The National Council of Teachers of Mathematics calls for an increased emphasis on proof and reasoning in school mathematics curricula. Given such an emphasis, mathematics teachers must be prepared to structure curricular experiences so that students develop an appreciation for both the value of proof and for those strategies that will assist them…

An undergraduate seminar was designed to help preservice teachers focus on students' learning. Preservice teachers planned and conducted weekly tutoring sessions with fourth graders and discussed their experiences in weekly discussions. The author investigated what preservice teachers learned about teaching mathematics from their focus on…

This paper describes the author's attempt to design assignments that engage preservice elementary teachers in original mathematical thinking. In particular, the choice of integer operations as the focus of a structured writing assignment that takes students two weeks to complete is explained and justified. Exemplary student work is quoted.…

Discusses figurate number learning activities using patterns and manipulative models. Provides examples of square numbers, triangular numbers, pentagonal numbers, hexagonal numbers, and oblong numbers. (YP)

Provides a discussion and an example of a problem which occurs in mathematical contests or entrance examinations and deals with the question of the magnitude of exponentials. Includes additional illustrative examples. (RT)

This paper describes a proportional reasoning problem set within a real-life context and a complete analysis of one small group discussion of this problem over the course of a 90-minute block. The seventh-grade students' discourse is described to provide insights into typical mathematical interpretations of this problem, as well as some…