Wednesday, July 7, 2010

Bell Curve

The bell curve is another name for the normal distribution. The bell curve is highest in the middle and lowest on the sides and is a common type of graph that has more or less the shape of a bell.

When educators grade on a bell curve, they assign grades to students based on their performance in comparison to their peers' performance. In the true use of bell curve grading, students' scores are scaled according to the frequency distribution shown by the normal curve. This is the grade an "average" score will earn, and will also be the most common earned by the class. In the educational system's "A" through "F" grading system, a grade of "C" is normal curve. The bell curve produces the thought “If too many students succeed, the class must be too easy. If too many students fail, the class must be too hard." How many courses have you walked into, only to have your professor begin by saying that you should feel lucky if you earn a "B" in his or her course? This means that your professor has already decided what portion of the frequency distribution (or the "bell") each grade can take up, and whether or not the bell will be proportionate. Will a certain percent of students receive an "A" while the same percent receive an "F"? If an educator grades purely on bell curve grading, the number of students who will receive each "A" through "F" has already been determined before the course has even begun. Such strict bell curve grading is not common among elementary, middle, or high school educators, but is a bit more prevalent at the university level.

A common adjustment to the bell curve grading is to find the difference between the top-scoring grade on a test and the maximum possible grade. For example, if a test had a maximum of 100 points, and the highest grade earned on it was a 94, a teacher would add an additional six points to each test, thus "curving" all of the tests. This form of bell curve grading is most commonly used to prevent very difficult tests or other grades from unfairly reducing students' overall grades. It relies on the assumption that the top scorer's performance is a good measure of how difficult the assignment was.

Many districts have transformed from "L" to "Bell" to "J" curve with their expectations for their students. They now set their standards high, expecting that scores might be a bit lower in the beginning of the year with such high standards to begin the year off with. By the middle of the year, a bell-shaped distribution of scores appears, as students learn at various rates, and by the end of the year, scores yield a "J" shaped curve, which represents a high level of student achievement. The "J curve" is a new philosophy that is rooted that all students are capable of doing well in school.

"The Bell Curve" was also the title of a highly controversial book published back in 1994. The book was about intelligence. If you graph scores on an IQ test on the horizontal axis, and number of people who got that score on the vertical axis, then you get the bell curve shape. The authors were talking about the way intelligence was distributed among people- it suggested that some races were more intelligent than others.


Resources:
http://www.jjburgard.com/sub/Support/jcurve2.htm
http://en.wikipedia.org/wiki/Bell_curve_grading
http://www.robertniles.com/stats/stdev.shtml

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