We investigated unjustified assumptions made by students when proving geometric statements. Geometric statements can be presented with a diagram or without. Diagrams can be accurate or sketchy. Unjustified assumptions may originate in an accompanying diagram. We thus asked whether the way in which a statement is presented has an effect on…

This paper uses two terms, "algorithmic mathematics" and "dialectic mathematics," and attempts to synthesize the two aspects from a pedagogical viewpoint with illustrative examples gleaned from mathematical developments in Eastern and Western cultures throughout history. Some examples from teaching experiences in the classroom…

This book helps teachers define good questions, offers tips on how to create their own good questions, and includes a wide variety of questions for use in the classroom. Each chapter of the book is organized by subject area and age group so that teachers can locate the topic their class is working on, then select probing, thought-provoking…

Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to do mathematical problems and to think about mathematical relationships. In this presentation, the discontinuities that occur in the learning path taken by different students, leading to a divergence between conceptual and…

In this paper, we explore the role of polygonal shapes as geometrical models in teaching mathematics, so as to elicit and interpret children's geometric conceptions and understanding about shapes. Primary pupils were asked to draw a stairway of figures (triangles, squares and rectangles) each one bigger than the preceding one. Pupils use two…

This report contains conference papers on geometry teaching. There were five plenary talks given and a review of Hungarian geometry teaching. The plenary talks addressed background theories of the psychology of learning such as constructivism, perceptional psychology, and motivational psychology. The themes of the 21 short talks were on a varied…

This book presents motivational ways to teach key concepts and topics common to all secondary mathematics curricula. It is arranged by subject matter which includes algebra, geometry, trigonometry, probability, statistics, and miscellaneous topics. The objective to be attained by implementing the unit on each of these subjects is stated, and the…

This paper examines the differences between student performance on two separate measures, the Spatial Visualization portion of the "Differential Aptitude Test" and the "Geometry Content Knowledge Test." Results from the hybrid quantitative/qualitative study indicate that although there were no differences in performance on spatial visualization…

This book contains a set of versatile enrichment exercises that cover a very broad range of mathematical topics and applications in pre-algebra from the Moebius strip to the googol. Several criteria have been used in developing the activities and selecting the topics that are included. All of them bear heavily and equally on concerns for…

Reports discriminate analyses using data from several National Longitudinal Study of Mathematical Abilities (NLSMA) measures for two groups from the NLSMA Y-population, high and low geometry achievers. The analysis correctly classified from 75 percent to 95 percent of the groups, depending on the measure used. (JP)

A college course using science fiction literature as a springboard into the study of geometries is described. (DT)

Fundamental concepts of symmetry and rigid motion are developed through activities using polygonal shapes made up of six congruent equilateral triangles. (DT)