Stand and Delivery Introductory Remarks

Facts that the ETS Knew or Could Have Found Out About Whether Some of the Students Cheated:
There were seven free response questions on the AP Calculus test. Students could get a passing score of 3 with correct answers to only three of the seven questions or with partially correct answers to six of the seven questions.

1. Free Response Question #6 is set out below:

A tank with a rectangular base and rectangular sides is to be open at the top. It is to be constructed so that its width is 4 meters and its volume is 36 meters. If building the tank costs $10 per square meter for the base and $5 per square meter for the sides, what is the cost of the least expensive tank? Mathews page 144.

Twelve of the eighteen Garfield students who took the calculus AP test in 1982 gave incorrect answers to Free Response Question #6. These twelve students began with an identical but incorrect formula for the cost of the rectangular tank. Each of them also made an identical mathematical error while simplifying a fraction. Students are taught how to simplify fractions in the 6th or 7th grade and perform the operation repeatedly thereafter. Specifically in the term 10hw they had to substitute 9/w for h and then simplify the term. The answer is 90.

If 9/w = h, then
10hw = 10 X 9 X w = 10 X 9 X w = 90
ww
The two w's cancel each other out and the expression simplifies to 90.

From the examinations that he saw, Mr. Mathews confirmed the ETS' claim that students who started with the incorrect formula also made the same mistake simplifying the fraction. Mathews pg. 175

2. The ETS employed a system of finding unusual patterns of similar answers in the multiple-choice portion of the AP Calculus test. This was called the "k" index. The index was controversial but the ETS relied on it in 1982. When ETS investigators examined the agreement on answers to the multiple choice section between all possible pairs of Mr. Escalante's 18 students, fourteen, including all twelve with similarities on the answer to Free Response Question 6, had answers on the multiple choice section that, under normal circumstances, would agree with each other in only one out of every 100,000 cases. Some Garfield High pairs had levels of agreement expected in only one in 10 million cases. Mathews pg. 157.

3. Mr. Escalante drilled and re-drilled his students in a system to approach questions in calculus.

4. The students at Garfield High who took the test scored well above the national average for students taking the test. They averaged four mistakes each, while the national average was 18.

5. As Mr. Escalante stated in the movie, it could have been that the teacher made the error and taught the students the incorrect formula. The class had been taught by a substitute teacher during Mr. Escalante's illness. This problem was covered at that time. However, six of Mr. Escalante's students got the correct answer or didn't use this particular incorrect equation.

6. The proctor who supervised the examination saw no suspicious behavior and no evidence of cheating. She reports that she was out of the room only for a very short period of time during the test.

7. The 18 students were together in a room and if they were copying on a massive scale one of the six students who didn't participate in the copying would have been likely to report them.

Bibliography: Escalante: The Best Teacher in America by Jay Mathews, 1988, Henry Holt and Company, New York.