In this paper we explore first-year students' difficulties with the use and interpretation of definitions of mathematical objects as they attempt proof construction exercises in the area of elementary set theory. The participants are students at a historically disadvantaged university in South Africa. In this study the activities and utterances of…

A facility with signed numbers forms the basis for effective problem solving throughout developmental mathematics. Most developmental mathematics textbooks explain signed number operations using absolute value, a method that involves considering the problem in several cases (same sign, opposite sign), and in the case of subtraction, rewriting the…

The aim of this study is to explain students' ability to transfer their knowledge about mathematical series to the problems that they encounter. The data of the study were obtained by using two different tests, namely "Problem Solving Test (PST)" and "Series Character Identification Test (SCT)" which were developed by the…

Solving problems in different ways is strongly advised for mathematics learning and teaching. There is, however, little data available on the examination of teachers' openness to and evaluation of different solutions to the problems. In this paper, the author examines classroom teachers' openness to different solutions (or to what extent they…

This article deals with a brief history of Fibonacci's life and career. It includes Fibonacci's major mathematical discoveries to establish that he was undoubtedly one of the most brilliant mathematicians of the Medieval Period. Special attention is given to the Fibonacci numbers, the golden number and the Lucas numbers and their fundamental…

In its mathematics standards, National Council of Teachers of Mathematics (NCTM) states that problem solving is an integral part of all mathematics learning and exposure to problem solving strategies should be embedded across the curriculum. Furthermore, by high school, students should be able to use, decide and invent a wide range of strategies.…

Four different types of problems from graph theory are presented and discussed. (MK)

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)

As part of the Mathematical Problem Solving Project, MPSP, the goals and purposes of miniprojects are explored. Various conjectures are presented which are based partially upon observation of children working on projects and partially upon the opinions of mathematicians who have observed how problem-solving processes are used in real-world…

Presented are eight student worksheets of block problems. Included are diagrams of the squares and hollow squares involved and a separate answer sheet for the problems. (CW)

An elementary knowledge of geometry is shown to be helpful in problem solving, especially in that the shortest distance between two points is a straight line. (MN)

The author gives a variety of literary questions and exercises that can be used to develop and test students' interpretation of the mean, median, and mode and their understanding of the usefulness and limitations of each. (MN)

An elective course aimed at giving tenth-grade students some experience with practical arithmetic problems is outlined. The two-week course is designed primarily for students who will be leaving at the end of the year and includes topics such as calculators; earning, spending, and saving money; tax; and buying a car. (MN)

Utilizes the problem of determining the number of different ice cream cones and cups that can be made from a choice of 31 flavors to investigate the concepts of combinations and permutations. Provides a set of six related problems with their answers. (MDH)

Various methods for solving the problem of finding when the hour and minute hand of a watch have the same direction are explored. The relationship of these problems to the educational environment and the maturity of the student are discussed. (CW)