Motivated by the question, "What exactly about a mathematical concept should students discover, when they study it via discovery learning?", I present and demonstrate an interpretation of discovery pedagogy that attempts to address its criticism. My approach hinges on decoupling the solution process from its resultant product. Whereas theories of…

Discusses the use of investigations in primary mathematics through an analysis of a beginning teacher's writings about the topic. Presents ideas on how to encourage teachers to use this method of teaching. (MKR)

A personal experience is described concerning problem solving that incorporates the computer to help generate multiple examples of proposed conjectures as solutions. The positive potential of technology to allow students of mathematics to experience the process of discovering mathematics through conjecture and generalization is emphasized. (MDH)

The roles and uses of symbols in mathematical thinking are discussed. The thinking process is further subdivided into specialization, generalization, and reasoning. (MP)

Discusses "connectionism," an alternative learning model wherein meaning resides in the function of the whole state of a network, rather than being localizable in certain symbols or areas. Topics discussed include integration with other learning models; the culture of the mathematics classroom; and characteristics of alternative…

Explores the use of dialogue and dramatization to reconstruct the formation of mathematical concepts. An appendix provides the synopsis of a 6-scene play that portrays the rise of negative numbers over a period of 300 years. (MDH)