This is the first of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. My explanation starts with the formation of arithmetical units, which presage…

This submission contains the Proceedings of the 2007 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the University of New Brunswick in Fredricton, New Brunswick. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning.…

Shares the results of a study in which 204 first grade students were interviewed. Interprets the findings in light of Piaget's emphasis on abstraction. Concludes that children represent ideas at their respective levels of abstraction. (Author/ASK)

Utilizes a psychological-constructivist perspective to examine the transitions that students make from arithmetic to algebra in the context of problems that, from an expert's perspective, involve the concept of linear inequality. Reports that students who completed a transition to algebra operated at higher levels of reflective abstraction than…

Discussed are preservice elementary teachers' misconceptions and inconsistent beliefs about multiplication and division with decimals. Sources of inconsistencies and recommendations for overcoming inconsistencies are included. (KR)

Problems were presented to 13 university students in which letters were to be added or subtracted (e.g., B + D = ? or F - ? = D). After each problem, each subject gave a retrospective protocol indicating the way in which the problem was solved. Models of performance by each subject in each experimental session shared major properties; choices by…

This study contributes to a growing body of research on the development of elementary teacher's content knowledge of mathematics. Individual clinical interviews were conducted with preservice elementary teachers (N=21) enrolled in a professional development course called "Foundations of Mathematics for Teachers." An instrument that…