In the rod flexibility experiment, the experimenter presents a subject with an array of rods that vary in length, diameter, material and point of attachment for a weight. The subject must place two weights on two rods at a time to deduce which of the three variables -- length, diameter and point of attachment -- makes a difference in the flexibility of the rods. The subject must use formal operational concepts such as hypothesis testing and logical deduction to separate the effects of the three variables on the rod.
The pendulum weight experiment consists of multiple strings of different lengths and sinkers of different weights. The string is tied to a T-bar and the sinker hangs from the other end, so that it may swing like a pendulum. The subject must test the different string lengths and sinker weights to determine how the combination of the two variables affects the speed with which the pendulum swings. The ability to formulate a hypothesis based on interacting variables is a fundamental concept in formal operations.
In the spinning wheel experiment, the subject must hypothesize what influences the amount of time that a marble remains on a spinning wheel before flying off the edge due to the centrifugal force. The variables in this experiment are the diameter of the holes, the distance of the hole from the edge of the spinning wheel, and the material of the marble (wood or steel). The subject places two marbles in two holes on the wheel, then spins the wheel at gradually increasing speeds until one or both of the marbles rolls off the edge. The subject must infer which of the three factors makes a difference in how long the marble remains in the hole.
The card experiment consists of four cards which have letters written on one side and numbers on the other. The subject is told that the rule for the arrangement of numbers and letters is that if there is a vowel on one side of the card, there must be an even number on the other side. The subject views an array of four cards such as "E K 4 7" and must determine the minimum number of cards to flip to demonstrate the truth or falsity of the rule. The subject must have the formal operational skills of modus tollens (affirming the antecedent of "If a, then b") and modus tollens (denying the consequent or "if not b, then not a") to understand that only the E and 7 cards must be flipped.