Various researchers have associated meaningful problem solving with methods guided directly by a conceptual knowledge base. By contast, a meaningless solving course, or sequence of operations, is essentially independent of the solver's conceptual understanding of the problem under consideration. This paper is the first to document a meaningless,…

Reform efforts in mathematics aim to increase conceptual understanding, an aim that can be supported through concept maps. This study compared the conceptual knowledge of function held by college students in reform and traditional calculus sections at a large state university. Fourteen students from reform sections and 14 from traditional sections…

Presents four questions to consider when supervising elementary mathematics teachers, who come with many preconceptions about teaching and learning mathematics: What mathematical concepts, procedures, or algorithms are you teaching? Are the concepts and procedures part of a unit? What types of questions do you pose? and What understanding of…