A range of estimation techniques are described, and a series of mental computation procedures based on concepts of measurement and real numbers are presented in detail. (MP)

Presents a framework for assessing probabilistic thinking based on validated data obtained from eight third grade children who served as case studies. Major constructs were sample space, probability of an event, probability comparisons, and conditional probability. Levels of thinking appear to agree with the levels of cognitive functioning…

Presents to second graders the concept of an n-gon, characterized by a commutative diagram which is composed of four ways of judging a given figure. Observes that some children gave persuading arguments containing a critical idea and the concept formation corresponding to a structure-preserved transformation in the diagram. (AIM)