct answer. Use only red ink or red pencil. In the appropriate space on the student’s answer sheet, record the number of multiple-choice questions the student answered correctly.
Machine-scorable answer sheets must be provided and scored by the school.
Answer sheets supplied by the school must provide the same number of response
options as are given in the examination questions, and the choices must be
labeled 1, 2, 3, 4, not A, B, C, D. Instructions for using the answer sheets
must be developed locally and provided to the proctors administering the examinations.
Before answer sheets can be machine scored, several samples must be both machine
and manually scored to ensure the accuracy of the machine-scoring process.
All discrepancies must be rectified before student answer sheets are machine
scored. When machine scoring is completed, a sample of the scored answer sheets
must be scored manually to verify the accuracy of the machine-scoring process.
The Score Conversion Chart for converting the student’s total-test raw
score to a scaled score is provided for each administration on the Department’s
web site at: http://www.emsc.nysed.gov/osa.
Because the scaled scores corresponding to raw scores in the Score Conversion
Chart change from one examination administration to another, it is crucial that,
for each administration, you use only the conversion chart provided
for that administration to determine the student’s final score. Take
extreme care in recording the student’s scores on each part of the examination,
adding these scores to determine the total-test raw score, and using the conversion
chart to obtain the correct scaled score.
For the Regents Examinations in Mathematics A and Mathematics
B, all student answer papers that receive a scaled score of 60 through
64 must be scored a second time. The principal may elect to have the scoring
committee also score a second time those student answer papers that received
a scaled score of 50 through 54, or all student answer papers. For the
second scoring, a different committee of teachers may score the student’s
paper or the original committee may score the paper. However, noteacher
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 examination score is based on a fair,
accurate, and reliable scoring of the student’s answer paper.
When the teacher scoring committee completes the scoring process, test scores
must be considered final and must be entered onto students’ permanent
records.
Principals and other administrative staff in a school or district do not have
the authority to set aside the scores arrived at by the teacher scoring committee
and rescore student examination papers or to change any scores assigned through
the procedures described in this manual and in the scoring materials provided
by the Department. Any principal or administrator found to have done so, except
in the circumstances described below, will be in violation of Department policy
regarding the scoring of State examinations. Teachers and administrators who
violate Department policy with respect to scoring State examinations may be
subject to disciplinary action in accordance with Sections 3020 and 3020-a
of Education Law or to action against their certification
pursuant to Part 83 of the Regulations of the Commissioner of Education.
On rare occasions, an administrator may learn that an isolated error occurred
in the calculation of a final score for a student or in recording students’ scores
in their permanent records. For example, the final score may have been based
on an incorrect summing of the student’s raw scores for parts of the
test or from a misreading of the conversion chart. When such errors involve
no more than five students’ final scores on any Regents Examination
and when such errors are detected within four months of the test date, the
principal may arrange for the corrected score to be recorded in the student’s
permanent record. However, in all such instances, the principal must advise
the Office of State Assessment in writing that the student’s score has
been corrected. The written notification to the Department must be signed by
the principal or superintendent and must include the names of the students
whose scores have been corrected, the name of the examination, the students’ original
and corrected scores, and a brief explanation of the nature of the scoring
error that was corrected.
If an administrator has substantial reason to believe that the teacher scoring
committee has failed to accurately score more than five student answer papers
on any examination, the administrator must first obtain permission in writing
from the Office of State Assessment before arranging for or permitting a rescoring
of student papers. The written request to the Office of State Assessment must
come from the superintendent of a public school district or the chief administrative
officer of a nonpublic or charter school and must include the examination title,
date of administration, and number of students whose papers would be subject
to such rescoring. This request must also include a statement explaining why
the administrator believes that the teacher scoring committee failed to score
appropriately and, thus, why he or she believes rescoring the examination papers
is necessary. As part of this submission, the school administrator must make
clear his or her understanding that such extraordinary re-rating may be carried
out only by a full committee of teachers constituted in accordance with the
scoring guidelines presented above and fully utilizing the scoring materials
for this test provided by the Department.
