This study investigates prospective elementary and secondary school mathematics teachers' ways of reasoning about differentiability at a point and corner points while working on a mathematical modelling activity. Adopting a multiple-case study design, the participants of the study were 68 prospective elementary school mathematics teachers enrolled…

In this study, we aim to explore the extent of mathematics pre-service teachers' ability to apply their procedural understanding combined with spatial perception for drawing conceptual conclusions related to angles in a pyramid. The participants are 16 pre-service high school mathematics teachers. They have studied solid geometry during one…

This paper compares sections on functions and linear functions from two Korean textbooks and an American standards-based textbook (University of Chicago School Mathematics Project [UCSMP] Algebra) to understand differences and similarities among these textbooks through horizontal and vertical analyses. We found that these textbooks provide…

Describes the results of part of a study into mathematical problem solving in secondary schools. Concludes that positive results were achieved, in part, as a consequence of the time that was spent in problem-solving lessons which allowed students to practice reading and working with word problems and working on basic material, particularly…

Symmetry is an important mathematical concept that plays an extremely important role as a problem solving technique. Presents examples of problems from several branches of mathematics that can be solved using different types of symmetry. Discusses teachers' attitudes and beliefs regarding the use of symmetry in the solutions of these problems.…

Examines situations from the viewpoint of how a solver sees a mathematics problem situation to obtain some insights into the kinds of activities that help solvers overcome states where they get stuck. Discusses the importance of investigating problem situations and gathering information about them and the relationship between such activities and…

Describes activities that have been successfully implemented by an expert during a mathematical problem-solving course. Focuses on the identification of the qualities of these problems used to promote the development of student strategies and values that reflect mathematical practice in the classroom. Contains 17 references. (ASK)

A programed unit on triangle constructions using an information processing prescriptive model was compared to a traditional model. The experimental group scored significantly higher on a retention test. (MP)

Aims to find the influence of overcoming fixation in mathematical problem-solving towards divergent thinking in open-ended mathematics problems. Presents findings from an investigation of Japanese junior high school students. Reports that students who can overcome fixation in mathematics can contribute varied and original ideas in open-ended…

Presents an analysis of written solutions to geometry exercises in the last year of Greek Lyceum which showed relatively low performance on vector methods. Justifies pupils' false preconceptions with regard to the concept of vectors, and the strong influence of classical geometry teaching in the previous years. (Author/ASK)

Pilot studies of instructional sequences using games showed that high ability junior high school students and their teachers improved significantly in the ability to select ideas relevant to solving particular problems. (SD)

Discusses software for geometric construction, measurement, and calculation, and software for numerical calculation and symbolic analysis that allows for new approaches to the solution of geometric problems. Illustrates these computer-aided graphical, numerical, and algebraic methods of solution and discusses examples using the appropriate choice…

Describes a newly designed interdisciplinary course called 'Algebra for the Sciences'. Studies the effects of the course on students' critical thinking skills, problem-solving skills, and attitudes towards mathematics. Concludes that students had larger gains in critical thinking skills and significantly more positive attitudes towards mathematics…

This study tested the existence of a positive relationship between interest and verbal problem solving when problems are set in the area of interest assessed among secondary school students. There was no evidence to indicate that prior knowledge of interests would help to predict with which type of problem a student would be most successful.…

A calculator solution of a simple computational problem is discussed with emphasis on its ramifications for the understanding of some fundamental theorems of pure mathematics and techniques of computing. (Author/MK)