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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 Regents Examinations in

Mathematics A and Mathematics B

(including a supplement to the Guide for Rating Regents Examinations in Mathematics)

General Information

The general procedures to be followed in administering Regents Examinations are provided in the publications Regents Examinations, Regents Competency Tests, and Proficiency Examinations: School Administrator’s Manual, 2001 Edition, and Directions for Administering and Scoring Regents Examinations (DET 541). The School Administrator’s Manual may be accessed on the Department’s web site: 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 518-474-5099. 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 may photocopy this booklet and distribute copies to school personnel who will be involved in the administration and scoring of these examinations.

Description of the Examination in Mathematics A

The Examination in Mathematics A has a total of 39 questions in four parts. Students are to answer all 39 questions. No choice is permitted. Students are to record their answers to Part I questions on the detachable answer sheet, which is printed as the last page of the examination booklet. They are to record their answers to the questions in Parts II, III, and IV in the examination booklet. Students must also clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc., they used in arriving at their answers to Parts II, III, and IV questions.

Mathematics A Breakdown

Part	Question Type	Number of Questions	Maximum Number of Credits per Question	Total Number of Raw Score Credits
I	multiple choice	30	2	60
II	open ended	5	2	10
III	open ended	2	3	6
IV	open ended	2	4	8
	TOTAL	39		84

The total-test raw score must be converted to a scaled score using the conversion chart provided for each administration on the Department’s web site: http://www.emsc.nysed.gov/osa.

Description of the Examination in Mathematics B

The Regents Examination in Mathematics B has four parts, with a total of 34 questions. Students are to answer all 34 questions. No choice is permitted. Students are to record their answers to Part I questions on the detachable answer sheet, which is printed as the last page of the examination booklet. They are to record their answers to the questions in Parts II, III, and IV in the examination booklet. Students must also clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc., they used in arriving at their answers to Parts II, III, and IV questions.

Mathematics B Breakdown

Part	Question Type	Number of Questions	Maximum Number of Credits per Question	Total Number of Raw Score Credits
I	multiple choice	20	2	40
II	open ended	6	2	12
III	open ended	6	4	24
IV	open ended	2	6	12
	TOTAL	34		88

The total-test raw score must be converted to a scaled score using the conversion chart provided for each administration on the Department’s web site: http://www.emsc.nysed.gov/osa.

Administering the Examinations in Mathematics A and Mathematics B

Students are to be allowed a maximum of three hours in which to complete each examination. They should write all work in pen except for graphs and drawings, which should be done in pencil.

Scrap paper is not permitted. Students may use the blank spaces in the examination 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.

Use of Calculator and Supplementary Material

Each student taking the Mathematics A Regents Examination must have a scientific calculator, a straightedge, and a compass available for his or her exclusive use during the entire scheduled time for the examination. Graphing calculators are permitted but not required. Each student taking the Mathematics B Regents Examination must have a graphing calculator, a straightedge, and a compass available for his or her exclusive use during the entire scheduled time for the examination. The memory of any calculator with programming capability must be cleared or reset when students enter the testing room. The use of operating manuals, instruction or formula cards, or other information concerning the operation of calculators is not permitted. Calculators that have symbol manipulation capabilities or that can be used to communicate with other calculators are not permitted.

Scoring the 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 more consistent and reliable scores and allows scoring to proceed more 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 should become thoroughly familiar with the rubrics for the questions they are scoring before beginning the scoring process.

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.

Determining the Student’s Final Examination Score

A 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: http://www.emsc.nysed.gov/osa. Because the scaled scores corresponding to raw scores in the 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 a Regents diploma, a score of 65 on a Regents examination in mathematics is passing. Public school districts and nonpublic schools may establish a passing score no lower than 55 for awarding a local diploma to those students first entering Grade 9 in the 1997–98 through the 2004–05 school years.

Rescoring Student Answer Papers

All student answer papers for the Mathematics A and Mathematics B examinations that receive a scaled score of 60 through 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 should 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 assure that the student’s final examination score is based on a fair, accurate, and reliable scoring of the student’s answer paper.

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 exami

nations 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 all but one 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 startups.

· 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, with one worth 4 credits and another 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 cannot 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, 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.

· 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.

Examples of Scored Student Responses with Comments

Sample Question 1 – Mathematics A

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, and appropriate work is shown.

[1] A fraction with a correct numerator or denominator is given, and some work is shown.

[1] 6/20, 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: 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.

Sample Question 2 – Mathematics A

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.

[2] Appropriate work is shown, but only a numerator or denominator is determined correctly.

[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 property position is correct, such as

[1] Only a tree diagram, sample space, or permutations are shown.

[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.

Student Response

Comment

Score: 0

The student’s response shows major misunderstanding of the problem.

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.

Sample Question 3 – 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.

[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.

[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