This paper deals with a set of geometrical problems for mathematical problem-solving at different difficulty levels. All of these are presented as national flags and one has to investigate invariant area proportions when changing the locus of any corner of the flag. This dynamic element suggests the usage of dynamical geometry environments.…

A selection of secondary school mathematics textbooks from twelve countries on five continents was analysed to better understand the support they might be in teaching and learning mathematical problem solving. Over 5700 tasks were compared to the information provided earlier in each textbook to determine whether each task could be solved by…

By working through well-designed tasks, students can expand their thinking about mathematical ideas and their approaches to solving mathematical problems. They can come to see the value of looking at tasks from different perspectives and of using different representations. This article discusses four tasks that encourage high school students and…

Investigated here are some of the results which can be obtained using the double-sided straight edge. Seventeen possible constructions are presented with solutions or partial solutions given to most. (MP)

This article describes a problem-centered curriculum for grades 9-12, using problem sets developed by a mathematics department and designed to take the place of textbooks. The students discover mathematical concepts in the context of the problems and activities in the materials.

A problem is posed concerning the area of certain parts of a plane geometric figure. The problem was used in a student contest with 71 of 270 mathletes answering correctly. An outline of the general proof is given. (LS)

The possibility of preparing a set of word problems of a predicted level of difficulty based on six variables (for multiplication, division, recall, conversions, operations, and number of words in the problem statement) and on regression equations developed in previous work was investigated. Four problem sets were used in grades four through six,…

This monograph was developed with the intention of addressing the concerns of high school mathematics teachers in Alberta (Canada) who want to base their programs on problem solving but have questions about effective and efficient ways to do so. Considered are the most basic philosophical questions, and a framework is provided to use in solving…

The author uses Stella the Spider as the main character in a number of three-dimensional geometry problems. Eight of these problems are discussed, with solutions. (MNS)

Fifteen mathematical puzzles and problems are presented. Areas investigated include pentominoes, arithmetic, fractions, and dissections (dissecting) a shape into two pieces that can be fitted together to form a square. Answers for each puzzle and problems are included. (JN)

Motivational classroom materials that provide direct instruction on problem-solving skills are given. The activity highlights and provides opportunities for practice with two problem-solving skills, make a drawing and work backward. (MNS)

A problem-solving approach involving systematic experimentation, one of the most-used problem-solving strategies, is advocated since it is useful beyond mathematics problems. Examples of its use are given, with two problems explored and four others noted. (MNS)

The problems in this book are intended mainly for students in junior high school and junior secondary classes, but many will interest students at higher levels. Most of the problems fit quite easily into the regular curriculum, and could be used by both teachers and parents. The book has 11 chapters, all but one of which contain problems and their…