Understanding frames of reference is critical in describing planetary motion and learning astronomy. Historically, the geocentric and heliocentric models were defended and advocated against each other. Today, there are still many people who do not understand the relationship between the two models. This topic is not adequately treated in astronomy…

This article reports on models of teaching that developed as outgrowths of a study of middle-grades mathematics classes. Three specific cases are highlighted that represent deductive (associated with univocal), inductive (associated with dialogic), and mixed (a hybrid of deductive and inductive) models of teaching. Teaching practices associated…