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…

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)

Examines the students' understanding of mathematical structure and the relationship between problem solving and the identification of the structure in 13 word problems. Multidimensional scaling and hierarchical cluster analysis were used to assess how subjects organized word problems in their minds. (YP)

Described is a two-week summer institute with 57 Ohio teachers in grades K-12. The teachers were given experiences in problem solving to help them broaden perceptions of real problem solving. Sixteen problem-solving strategies and four illustrative problems are included, and teachers' evaluative comments are discussed. (MNS)