Scoring MCAS Mathematics Items. Three Types of MCAS Math Items Multiple Choice- Machine Scored ...

Scoring MCAS Mathematics Items

Massachusetts Department of Elementary and Secondary Education

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Three Types of MCAS Math Items Multiple Choice- Machine Scored

Short Answer- Hand Scored

Open Response- Hand Scored

Short Answer Items


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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.


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Scoring a Short-Answer ItemEquivalent 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 repeatingany numbers. Doug will reach into the bag withoutlooking and take out a tile.

What is the probability that Doug will take out a tile witha number greater than 20?

Answer posted on ESE’s website: 1/3 or equivalent

Answers accepted: or 33% or 33 % or 33.3% or “10 out of 30”

30

103

1


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Scoring a Short-Answer ItemEquivalent 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

4

12

1

4

12

4

15

4

3

240

112

4

13

4

14


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Multiple Possible Answers

Write a number that has the digit 1 in the hundredsplace 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: 125.43 or 2146.03 or 189.931 etc.


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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: 0.032

Answers Accepted: 0.032


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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


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Samples of Scoring Challenges

or 30%30

10

3000

10001 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1/3

Example 1 Example 2

Example 3Work Contradicts Far out!!

Two Answers+ Not Equivalent= No Credit


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“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

Open Response Items


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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.


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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


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How does Benchmarking Work?

Scoring team reads hundreds of papers to collect 40-50 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


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A Common Question What does “show” mean in “show or

explain”?


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“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.


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A Common Question Will a student automatically lose a point

whenever explanation is requested but not provided?


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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


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No Explanation, No Loss of CreditJohn 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


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A Common Question Should students SHOW and EXPLAIN?


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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...


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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) ?


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Reading along with the student Correct uses of an incorrect answer can

earn credit!


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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.


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“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.

Scoring MCAS Mathematics Items. Three Types of MCAS Math Items Multiple Choice- Machine Scored ...

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