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The purpose of this investigation was to evaluate the effects on achievement in and attitude towards mathematics of teaching certain elementary-logic concepts to high school mathematics students. To achieve this purpose, four classes of tenth-grade geometry students were selected from a single school of the Vancouver School District. Two of the classes served as the experimental group for this investigation. Both the experimental and control groups were taught by the investigator. The program for the experimental group involved a one-week introduction to elementary logic concepts followed by a two week study of "Similarity" concepts. The control group's program involved only the two-week study of the "Similarity" concepts. The students were evaluated at the beginning and end of the treatment period and again three weeks later. Most of the instruments administered were developed by the investigator and consequently not standardized. The mean test scores obtained were statistically analyzed for significance of differences using t-statistics. The null hypothesis was tested at the five percent level of confidence. Analysis of the data collected showed that the null hypothesis is accepted at the high, medium, and low ability levels. The acceptance of the null hypothesis implied that the teaching of logic concepts to tenth-grade geometry students had no significant effects on achievement in mathematics or attitude towards mathematics. / Education, Faculty of / Graduate

This study was an attempt to determine the effect of the use of models in learning the volume and total surface area of various polyhedra. It was hypothesized that the classes who were allowed, to construct models of various space figures would achieve significantly better results on a test of the work covered than would those classes who were taught the same material by sketches and notes on the chalkboard. It was further hypothesized that the classes which had utilized the models would score significantly higher on a retest which was held approximately two weeks after the initial test. Five teachers and eight classes were involved in the study. Two teachers taught a control group and an experimental group of grade seven students while a third teacher had a control group and an experimental group of grade six students. The fourth teacher taught one control group of grade seven students and the fifth teacher taught one experimental group of grade seven students. Mental age, previous mathematical achievement (teachers' Easter grades) and scores on the geometry unit test and retest were recorded for ninety-four control group students and ninety-seven experimental group students. Any student who had not attended eighty percent of the teaching periods or for whom no mental age or previous mathematical achievement was available were not included for purposes of this study. The geometry unit, which was, of two weeks duration, was followed by a multiple-choice test of twenty-five items and a retest two weeks later. The usual correction factor was applied to offset the effect of guessing by the examinees. A covariate analysis was then done in which the two independent variables, previous mathematical achievement and mental age were partialled out and the adjusted means for the test and retest were recorded. The results Indicated that there was no significant difference in the mean scores obtained by the two groups on the initial test - 14.647 for the control group and 14.6822 for the experimental - but that there was a significant difference in the mean scores obtained by the two groups on the retest held two weeks later. The mean score of the experimental group was 14.4124 as compared to 13.9255 for the control group. Although this difference was significant at the .005 level it was recognized that, for all practical purposes, a difference of half a point in a total of twenty-five items must be considered unimportant for the practising teacher. A superficial examination of the data indicated two questions that might be answered by further related study: (1) Would a longer period between the test and the retest show a greater difference in the mean scores, of the two groups? and (2) Would the use of models be of greater benefit to a particular age group or i to a homogeneous group of high or low achievers? The results obtained by this and other related studies seems to militate against any definitive conclusions as to the merit of using models in the teaching of mathematics as a whole. It appears that if any significant ,benefit is to be derived from their use it will be in particular subject areas that will be determined only through carefully designed research. / Education, Faculty of / Graduate

The purpose of this investigation was to evaluate the effect of two modes of exposition of tenth-grade incidence geometry on logically evaluated problem solving ability. To achieve this purpose two classes of tenth-grade geometry students were chosen to be the experimental and control groups. The two treatments, which were of nine class hours duration per group, and were both taught by the investigator, involved the use of a set theoretic symbolic-nonrepresentational mode for the experimental group, and a pictorial-representational mode for the control group. The content of the treatments was Euclidean incidence geometry. At the termination of the treatment a criterion test was administered to both groups. The criterion test was composed of two types of problems- Type NR problems, which were believed to be most successfully solved by a symbolic-nonpictorial analysis, and Type R problems, which were believed to be most successfully solved by a pictorial analysis. Two hypotheses, of null form, were considered: that the mean scores of both groups on Type NR problems would be equal and that the mean scores of both groups on Type R problems would be equal. Both hypotheses were tested by means of an appropriate t-statistic at the .05 level of significance. Analysis of the data indicated that both null hypotheses were not to be rejected. A difference in means on Test NR of the control over experimental group was observed at the .20 level of significance. The implication of the analysis of the data and the restrictions imposed by the limitations of the study is that the pictorial-representational exposition was as effective as the experimental symbolic-nonrepresentational exposition for Type NR problems and for Type R problems. Since the pictorial-representational mode of exposition is generally considered standard practice in the teaching of tenth grade geometry it should be continued for the present. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate

