This study examined teachers' learning and understanding of mathematical representation through the Middle School Mathematics Project (MSMP) professional development, investigated teachers' use of mathematics representations in teaching fractions and algebraic functions, and addressed patterns of teachers' changes in learning and using representation corresponding to Teachers' Zone of Proximal Development (TZPD). Using a qualitative research design, data were collected over a 2-year period, from eleven participating 6th and 7th grade mathematics teachers from four school districts in Texas in a research-designed professional development workshop that focused on helping teachers understand and use of mathematical representations. Teachers were given two questionnaires and had lessons videotaped before and after the workshop, a survey before the workshop, and learning and discussion videotapes during the workshop. In addition, ten teachers were interviewed to find out the patterns of their changes in learning and using mathematics representations. The results show that all teachers have levels of TZPD which can move to a higher level with the help of capable others. Teachers' knowledge growth is measurable and follows a sequential order of TZPD. Teachers will make transitions once they grasp the specific content and strategies in mathematics representation. The patterns of teacher change depend on their learning and use of mathematics representations and their beliefs about them. This study advocates teachers using mathematics representations as a tool in making connections between concrete and abstract understanding. Teachers should understand and be able to develop multiple representations to facilitate students' conceptual understanding without relying on any one particular representation. They must focus on the conceptual developmental transformation from one representation to another. They should also understand their students' appropriate development levels in mathematical representations. The findings suggest that TZPD can be used as an approach in professional development to design programs for effecting teacher changes. Professional developers should provide teachers with opportunities to interact with peers and reflect on their teaching. More importantly, teachers' differences in beliefs and backgrounds must be considered when designing professional development. In addition, professional development should focus on roles and strategies of representations, with ongoing and sustained support for teachers as they integrate representation strategies into their daily teaching.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 130-137). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 130-137). Also available on the Internet.

This study examined the effect of problem-based instruction (PBI) on undergraduate students and prospective secondary mathematics teachers’ perceptions of mathematical proof and pedagogical views. Quantitatively, the Mathematical Proof Survey (MPS) was developed and used to assess the views of mathematical proof held by undergraduates in lecture-based and PBI mathematics courses. Qualitatively, research interviews examined the way teacher candidates’ experiences as mathematics learners in the courses affected their conceptions of mathematical proof and views of learning and teaching mathematics and proof. Findings from quantitative analysis of MPS data and qualitative analysis of interview data are presented, and results from the comparative analysis are discussed for implications. The results of the study suggest that experiences with proof and instruction in such PBI courses provide opportunities for undergraduates and prospective mathematics teachers to develop more humanistic perspectives of proof and process-oriented pedagogical views than do lecture-based courses. / text

With advancements in information technology, people can now access enormous amounts of information with ease. The education system, which plays a vital role in developing our future, has undergone important changes. In the past decades, nearly every part of the education process, from curricula design, assessment methodologies, to teaching methodologies, have been scrutinized. As a result, a series of reforms or changes have been implemented. The purposes of the present study are to investigate more about perceptions and attitudes of secondary school mathematics teachers towards the use of computers in their teaching. Besides, the factors affecting teachers’ attitudes towards computer application in teaching are also analyzed. Finally, the study will also explore the effectiveness of students’ learning through cooperative learning One class of 36 students from 5C, aged 14-16, were invited to participate in this research by using the DMS of GeoGebra for teaching the topics of ‘Basic Properties of Circles’. The teaching outcome of 5C would then be compared with 2 other classes of 5A and 5B, which would be taught by my peer teachers. 5A and 5B’s teachers would employ conventional teaching methods to teach ‘Basic Properties of Circles’ (i.e. the Control Group). Five student worksheets for Basic Operation of GeoGebra and each sub-topic of “Basic Properties of Circles” were devised (see Appendices I to V). Those 5 students were all asked to fill in the questionnaire I. Besides, 12 mathematics teachers were asked to fill in the questionnaire I (see Appendix VIII) of Mathematics with Technology Perceptions Survey (MTPS) in order to investigate their perceptions of using information technology (IT) in teaching mathematics. The purpose of the MTPS items was to ascertain the prevalence of key attitudes and perceptions creating barriers or enabling teachers’ intentions to alter their practice and to teach mathematics with technology. Demographic data of MTPS items were collected on gender, age group, years of teaching, education level, teacher training, teaching level and subject taught. During the whole study, video-recording was taken. In addition, my two peer teachers from classes 5A and 5B were also invited to have an interview. Then, they were asked to fill in the questionnaire II (see Appendix XIII) in order to investigate their’ intention in using the DMS of GeoGebra for teaching and learning mathematics in Secondary 5 classes. Besides, 14 students were randomly selected in order to find out the effects of their learning by using DMS of GeoGebra through peer groups, and these 14 students were invited to complete an extended version of questionnaire II (see Appendix X). Finally, students were asked to conduct a test (see Appendix VI) in order to compare the learning outcome of students learning ‘Basic Properties of Circles’ with the DMS of GeoGebra with those learning in its absence. It is suggested that the integration of computer in learning mathematics should be required. Schools need to make full use of technology to guide students to learn as much as possible. Also, leadership needs to be available to teachers and to provide an in-service education in technology use, so that technology use was operating as well as possible. / published_or_final_version / Education / Master / Master of Education

Not available / text

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education

published_or_final_version / abstract / toc / Education / Master / Master of Science in Information Technology in Education

This study explores the ways in which teachers' interventions interact with and occasion the growth of students' mathematical understanding. Two 'cases' were documented, and these form the two strands of my research. The first strand concerns data collected in my own high school classroom at a time when I was a full-time teacher of mathematics in a small, rural secondary school in the United Kingdom. The second strand concerns data collected in a mathematics classroom in a large, urban high school in Vancouver, British Columbia. The data consist of videotaped lessons in each of the two classrooms, videotaped interviews with students from both strands of the data, copies of students' work from both strands, videotaped interviews with the Vancouver teacher, and my own journal entries. Analysis of the data, which is described in six stages, resulted in the generation of fifteen themes to describe the teachers' actions-in-the-moment. Three of these themes are distinguished from the others as teaching styles, as contrasted with the remaining twelve teaching strategies, and a number of the teaching strategies are clustered within the three teaching styles. The notion of a 'continuum of telling' is developed, upon which the three teaching styles lie, and this continuum is explored in order to probe the ways in which teachers' interventions interact with the growth of students' mathematical understanding. The ways in which teachers' interventions occasion the growth of students' mathematical understanding is probed through an integration of detailed traces of the students' growth of understanding with contemporaneous considerations of the teachers' strategies and styles. Implications to be drawn from these analyses, both for the research community and for teaching and learning, are discussed. I also share my reflections on my own growth as a teacher and as a researcher that I have experienced as a result of participating in, and conducting, this study.