Crumbling the Pyramids

A Florida whiz kid beats the experts at the testing game

Most teen-agers would probably have been delighted to learn they had got 48 out of 50 questions right on a tough mathematical aptitude test. Not Daniel Lowen, 17, a junior at Cocoa Beach High School in Florida. Told his score in the math portion of the Preliminary Scholastic Aptitude Test that he took last fall along with 830,000 other students nationwide, Dan was displeased. He was convinced that his answer to question No. 44--one of those marked incorrect--was in fact correct. He even made a model to prove his case to his father, Douglas Lowen, an environmental system engineer on the space shuttle. Recalls Dan: "My dad tried to prove that I was wrong, but he couldn't."

Neither could the Educational Testing Service of Princeton, N.J., which prepared the aptitude test with the help of professional mathematicians. Alerted by Lowen pere, the testmakers studied Dan's argument and had to concede that his answer was at least as good as their own, perhaps better. As a result, the testing service raised Dan's score, as well as the scores of 250,000 other students who picked the same answer in the multiple-choice exam, though probably for the wrong reason.

How had this young David managed to outwit the Goliaths of the testing world? In the disputed question, the students were shown a diagram of two pyramids. One consisted of four triangles, the other of four triangles plus a rectangular base. All the triangles were equilateral (that is, their sides were of the same length) and of the same size. The problem: if the two pyramids were joined by setting two triangles next to each other so they precisely coincided, how many faces would remain "exposed" in the resulting solid? The testers expected simple reasoning to provide the answer: together the pyramids had a total of nine faces; thus when two triangles are eliminated by joining the pyramids, seven faces are left in view.

Right? Yes, said a panel of college math professors who reviewed the question. No, said Dan Lowen, who realized that if the triangular faces of the pyramids are placed together, something else happens as well. Four other triangles--two on each pyramid--form two planes, thereby reducing the number of exposed faces by still two more. So the new solid has only five faces in all. After making models of their own, the math experts confessed that Lowen was right. Admitted University of Georgia's Jeremy Kilpatrick: "Our faces are red." Testing Service Vice President Arthur Kroll added, "We thought it was a test of logic and reasoning, but it turned out to be a problem in solid geometry." Because it was so easily misinterpreted, he says, "the question should not have been there at all."

The testing service acknowledges that a few slips have occurred in the exams before--"maybe half a dozen times in the past decade," says Kroll. What brought the latest error to light was a new policy, encouraged by truth-in-testing laws, of disclosing test answers to students.

Despite his triumph, Lowen has no plans at the moment to use his victory to advance a career in mathematics or the sciences. Says he: "Math is all right. But I prefer literature." qed

This file is automatically generated by a robot program, so viewer discretion is required.