Mathematical conjectures and theorems are most often of the form P(x) ? Q(x), meaning ?x,P(x) ? Q(x). The hidden quantifier ?x is crucial in understanding the implication as a statement with a truth value. Here P(x) and Q(x) alone are only predicates, without truth values, since they contain unquantified variables. But standard textbook…

The initial steps necessary for constructing an analogies test are described. Basic mathematics being the context, the aim of the test is to predict student performance in research statistics courses characteristic of graduate education and social science programs. Items involving analogies in a quantitative context were built, sorted into two…

We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…

Theoretical and empirical research derived from Piagetian theory is collected on the intellectual development of the elementary school child and his acquisition and utilization of conservation concepts. The articles present diversity of method and motive in the results of replication (validation studies of the description of cognitive growth) and…