The development of quantitative-relational abilities from childhood to adolescence: Structure, scaling, and individual differences

Abstract

The present article discusses the nature of the quantitative-relational system, which involves the basic arithmetic operations, proportional reasoning, algebraic ability, and the integration of these three abilities. Representative sets of tasks that assess each of these abilities were administered to 372 Greek subjects aged 9 to 16 to test hypotheses about (a) the structure and (b) the development of this cognitive system, and (c) about the role of individual differences variables, such as subjects' gender and SES. (a) Structural equations modelling revealed three specific ability factors (execution of arithmetic operations, proportional, and algebraic reasoning) and a higher-order general factor that loaded all specific factors. The higher-order factor may be abolished once the relations between the first order factors are specified. (b) Recently developed techniques (discrimination and rating scale analysis) basically confirmed the developmental levels initially assigned to most of the tasks. More importantly, the tasks pertaining to the different partial abilities could be ordered along a single developmental dimension with items from different abilities intertwined. This intertwining suggested that each ability's development precipitates and is precipitated by the development of the other abilities. (c) The structure of abilities was found not to be affected by individual differences factors. (d) Using the unified developmental scale as a frame of reference, gender and SES differences were found at age points associated with major developmental changes. Implications of these findings for theories of cognitive development and education are discussed within the framework of experiential structuralism.