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Methods of Adjusting Assessment Scores

Joe Large

ETR 530

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Topic Overview

How you are interpreting the data Fitting assessment results with preset

grades/categories Criterion-based vs Peer-based grading Obtaining useful results Usually associated with paper-and-pencil

tests

Why Adjust Scores?

Test was not properly constructed Poor Alignment (Content Validity) Test items were too difficult Test was too long Students were not properly prepared

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Method #1: Normalizing Scores

Fits score to the Normal Curve Peer-Based Grading Uses Z-Scores to determine placement How far from the mean? Pre-determines how many A’s, B’s, etc.

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Method #1 (cont.)

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x

Z

Method #1 (cont.)

10/20/40/20/10 Method A = Z>1.28

(1.28, .92)

B = .52<Z<1.28 (.52,.83)

C = -.52<Z<.52 (-.52,.75)

D = -1.28<Z<-.52 (-1.28,.70)

F = Z<-1.28

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3 2( ) .00659 .01462 .07514 .786f x x x x

Method #1 (cont.)

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Method #2: Total Points Change

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“Throwing out” a problem Item too difficult Test too long Includes Extra Credit problems Helps high-level students more Increase range of scores

Method #2 (cont.)

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Method #2 (cont.)

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( )

( )

( ) ( )

( ) ( )

( )

( ) ( )

5 1: ( )

30(30 5) 150

1(27.5) 27.5 .1833

1501

(10) 10 .0667150

X XD X

T P TTX X T P

T T P T T P

TX XT XP

T T P T T P

TX TX XP

T T P

XP PX

T T P T T P

Ex D X X X

D

D

D(X)=Difference X=Raw Score T=Original Total P=Points Dropped Difference is directly

proportional to the student’s raw score

Method #2 (cont.)

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Method #3: Percentage Increase

Students get back a percentage of the points that they missed

Each student’s score is increased equally, relative to the amount they missed

Helps low-level students more Compresses the range of scores Can be used with test corrections

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Method #3 (cont.)

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Method #3 (cont.)

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( ) ( )

( ) .425(100 )

42.5 .425

.575 42.5

F X X K T X

F X X X

X X

X

F(X)=Adjusted Score X=Raw Score T=Original Total K=Adjustment Level Difference is directly

proportional to the missed points

Method #4: Linearization2

Choose two students and set their grades Use those two points to create a linear

regression function for the rest of the data Teacher must determine the adjusted

scores for exactly two students Compresses the range of scores Very similar to Method #3

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Method #4 (cont.)

Adjust the 91.6 score to 98 Adjust the 33.3 score to 60

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98 60 38.651

91.6 33.3 58.3( ) .651( 33.3) 60

.651 38.3

m

F X X

X

Method #4 (cont.)

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Other Methods…

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Flat Increase Square Root / Logarithmic

Curve Gap Distribution (aka

Staring Method) Gravity Curve!

Conclusion/Discussion

Ideal World = No Adjustments Don’t “bury” a student with a low score Questions

Does “curving” lower student motivation?Which method do you prefer?Have you used or heard of other methods?What about equity?

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References/Suggested Reading 1) http://129.3.20.41/eps/em/papers/0305/0305001.pdf   2) http://divisbyzero.com/2008/12/22/how-to-curve-an-exam-and-assign-grades/   3) http://www.cat.ilstu.edu/resources/teachTopics/tips/twoGradings.php   4) http://www.astronomy.ohio-state.edu/~pogge/Ast162/Quizzes/curve.html   5) http://scienceblogs.com/principles/2009/01/grading_methods_dont_matter.php#more   6) http://forums.atozteacherstuff.com/showthread.php?t=49582   7) http://www.blackboard.niu.edu/blackboard/faq/qa/gradescurve.shtml   8) http://www.daggerpress.com/2009/05/17/harford-county-public-schools-curving-math-grades-in-some-middle-

schools/   9) http://oas.uco.edu/03/paper/wall.htm

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Dedication

Special thanks to Fr. Kenneth Theisen for his words of wisdom on different curving methods.

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