"The purpose of the study is to determine if there is a difference between students who study certain topics from plane geometry using a geoboard and those who study the same topics in the conventional classroom. A three part criterion test will be used as the evaluative instrument"--Introduction. / Typescript. / "December, 1971." / "Submitted to the Department of Mathematics Education in partial fulfillment of the requirements for the degree of Doctor of Philosophy." / Advisor: E. D. Nichols, Professor Directing Dissertation. / Includes bibliographical references.

The purpose of this study was to develop a course of study on Plane Geometry for the 8th grade, based upon the Instructional Systems Analysis technique. The systems model used was that developed by Bartel.The entire study involved identifying, selecting, and sequencing learning tasks. An elaborate review of resource materials on Plane Geometry yielded one hundred and fifty-five related tasks.The instrument developed to gather pertinent data had two parts to it. Part one contained seventeen items relating to the personal profile of the respondent. Part two consisted of the one hundred and fifty-five identified, verified, and correctly stated manipulative tasks. The tasks were grouped into two broad divisions. Each respondent rated each task on a 3-point scale according to the level of instructional importance he/she judged the task(s) should receive. A rating of 3 represented the highest level of importance; 2, average; and 1, least.The survey utilized the services of sixty-eight Nigerians currently on the Technical Teachers Training Program (TTTP) in the U.S. Information regarding the institutions and population of Nigerians on the program was obtained from the Training and Development Program (TDP) office in Washington, D.C. From the list of thirty-two possible institutions, twelve institutions met the criterion for participation.A Five-Interval Sampling Technique (FIST) was used to select subjects from the participating institutions. This gave the researcher a possible seventy subjects. Each subject's participation was purely voluntary. Thus the 73.6 percent return was considered satisfactory.The interpretation of data involved two analyses. Analysis one dealt with biographical information on each participant. The second analysis computed the summary of task ratings on the one hundred and fifty-five instrument items.Selection of tasks for inclusion in the course of study reported in this study was based on the judgments of the subjects. Higher mean values were used as the basis for selection. Overall, thirty top tasks were selected and sequenced for the purpose of the course of study under investigation.

A thesis submitted in fulfilment of the requirements for the degree of DOCTOR OF PIIILOSOPHY in the SCHOOL OF SCiENCE EDUCATION (MATHEMATICS) UNIVERSITY OF THE WITWATERSRAND / Cognitive gender differences in mathematics, which were noted in past research have latterly been found to be declining. but are still observed at secondary school level in the field of spatial skills and geometry. However, due to divergent geometry curricula and the multidimensional nature of spatial skills, results from gender studies have led to broad conclusions being drawn from investigations which were affected by random elements. Research results have been influenced by imbalanced representation of the two gender groups in samples and also by differential gender exposure to previous mathematical experience. Both these limitations in research have produced outcomes reflecting negatively On females. Internationally divergent geometry curricula are a result of the traditional synthetic approach to the teaching of Euclidean geometry falling Into disfavour in western countries. Thus, Euclidean geometry has been largely overlooked in current educational research and the cognitive processes such as deductive reasoning, proof writing and hypothesis testing, have received scant attention within geometry teaching over the past decade. The standardized system in most South African secondary schools coupled with a uniform core curriculum for mathematics lends itself to an advantageous environment for empirical studies in mathematics performance. The present gender investigation involved almost an equal number of males and females from 5' selected secondary schools near Johannesburg in South Africa. Performance in Euclidean geometry was evaluated for possible gender differences by means of multiple choice and open ended questions. In keeping with most existing research, mean differences were compared. No statistically significant gender difference in mean performance on Euclidean geometry was found. Further analysis at item level was undertaken for the multiple choice component of the test instrument by means of the one dimensional three parameter logistic model in Item Response Theory, This model, is considered to be very sensitive in identifying differences at different ability levels -a shortcoming in existing research. Four out of a total of twenty Euclidean geometry items, were identified as producing differential gender performance. Similar gender tendencies were observed for all four items. The performance was in favour of most males for each of these items. Females of lower ability (as measured by the item) did not perform as well as males of similar ability level. In all four Cases females of higher ability surpassed males of a corresponding ability level. Perceptual difficulties in females were more pronounced than in males for some of the items. / AC 2018

No abstract. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2011.

University of Macau / Faculty of Education