Scoring MCAS Mathematics Items

Three Types of MCAS Math Items  Multiple Choice- Machine Scored  Short Answer- Hand Scored  Open Response- Hand Scored Massachusetts Department of Elementary and Secondary Education 2

Short Answer Items

Scoring a Short-Answer Item  Short-Answer items are worth one (1) point.  In a short-answer item the student is only required to generate a brief response. Massachusetts Department of Elementary and Secondary Education 4

Scoring a Short-Answer Item Massachusetts Department of Elementary and Secondary Education 5 Equivalent Answers That Are Acceptable Doug put 30 tiles of the same size and shape into a bag. The tiles are numbered 1 through 30 without repeating any numbers. Doug will reach into the bag without looking and take out a tile. What is the probability that Doug will take out a tile with a number greater than 20? Answer posted on ESE’s website: 1/3 or equivalentequivalent Answers accepted: or 33 % or 33 % or 33.3 % or “10 out of 30”

Scoring a Short-Answer Item Massachusetts Department of Elementary and Secondary Education 6 Equivalent Answers That Are Not Acceptable Write a mixed number that is greater than and less than. Answer posted on ESE’s website: Any mixed number greater than 3 and less than 3. Answers Accepted: 3 or 3 or 3 etc. Answers Not Accepted:,, 3.25 and 3.5

Scoring a Short-Answer Item Massachusetts Department of Elementary and Secondary Education 7 Multiple Possible Answers Write a number that has the digit 1 in the hundreds place and the digit 3 in the hundredths place. Answer posted on ESE’s website: Any number with a 1 in the hundreds place and a 3 in the hundredths place. Answers accepted: or or etc.

Scoring a Short-Answer Item Massachusetts Department of Elementary and Secondary Education 8 Single Answer Jordan has a machine part that is thirty-two thousandths of an inch thick. What is thirty-two thousandths written as a decimal? Answer posted on ESE’s website: Answers Accepted: 0.032

Scoring a Short-Answer Item Massachusetts Department of Elementary and Secondary Education 9 The diagram below shows a triangle and some of its measurements. What is the area, in square feet, of the triangle? Answer posted on ESE’s website: 6 square feet Answers Accepted: 6

Samples of Scoring ChallengesChallenges Massachusetts Department of Elementary and Secondary Education 10 or 30% /3 Example 1Example 2 Example 3 Work Contradicts Far out!! Two Answers+ Not Equivalent= No Credit

“Take Aways” on Short Answer items  Students should not be putting work into the answer space  Students should always be expected to have units with their work, but are not losing credit when omitted  Students should be careful when deciding to show equivalent answers Massachusetts Department of Elementary and Secondary Education 11

Open Response Items

Scoring an Open Response Item  Open Response items are worth 4 points, except in Grade 3 where they are worth 2 points.  In an Open Response item the student is expected to answer a series of related questions.  In many instances, an explanation for the answer is requested. Massachusetts Department of Elementary and Secondary Education 13

What is Benchmarking ?  A meeting between….  ESE Math Assessment Team  Measured Progress’s Item Development Team  Measured Progress’s Scoring Team …where decisions are made on how to score Short Answer and Open Response Items Massachusetts Department of Elementary and Secondary Education 14

How does Benchmarking Work?  Scoring team reads hundreds of papers to collect student responses  Benchmarking Team reviews and scores the responses independently  Benchmarking Team meets to come to consensus on scores  Anchor Set and Scoring Notes are created Massachusetts Department of Elementary and Secondary Education 15

A Common Question  What does “show” mean in “show or explain”?show Massachusetts Department of Elementary and Secondary Education 16

“Show” in “Show and explain how you got your answer” C. Use the equation you wrote in part (b) to find the score Catherine earned on her second test. Show or explain how you got your answer. Show Massachusetts Department of Elementary and Secondary Education 17

A Common Question  Will a student automatically lose a point whenever explanation is requested but not provided?automatically Massachusetts Department of Elementary and Secondary Education 18

Explanation Imperative, or No Credit  Dichotomous Answer: Suppose the vertices of J″K″L″ are reflected over the y-axis and then reflected over the x- axis. Do the vertices of the resulting triangle have the same coordinates as the vertices of triangle JKL? Show or explain how you got your answer. Yes Massachusetts Department of Elementary and Secondary Education 19

No Explanation, No Loss of Credit John has a rectangular prism with the dimensions shown in the diagram below. What is the surface area, in square feet, of John's rectangular prism? Show or explain how you got your answer.  72 square feet 72 Massachusetts Department of Elementary and Secondary Education 20

A Common Question  Should students SHOW and EXPLAIN?and Massachusetts Department of Elementary and Secondary Education 21

Show AND Explain?  Some students are comfortable writing a lot, but that isn’t necessary to earn full credit  Different learning styles are a factor  Geometry lends itself to showing...  Estimation lends itself to explaining... Massachusetts Department of Elementary and Secondary Education 22

A Common Question  Do students lose credit for all parts when a wrong answer for part (a) is used in parts (b), (c), and (d) ? Massachusetts Department of Elementary and Secondary Education 23

Reading along with the student  Correct uses of an incorrect answer can earn credit! Massachusetts Department of Elementary and Secondary Education 24

Incorrect part (a) used in (b) Chet shaded part of the two large rectangles shown below. a. Write a fraction that represents the shaded part of the two large rectangles. b. Write a different number that is equivalent to the fraction you wrote in part (a). Show or explain how you got your answer. Massachusetts Department of Elementary and Secondary Education 25

“Take Aways” for Open Response items  Students should show OR explain their work, both are not necessary.  Students can earn some credit when an incorrect answer is used correctly in subsequent parts of an item.  Students should always try all parts of an item, there can be partial credit earned when appropriate skills are demonstrated. Massachusetts Department of Elementary and Secondary Education 26