The purpose of this study was to investigate elementary children's conceptions that might serve as foundations for integer reasoning. Working from an abstract algebraic perspective and using an opposite-magnitudes context that is relevant to children, we analyzed the reasoning of 33 children in grades K-5. We focus our report on three prominent…

High school students (n=295) were administered variants of the student-professor problem to ascertain whether errors could be traced to implicit versus explicit relationships between the variables. Concludes that implicit variable relationship problems were harder than explicit variable relationship problems. A follow-up study to explore why is…

Characterizes the commonalities of four exemplary mathematics teachers based on data gathered from interviews, tests on content knowledge, discussions, and observations in terms of their mathematical preparation; conceptions of mathematics, roles of teachers and students, assessment, and teaching; and teaching practices. (43 references) (MKR)