A test was given to 322 secondary students to develop a profile of mathematical ability based on four components: computation, pattern recognition, logical reasoning, and symbolic manipulation. These profiles were compared to mathematics test scores; the results verified hypotheses about individual differences in mental processes and knowledge…

This study examined the development of the rational number concept as a ratio. Preliminary to the description of the study is an introduction discussing constructivism and equilibration. The study itself tests whether equilibration theory holds, and if so, what is the nature of its "phases" and whether these are found at each of the "periods" of…