The Department sometimes finds it necessary to notify schools of a revision
to the scoring key and rating guide for an examination. Should this occur after
the scoring committee has completed its work, the principal is authorized to
have appropriate members of the scoring committee review students’ responses
only to the specific question(s) referenced in the notification and to adjust
students’ final examination scores when appropriate. Only in such circumstances
is the school not required to notify or obtain approval from the Department
to correct students’ final examination scores.
Specific Information for Scoring the
Regents Examinations in Mathematics A and Mathematics B
The information below refers to the scoring of open-ended questions on the
Mathematics A and Mathematics B Regents Examinations 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 and Mathematics
B examinations should be scored in accordance with these guidelines:
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, with one worth 4 credits
and another worth 3 credits, the student should be awarded 3 credits for the
question.)
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.
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.
This last statement is illustrated by a student who, when asked to find one
leg of a right triangle if the hypotenuse is 5 and the other leg is 3, 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.
Examples of Scored Student Responses with Comments
The graph below shows the hair colors of all the students in a class. What is the probability that a student chosen at random from this class has black hair?
Rubric
[2] 6/20 or an equivalent answer, and appropriate work is shown.
[1] Appropriate work is shown, but one
computational error is made.
or
[1] 6/20 or an equivalent answer, but no
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.
Score: 0
The student has crossed out the first part of the response, so only the second
part is scored. The student has confused probability with combinations, which
is irrelevant in this problem.
Student Response
Comment
Score: 1
The student has a correct numerator but did not compute a proper denominator.
The student has shown work and has an answer in fractional form.
Student Response
Comment
Score: 2
The student has a correct answer with appropriate work shown.
There are four students, all of different heights, who are to be randomly arranged in a line. What is the probability that the tallest student will be first in line and the shortest student will be last in line?
Rubric
[3] 
or
an equivalent answer and an appropriate explanation are given or appropriate
work is shown, such as a tree diagram, sample space, or permutations.
[2] Appropriate work is shown, but one
computational error is made.
or
[2] Appropriate work is shown, but only
a numerator or denominator is determined correctly.
or
[2] 
or
an equivalent answer is given, but only work for either the numerator or denominator
is shown.
[1] The probability of the tallest or
the probability of the shortest student being in the proper position is correct,
such as 
or
[1] Only a tree diagram, sample space,
or permutations are shown.
or
[1] 
or
an equivalent answer, but no 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.
Comment
Student Response
Comment
Score: 1
The student has given a correct answer but has not shown
any work.
Student Response
Comment
Score: 2
The student has shown appropriate work but has determined correctly only a
numerator or a denominator.
Student Response
Comment:
Score: 3
The student has a complete and correct response.
Solve the following system of equations algebraically.
y = x2
+ 4x – 2
y =
2x + 1
Rubric
[4] (–3,–5) and (1,3), and appropriate algebraic work is shown.
[3] Appropriate work is shown, but one
computational error is made.
or
[3] Appropriate algebraic work is shown,
but only one solution is found or only the x- or the y- values
are found.
[2] Appropriate work is shown, but two
or more computational errors are made.
or
[2] Appropriate work is shown, but one
conceptual error is made.
or
[2] (–3,–5) and (1,3), but
a method other than algebraic is used.
or
[2] The correct quadratic equation in standard
form, x2 + 2x – 3 = 0 is written, but no further correct
work is shown.
[1] Appropriate work is shown, but one
conceptual error and one computational error are made.
or
[1] A correct substitution is made, but
no further correct work is shown.
or
[1] (–3,–5)
and (1,3), but no further correct 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.
Comment
Score: 0
Student Response
Comment
Score: 1
The student correctly substituted for y, but has shown no further
correct work.
Comment
Score: 2
The student has put the equation in standard form (set equal to zero) but has
shown no further correct work.
