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…

This study compared one lesson across four U.S. "traditional" textbook series, two U.S. reform-based textbook series, and one Chinese mathematics textbook series in teaching the connection between multiplication and division. The results showed the differences across U.S. and Chinese lessons in both the teaching and the practice parts of…

A central goal of secondary mathematics is for students to learn to use powerful algebraic strategies appropriately. Research has demonstrated student difficulties in the transition to using such strategies. We examined strategies used by several thousand 8th-, 9th-, and 10th-grade students in five different school systems over three consecutive…

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.…

A game modelled on football can be used to provide students with practice in solving algebraic equations. (SD)

The history of alligation problems as a part of the mathematics curriculum is briefly reviewed, and the non-unique nature of the solutions to many problems is discussed. (SD)

Examples of the presentation and solution of variations on a common projectile trajectory problem are presented. (BB)

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)

Six mathematics problems are posed; details are given of the solutions for six other problems. (DT)

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…

Analyzed are textbook word problems that are typically used as applications of mathematics and shows some of the difficulties in making these problems realistic. A discussion and examples of sources of genuine mathematical applications in real life follows. (MN)

Suggested is the presentation of problems for which student teams are to write computer programs which will reveal the results of guesses at the answer by users of the program. Illustrative problems and programs are included. (MNS)

To help mathematics teachers introduce and reinforce concepts and processes by using relevant problems, several such problems are presented and discussed. (MNS)