A familiar Christmas song described as a second-year algebra problem is presented in "The Twelve Days of Christmas". Five strategies for solving inequalities are discussed in "Solving Algebraic Inequalities". (JT)

Develops a division algorithm in terms of familiar manipulations of concrete objects and presents it with a series of questions for diagnosis of students' understanding of the algorithm in terms of the concrete model utilized. Also offers general guidelines for using concrete illustrations to explain algorithms and other mathematical principles.…

termined that students who completed writing assignments on mathematics problems were better problem solvers than students in control groups, supporting the contention that expository writing is an effective, practical, and innovative tool for problem solving. (Sample problems and writing assignments are included.) (DH)

The meaning of problem solving and investigations, what investigations are intended to achieve, the teacher's role, and how to introduce investigations in the curriculum are discussed. (MNS)

Results of 120 studies were combined by meta-analysis to determine effects on mathematics test performance of factors other than knowledge of content. Conditions that enhanced performance included testwiseness training, praise, word problem pictures, and frequent testing. Conditions depressing or not affecting performance were also noted. (MNS)

A slight rewording can often transform a routine exercise into a nonroutine one. Three problems (with solutions) from first-year college calculus are presented to illustrate how the technique can be used and how it is applicable to any course. (JN)

The mental activities involving functions were studied with 60 children aged 4-15. Search strategies used for solving a problem reveal different stages toward the discovery of the monotonic property, which correspond to stages of proportional reasoning found by Piaget. Dependence between stage and age is confirmed. (Author/MNS)

One mathematician's view of real problems is given. Described (with some humor) are magic retail numbers, the highway bypass, the elliptical table, and the senior-class schedule. (MNS)

A one-semester course at the third-year level at York University is described. It tries to legitimize in students' eyes that it makes sense to talk about mathematics as well as do mathematics. Seven course themes are discussed, followed by nine problems used in the course. (MNS)

Presents a problem-solving activity in which students first guess and then check their answer. Also presents an activity to help students develop skill in understanding the question in a problem and a suggestion to help develop a classroom climate conducive to problem-solving. (JN)

A way to schedule tournament tennis matches so time-use is improved is presented. The mathematical application of a linear function is described in some detail. (MNS)

Discusses the nature of and the steps involved in a mathematical investigation, suggesting that a mathematical investigation can be used as a tool for developing mathematical processes in learners. Several examples of investigations suitable for secondary levels are included. (JN)

Describes three studies in which students (N=515; N=60; N=135) were asked to indicate appropriate operations and numbers used in solving open mathematical sentences. Analysis of data and interviews suggest two error patterns: "finding a solution" and "inverse operation." Indicates that "finding a solution" strategy…

Math Mountain is a special section on the Comprehensive School Mathematics Program (CSMP) web site just for kids. It features challenging problems for primary and intermediate grade students. This booklet contains problems featured in Math Mountain over the past year and can be used as a source of additional problems to challenge students or to…

Most mathematical ideas can be taught with simplicity. It may be necessary to give up the phrase "mathematics education" and replace it with "basic quantitative literacy." (Author)