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.
A survey of the soda drinking habits of the population in a high school revealed
the mean number of cans of soda consumed per person per week to be 20, with
a standard deviation of 3.5. If a normal distribution is assumed, find an interval
that contains the total number of cans per week that approximately 95% of the
population of this school will drink.
Explain why you selected that interval.
[2] 13–27, a curve is drawn and
labeled correctly, and a correct explanation is given.
or
[2] 13–27, and a statement explaining
how to interpret the curve are given, but no curve is drawn.
[1] An appropriate method is used, but
one computational error is made.
or
[1] A correct answer based on an incorrect
curve is given.
or
[1] 13–27, but no further correct
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.
Comment
Score:
1
The student’s answer shows partial understanding.
The range is slightly off, and the explanation is somewhat vague.
Student Response
Comment
Score:
2
The
student has provided a correct answer and an appropriate explanation.
In the equation y = .5(1.21x), y represents the number of snowboarders in millions and x represents the number of years since 1988. Find the first year in which the number of snowboarders will be 10 million. (Only an algebraic solution will be accepted.)
[4] 2004, and appropriate algebraic work is shown, such as solving the log problem algebraically.
[3] Appropriate algebraic work is shown
to find 15.7, but the correct year is not determined.
or
[3] Appropriate algebraic work is shown,
but one computational or rounding error is made.
[2] Appropriate work is shown, but two
or more computational or rounding errors are made.
or
[2] Appropriate work is shown, but one
conceptual error is made.
or
[2] A correct logarithmic equation is written,
but no further correct work is shown.
or
[2] 2004, but a method other than an algebraic
solution is used.
[1] Appropriate work is shown, but one
conceptual and one computational or rounding error are made.
or
[1] The equation is set equal to 10 or
10,000,000, but it is not solved.
or
[1] 2004, but no 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: 1
The student set the equation equal to 10 and properly divided by 0.5 but never
showed log analysis.
Student Response
Comment
Score: 2
The student set up a correct log equation but went no further.
Student Response
Comment
Score: 3
The student has made only one minor error, using 10,000,000 instead of 10.
Student Response
Comment
Score: 4
The volume of a particular gas was determined at various pressures. P represents the pressure (in atmospheres) and is the independent variable on the horizontal axes, and V represents the volume (in liters) and is the dependent variable on the vertical axes. Create a scatter plot and find the curve of best fit. (Round answer constants to the nearest tenth.) Using the regression equation found, estimate V if P = 2.5.
P |
V |
0.1 |
225 |
[6] A correct scatter plot, including labeled axes, V = 22.5 P–1, and 9, and appropriate work is shown.
[5] Appropriate work is shown, but one computational or graphing error is made.
[4] Appropriate work is shown, but two
or more computational or graphing errors are made.
or
[4] A correct scatter plot is drawn, but
an incorrect type of function for the equation is used, but the volume is found
based on the incorrect equation.
or
[4] A correct scatter plot is drawn, V =
22.5 P–1, but no further correct work is shown.
[3] V = 22.5 P–1
and 9, but no further correct work is shown.
or
[3] A correct scatter plot is drawn, but
no further correct work is shown.
[2] V = 22.5 P–1, but no further correct work is shown.
[1] A correct scatter plot is given, but
minor errors on intervals of the axes are made.
or
[1] 9, but no 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: 1
The student has shown minimal work in an attempt to draw a scatter plot.
Student Response
Comment
Score: 2
The student has shown only a correct equation.
Student Response
Comment
Score: 3
The student has drawn an acceptable graph but has not shown any regression
equation.
Student Response
Comment
Score: 4
The student has shown an incorrect regression line but has continued to find
an appropriate value for y (V). Also, no labels appear
on the axes.
Student Response
Comment
Score: 5
The student has made a minor error labeling the axes, showing the y-axis
equal to P when it should be V.
Student Response
Comment
Score: 6