Recent literature on mathematics education, and more especially on the teaching and learning of geometry, indicates a need for further investigations into the possibility of devising new strategies, or even developing present methods, in order to avert what might seem to be a "problem" in mathematics education. Most educators and textbooks, it would seem, do not address the need (function and meaning) of proof at all, or those that do, only address it from the limited perspective that the only function of proof is verification. The theoretical part of this study, therefore, analyzed the various functions of proof, in order to identify possible alternate ways of presenting proof meaningfully to pupils. This work further attempted to build on existing research and tested these ideas in a teaching environment. This was done in order to evaluate the feasibility of introducing "proof" as a means of explanation rather than only verification, within the context of dynamic geometry. Pupils, who had not been exposed to proof as yet, were interviewed and their responses were analyzed. The research focused on a few aspects. It attempted to determine whether pupils were convinced about explored geometric statements and their level of conviction. It also attempted to establish whether pupils exhibited an independent desire for why the result, they obtained, is true and if they did, could they construct an explanation, albeit a guided one, on their own. Several useful implications have evolved from this work and may be able to influence, both the teaching and learning, of geometry in school. Perhaps the suggestions may be useful to pre-service and in-service educators. / Thesis (M.Ed.)-University of Durban-Westville, 1998.

This qualitative naturalistic research study investigated peer interaction and its relationship to the learning of Logo geometry concepts within an elementary school computer lab classroom environment. The work of four focal children (10-11 years old) and their partners was analyzed. The study looked at (1) the kind of working relationships which existed between the partners, (2) the verbal strategies used by the partners during their mathematics disagreement, and (3) the ways in which the talk between the partners and the strategies they used both contributed to their learning, and reflected their learning, of the geometry concepts (with an emphasis upon the aspect of angular rotation). / The findings revealed that all but one of the dyadic (and triadic) partnerships were collaborative and symmetrical: the children took turns giving information and explanation. At times the information was incorrect. The number of explanations given was very small. A range of peer teaching skills was in evidence. There was no correspondence found between the rate of use of higher level strategies (which included talk supported by reasons), and the child's general Logo achievement. However, the verbal strategies used during disagreements did reveal the children's modes of working and thinking. Seven of the ten children worked in an algorithmic way; the other three seemed to understand what they were doing when they worked with angular rotations. The study was able to report on aspects concerning the children's understanding of angular rotation in the early stages of Logo learning, as well as on the sociocognitive aspect concerning the effects that children working together can have upon their learning of Logo geometry concepts.

The aim of this case study was to examine, analyze and report on the findings of the experiences of selected mathematics teachers when they used the van Hiele phases of instruction in designing and implementing a Grade 11 circle geometry teaching programme. The sample consisted of three selected mathematics teachers from the school where the researcher teaches. This school is located in the Oshikoto Education Region in Namibia. The school serves a multicultural group of 759 learners from a middle-class economic background. The site and participants were selected conveniently as the researcher had unrestricted access to both the facilities and the participants. This research takes the form of a case study and is underpinned by the interpretive paradigm. Data for this research was collected using a variety of techniques such as interviews, classroom observation and document analysis. This facilitated easy triangulation of the data. The findings of this research make four claims with regard to the experiences of the mathematics teachers with designing and implementing the circle geometry teaching programme using the five van Hiele phases of instruction as a conceptual framework. The findings revealed that firstly, all three participating mathematics teachers used and implemented all the five van Hiele phases of instruction in their lessons I observed. Secondly, the teachers navigated quite freely from one phase of instruction to the next, but also returned to the earlier phases for clarification and reinforcement in their teaching. Thirdly, the teachers saw the phases of instruction as a good pedagogical tool or template for planning and presenting lessons. Fourthly, the majority of the learners followed the instructions and seemed to obtain the answers faster than expected. The lesson presentations were lively and both teachers and learners communicated at length to discover angle properties of circles while developing and nurturing the technical language of geometry.

This study investigates the effect of using Van Hiele’s instructional model in the teaching of congruent triangles in grade 10 in Gauteng high schools. Three randomly selected high schools in Gauteng formed the research fields, while intact groups of grade 10 learners in these schools formed the study participants (136 learners) for the study. A mixed method approach which was adopted for the study, using pre-test/post-test matching control group design and classroom observation. The pre-test/post-test was used to collect quantitative data, while classroom observation was used to glean qualitative data. Some of the findings from the quantitative data analysis suggested that the intervention improve the achievement scores in the experimental groups while the qualitative data was revealed that the intervention facilitated the learning of the concepts of congruent. It was recommended that Van Hiele learning and instructional model be adopted and applied in the teaching of other areas of mathematics / Mathematics Education / M. Sc. (Mathematics Education)

South African learners perform poorly in the geometry sections of both national and international assessments. Numerous assessment reports mention multiple errors that keep re-occurring and play a big role in the learners’ poor performance. For this research, the link between the grade 9 learners Van Hiele levels of thought and the typical errors that they made were investigated. In this mixed method study, 194 grade 9 learners in two schools in Port Elizabeth, South Africa were tested using a Van Hiele based test. A test was set up containing multiple-choice and open-ended questions and was used to determine firstly, the predominant level of geometric reasoning of the learners and secondly, to determine their typical errors. Semi-structured interviews were held with six learners to gain more insight into some of the typical errors uncovered in the tests. The quantitative data revealed that the learners’ predominant levels of geometric thought were low. Furthermore, the qualitative data revealed typical error patterns concerning angles and sides, parallel lines, hierarchy of quadrilaterals and incorrect reasons in the proofs. The quantitative and qualitative data was merged to determine if the errors could be linked to the Van Hiele levels. From the findings, it was concluded that most of their typical errors could be linked to the Van Hiele levels of the learners.

No description available.

No description available.

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education