The purpose of this investigation was to describe tenth grade students' views of the purposes of geometric proof within the context of their learning. Classroom observations, the curriculum, assessment tools, journal questions, and a preconceptions questionnaire were used to provide context for the views expressed by students from a single classroom. Eleven classroom episodes selected from the classroom observations were used to describe the instructional context as well as discourse among the students during group work. The episodes provided details about how and when the classroom teacher addressed various purposes of proofs involving geometry concepts throughout two instructional units on coordinate geometry proofs and two-column proofs. The episodes also consisted of student discourse relating to the purposes of geometric proof as students worked on assigned proof problems. The students' views were examined through journal questions given at the beginning of selected days and through a post-instruction questionnaire and individual interviews. There were three main findings of the study. First, several students experienced difficulty in expressing their views of the purposes of geometric proof when asked directly. One-third of the students could only list properties or theorems they encountered during the unit on geometric proof. However, when these students were asked to describe the purpose for each column, all of the students listed both explanation and verification. Second, the students expressed limited views of the purposes of proof, referring mainly to verification. Only a few students mentioned explanation, systematization, and communication. However, students generally referred to at least two purposes of proof (explanation, verification, and communication) when describing the proving process involved in coordinate geometry. Third, the students' views of various purposes of geometric proof were diverse. Recommendations for future research include the examination of students' views of the purposes of geometric proofs for students who use paragraph form and studies to investigate the development of students' views of the purposes of proof as they gain more experience with formal proof writing and other methods of proof. / Graduation date: 2004

There is no abstract available for this thesis.

There is no abstract available for this thesis.

This dissertation is intented to explore the similarities and differences of pedagogical characteristics in geometry though analyzing the contents of the junior Secondary school (grade 7-9) mathematics textbooks of England, Hong Kong and Taipei. By studying the topic of “Relationships for angles at a point, angles on a line, vertically opposite angles, angles associated with a transversal cutting parallel lines and perpendicularity” of the textbooks, the textbooks of the three places have demonstrated how they organize the contents to achieve the various aims with different means and different emphasis. For English textbooks, their contents are characterized by using geometric intuition for verifying the properties of geometric objects and the theorems. On the contrary, for Taipei textbook, their contents are characterized by the extensive use of deductive reasoning and proof for verifying the properties of geometric objects and the theorems. Lastly, for Hong Kong textbooks, their contents are characterized by encouraging conjecturing through various explorative activities. For developing students’ cognitive thinking in geometry, the progress of developing students’ level of sophistication in deductive reasoning is depended upon their age for England while Hong Kong and Taipei do not. Process of visualization is commonly used in the three countries for enhancing the reasoning process and various apprehensions of geometric objects. On the other hand, Hong Kong and Taipei textbooks tend to apply more on the process of reasoning in the teaching activities while English textbooks apply more on the process of construction. / published_or_final_version / Education / Master / Master of Education

The teaching of geometry has been neglected at the expense of other disciplines of mathematics such as algebra in most secondary schools for Africans in South Africa. The research aimed at establishing the extent to which creativity and divergent thinking enhance the internalisation of geometry concepts using the problem-based approach and on encouraging learners to be creative, divergent thinkers and problem solvers. In the research, Grade 7 learners were guided to discover the meaning of geometric concepts by themselves (self-discovery) and to see concepts in a new and meaningful way for them. This is the situation when learners think like the mathematicians do and re-invent mathematics by going through the process of arriving at the product and not merely learn the product (axioms and theorems), for example, discover properties of two- and three-dimensional shapes by themselves. Furthermore, learners were required to use metaphors and analogies, write poems, essays and posters; compose songs; construct musical instruments and use creative correlations in geometry by using geometric shapes and concepts. They tessellated and coloured polygons and pentominoes in various patterns to produce works of art. Divergent thinking in geometrical problem solving was evidenced by learners using cognitive processes such as, amongst others, conjecturing, experimenting, comparing, applying and critical thinking. The research was of a qualitative and a quantitative nature. The problem-based approach was used in teaching episodes. The following conclusions and recommendations were arrived at: * Geometric shapes in the learner's environment had not been used as a basis for earning formal geometry. * Second language learners of mathematics have a problem expressing themselves in English and should thus be given the opportunity to verbalize their perceptions in vernacular. * Learners should be made to re-invent geometry and develop their own heuristics/strategies to problem solving. * Learners should be trained to be creative by, for example, composing songs using geometric concepts and use geometric shapes to produce works of art, and * Activities of creativity and divergent thinking should be used in the teaching and learning of geometry. These activities enhance the internalisation of geometry concepts. Groupwork should be used during such activities. / Educational Studies / D. Ed. (Didactics)

NAVORSINGSVERSLAG voorgele ter gedeeltelike vervuiling van die vereiste vir die graad MAGISTER IN NATUURWETENSKAPPE in die FAKULTEIT NATUURWETENSKAPPE aan die UNIVERSITEIT VAN DIE WITWATERSRAND. / There is widespread concern over some of the problems encountered in the teaching of Euclidean Geometry in secondary schools and also over the fairly negative attitudes experienced by pupils towards Geometry. This piece of research was designed to improve attitudes of Std.9 pupils towards Euclidean Geometry by making use of guided discovery and the integration of the history of Mathematics into the teaching method used. The latter was done in order to humanise the subject and to make it more interesting to pupils who otherwise experience it as very rigid and abstract. Active participation of pupils in developing the Geometry was central to the method employed. The outcome of the research was positive. It showed that attitudes towards Geometry can be improved if a deliberate attempt to do so is made. The results of this research suggest guidelines by which the teaching of Euclidean Geometry in secondary schools could be improved. / AC 2018