## Education

# Grading on the Curve

*by Clyde Spencer*

The many ways to assign student's grades all seem to have their advantages and disadvantages. It is likely that the technique you use was originally adopted for its simplicity, speed and ease of use. Tossing the papers down the stairs and giving A's to the farthest even has some merit. However, a more professional approach might be desired.

Most approaches require additional effort and varying degrees of mathematical expertise, and the more rigorous, statistically-based ones have not been in favor.

Let's assume you are teaching a course where frequent standardized testing is appropriate and the students' abilities and accomplishments can be expected to be "normally distributed". If you plotted the numeric scores against the number of students that received scores within a given small interval, the plot would approximate the standard "Bell" shape. You should have at least 20 students minimum-a typical class size.

In a classroom like this you might be interested in a method utilizing "McCall's T Scores". It is a statisticallybased technique that can be quite objective. Its singular greatest disadvantage used to be the amount of time it took to do the calculations. It used to take me about 21/z hours with a powerful hand calculator for a class of 30 to 40 students. With your ATARI computer it takes about as much time to enter raw scores in your gradebook as it takes to enter the scores on your computer keyboard. Twenty minutes later you can have a list from your printer that may be acceptable by your school administrators in lieu of your gradebook. It is also a relatively minor task to change a grade (especially with Visicalc) when you find that you have made the inevitable mistake.

This approach also takes into account variations in the level of difficulty of your tests and a student's preparation. In your current grading system you may assign 70% as the breaking point between a "C" and a "D", and this will be much too subjective and totally unreasonable for some exams.

An important advantage of this method is that both you and the students can have a good idea of what a student's class standing is at any time. The student's grade is determined by adding together all his McCall's T scores and dividing by the number of scores. That average is then compared with the equivalent letter grades.

The McCall's T score will "normalize" all the scores and compare the class performance as a whole against the individual scores, not some predetermined absolute. If your mathematics is strong, you can verify the algebraic manipulations from the BASIC program listing which follows. For the rest of you, you must trust that the approach calculates the class average (mean) and standard deviation. The mean is then subtracted from the individual student's score and divided by 1/lOth the standard deviation. This gives a number between about -25 and + 25, with most near zero. The constant 50 is then added to be sure all the numbers are positive. That is your McCall's T score. Fifty percent of the students will always have scores greater than 50. Sixtyeight percent will have scores between 40 and 60 and better than ninety-five percent of all the students will have a score between 30 and 70.

If you've ever been exposed to statistics, those numbers should look vaguely familiar. They represent 1 and 2 standard deviations from the mean. If you wanted to give no more than 15% A's, you would see that about 15% of the area in a normal curve is found above a value of 1.04 standard deviations above the mean. That would translate into a McCall's T score of 60.4 (10 x 1.04 + 50). I have in the past adopted cutoffs of 30, 40, 50 and 60. That effectively gives 50% A's and B's which is in line with a community college average.

If I've convinced you to try something new, what follows are a Visicalc template and a less elegant BASIC program along with sample printouts. You will find the BASIC program easier to type in than the Visicalc template, but Visicalc is definitely the preferred way to go!

Your students, being human, will never have seen anything like this before and some will resist change. You will need to explain the procedure to them, and re-explain it. If you think the method has merit, hang in there, but expect and be prepared for complaints. Just as there is no perfect form of government, these is no perfect grading system!

## Grading

All grade scores will be reported in terms of McCall's T score as well as the raw score.McCall's T score is defined as follows: T=50+10Z, where Z=(Y1-Y)/S and

S=sample standard deviation

Y1=student's raw score

Y=class mean

N=total sample number

therefore T=50+10(Y1-Y)/S

COURSE: TYPING 001 DATE: 14 FEB. 1983 QUIZ #1 STUDENT NAME RAW SCORE "T" SCORE Abbey, James 42 58.79 Blake, John 34 51.37 Castro, Jessee 49 65.29 Dalton, Maria 24 42.09 Ellis, Mark 35 52.30 Felix, Gloria 26 43.95 Gallo, Joe 30 47.66 Hanes, Sam 22 40.24 Ivanovich, William 41 57.86 Jackson, Anthony 40 56.94 Kaufman, David 31 48.59 Lang, Mary 47 63.43 Malone, Kathy 22 40.24 Nguyen, Kim 32 49.51 O'Neal, Doug 12 30.96 Perez, Delores 25 43.02 Quezada, Betina 21 39.31 Reddy, Barbara 18 36.52 Sanford, Tom 41 57.86 Takahashi, Isao 41 57.86 Unger, Max 50 66.21 ---------------------------------------------- TOTAL 683 NUMBER 21 AVERAGE (MEAN) 32.52 STAN. DEV 10.78 HIGH 50 LOW 12

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