This article, written in French, describes part of the research conducted in a French research institute concerning plane Euclidean geometry. Fifty secondary school students were given a problem concerning points of intersection of a rectangle and two circles. Typical trains of thought during problem solutions are discussed. (MNS)

Presents evidence that there exists much confusion regarding the connection between the algebraic and geometric aspects of slope, scale, and angle. Participants responded to a simple but non-standard task concerning the behavior of slope under a non-homogeneous change of scale. Analysis of the responses reveals two main approaches termed…

The relationship of performance in mathematics to syntactical language factors obtained from speech samples was investigated with 95 senior high school geometry students. Statistical procedures included correlation analysis and stepwise regression. The findings indicated that certain syntactical measures indicating logical thought processes…

The research reported in this paper was designed to analyze the incidence of use of higher-order rules by students solving geometric construction problems. A carefully selected set of construction problems was subjected to rigorous a priori analysis by mathematics educators to determine what basic and second-order rules might be used by able high…

This study was undertaken as an effort to inform secondary school planners relative to the effects of the long block-of-time class period for fewer days on the achievement, retention and attitudes of pupils. The study was limited to six class groups enrolled for Biology I and six class groups enrolled for Plane and Solid Geometry at Cape…

Investigates the effects of inquiry activities on a dynamic geometry environment designed to confront students with contradictions and uncertainties. Characterizes epistemological, didactic, and cognitive aspects of the activities. Analyzes the interplay among these three aspects, students' investigations, and their explanations. (Author/KHR)

In this study with 132 secondary school geometry students, three significant aptitude by treatment interactions were found. Students with high reasoning scores and those with high processing scores profited more from the transformational treatment on point and line symmetry. (MP)

This research involved the observation and audio-recording of 30 ninth-grade mathematics students recommended as being outstanding by their mathematics teachers. Each student was presented with five different problem situations for which he or she was to make mathematical conjectures. During the interview, the students thought aloud and all of…

This study examined the effects of inquiry training on students' ability to think analytically and the relationships of that ability with achievement in geometry and algebra. Results indicated that inquiry-trained students were not more analytical in approaching mathematics than others. (SD)

An approach to teaching geometry is promoted that allows students to decide for themselves what they could prove from given information. Such an approach allows pupil involvement in the personal process of discovering mathematical ideas and formulating problems. It is noted these methods will not work for all. (MP)

Five geometry experiments with 127 Australian high school students found that guidance provided in a format requiring attention to two sources of information resulted in performance no better than that on conventional problems. A format not requiring split attention resulted in the superiority of worked examples over conventional problems. (SLD)

A study was conducted in Israel to determine effects of external similarity in problem structure on students' responses. Fifty students from each of the 7th, 8th, 10th, and 12th grade levels were presented with three problems involving successive divisions that were similar in structure. The problems asked separately whether the processes of…

The ability of tenth grade plane geometry students to structure concepts and relationships from a geometry unit on ratio, proportion and similarity was tested. Analysis of cognitive "maps" of the structural relationships possessed by twenty concrete and twenty formal subjects indicated that formal operational subjects structure subject…

This paper presents learning tasks of a new type that are made possible by dynamic geometry software and discusses reasons why it takes time for teachers to design and use such tasks. The paper is divided into four sections: (1) The Spatial and the Theoretical; (2) Tasks in Dynamic Geometry Software Fostering the Learning of Geometry; (3) The…

The study investigated whether (1) instruction providing for experimental manipulation by students was superior to instruction in which teachers perform the manipulations and children observe, and (2) spatial ability was related to mode of instruction. Participating in the 8-week study were 141 students aged 12-15 in seven intact eighth-grade…