boy who is too young to attend secondary school but could solve the problem through the application of fluid ability: "He may reason that if half the two-legged people are without shoes, and all the rest (an even number) are one-legged, then the shoes must average one per person, and the answer is 100." Relationship to Piaget's theory of cognitive development Researchers have linked the theory of fluid and crystallized abilities to Piaget's theory of cognitive development. Fluid ability and Piaget's operative intelligence both concern logical thinking and the "eduction of relations" (an expression Cattell used to refer to the inferring of relationships). Crystallized ability and Piaget's treatment of everyday learning reflects the impress of experience. Like fluid ability's relation to crystallized intelligence, Piaget's operativity is considered to be prior to, and ultimately provides the foundation for, everyday learning. Measurement of fluid intelligence Various measures have been thought to assess fluid intelligence. Raven's Progressive Matrices The Raven's Progressive Matrices (RPM) is one of the most commonly used measures of fluid ability. It is a non-verbal multiple-choice test. Participants have to complete a series of drawings by identifying relevant features based on the spatial organization of an array of objects and choosing one object that matches one or more of the identified features. This task assesses the ability to consider one or more relationships between mental representations or relational reasoning. Propositional analogies and semantic decision tasks are also used to assess relational reasoning. Woodcock–Johnson Tests of Cognitive Abilities, Third Edition In the Woodcock–Johnson Tests of Cognitive Abilities, Third Edition (WJ-III), gf is assessed by two tests: Concept Formation and Analysis Synthesis. Concept Formation tasks require the individual to use categorical thinking; Analysis Synthesis tasks require general sequential reasoning. Concept Formation Individuals have to apply concepts by inferring the underlying "rules" for solving visual puzzles that are presented with increasing levels of difficulty. As the level of difficulty increases, individuals have to identify a key difference (or the "rule") for solving puzzles involving one-to-one comparisons. For more difficult items, individuals need to understand the concept of "and" (e.g., a solution must have some of this and some of that) and the concept of "or" (e.g., to be inside a box, the item must be either this or that). The most difficult items require fluid transformations and cognitive shifting between the various types of concept puzzles that the examinee had worked with previously.