Thesis (M.ED. (Mathematics Education)) -- University of Limpopo, 2012 / This study investigated Mathematics teachers’ beliefs about the nature of Mathematics and their impact on classroom practices. It was conducted in a public semi-urban school in the Capricorn District-Limpopo Province. It was a case study targeting two FET teachers with teaching experiences of 15 years or more. The central research questions addressed in this study are, namely: What are Mathematics teachers’ beliefs about the nature of Mathematics? And, what is the relationship between teachers’ beliefs and their classroom practices? Data were collected through pre-observation interviews, classroom observation and through post observation interviews. Pre-observation interviews were conducted once before the participants were observed. I was a complete observer during my colleagues’ lessons. Interviews and observations data were analysed using categorisation and interpretation of data in terms of common themes and synthesis into an overall portrait of the case. Each case study teacher’s data were analysed individually (that is within-case analysis) first and thereafter cross-case analysis was done in order to compare the two case studies.

The purpose of this investigation was to explore how differences in an elementary mathematics teacher's subject matter knowledge structure impact classroom teaching and student learning. The study included two phases. Phase 1 focused on the selection of a single case. An open-ended questionnaire and interview were used to identify the subject matter knowledge structure for addition, subtraction, multiplication, and division of three elementary teachers. One teacher was selected who demonstrated clearly different levels of knowledge for multiplication and division. An additional interview provided information on the teacher's specific climate for teaching mathematics and details about the unit on multiplication and division to be observed. Phase 2 included daily classroom observations for approximately one hour each day of a seven-week unit on multiplication and division. Informal interviews were conducted with the teacher throughout the unit to better understand the lessons and allow the teacher an opportunity to clarify statements and actions. A final teacher interview occurred after the last classroom observation. At the conclusion of the observations, the students were assessed to determine their knowledge of multiplication and division based on the teacher's unit objectives. And six students, representing the range of class performance, were interviewed to provide additional insights into the students' learning. The teacher's subject matter knowledge of multiplication was strong but her knowledge of division was faulty and incomplete on several topics including the different meanings of division, the conceptual underpinnings of division procedures, the relationships between symbolic division and real life problems, and the idea of divisibility. Although the translation of the teacher's subject matter knowledge was complex, it seemed to be directly related to classroom teaching and students' learning. The teacher's narrow understandings were associated with an incomplete developing of the full range of division situations. Although the students had significantly more success on the post assessment problems involving multiplication than on those involving division (understandable since the teacher spent more time teaching multiplication than division), a more worrisome concern was that the students in this study exhibited serious misconceptions associated with the meanings of division, division computation, and notions of divisibility. / Graduation date: 2000

As a result of the calls for reform in mathematics education and the ever-changing nature of mathematics, today's teachers face the challenge of teaching unfamiliar content in ways that are equally unfamiliar. In view of this challenge, the purpose of this study was to investigate middle school teachers' subject matter and pedagogical content knowledge of probability and its relationship to the teaching of probability. The study also explored the nature of the instructional tasks and classroom discourse during probability instruction. Case study methodology was used to examine the knowledge and practice of 4 middle school teachers. A pre-observation interview assessed the teachers' subject matter knowledge of probability. The teachers were then observed as they taught probability. Post-observation interviews further explored teacher knowledge and its relationship to teaching practice. Data sources included interview transcripts, observational field notes, video and audiotapes of classroom instruction, and written instructional documents. Individual case studies were written describing the teachers' background and probability instruction. Cross-case analyses compared and contrasted the cases in response to the research questions. The results of this study indicate the teachers generally (a) lacked an explicit and connected knowledge of probability content, (b) held traditional views about mathematics and the learning and teaching of mathematics, (c) lacked an understanding of the "big ideas" to be emphasized in probability instruction, (d) lacked knowledge of students' possible conceptions and misconceptions, (e) lacked the knowledge and skills needed to orchestrate discourse in ways that promoted students' higher level learning, and (f) lacked an integrated understanding of the nature of the reform. One teacher captured the essence of the reform effort in her probability instruction; the other 3 teachers generally fell short of the goal despite their efforts to implement aspects of the reform. Although students were actively involved in exploring probability content through the use of games, simulations, and other hands-on instructional tasks, the cognitive level of the tasks and discourse was limited by the nature of instruction. The findings of this study have implications for mathematics education reform, preservice teacher preparation, staff development, and curriculum development. / Graduation date: 1998

This investigation of secondary geometry teachers' decision making in a mathematics curricular reform context examined the following questions: (a) What planning and interactive decisions were secondary geometry teachers making during this time of reform, and (b) what factors influenced the decisions that these teachers made? In addition, comparisons were generated between influential factors identified during a mathematics reform context and the stable context of previous decision making studies. A multi-case study approach involving detailed examination of five geometry teachers' decision making was used. The data collected and analyzed included a questionnaire, interviews, observational field notes, audiotapes and videotapes of classroom instruction, and written instructional documents. Teachers' profiles were created describing geometry and teaching biographies, views toward curricular change, the classroom, planning decisions and influential factors, and interactive decisions and influential factors. Findings were developed by searching for similarities and differences across the sample. Teachers' decisions generated descriptions of their geometry courses. One teacher promoted geometry as a mathematical system using predominantly a lecture approach. The other four teachers advocated a multifaceted view of geometry recognizing geometry as a mathematical system and as a setting for developing communication and problem solving skills. In addition, the four teachers' courses included references to connections between geometry and the real world. These four teachers used a variety of instructional approaches that encouraged students' active involvement in their geometry learning with an emphasis on developing student understanding. Factors influencing teachers' decisions included: (a) past geometry experiences, (b) professional development experiences, (c) articulated course goals, (d) advanced planning decisions, (e) teachers' beliefs, (f) the geometry textbook and other materials, (g) teachers' school settings, and (h) students' needs and actions. Some findings highlighted differences between this study and previous decision making studies. All teachers in this study appeared to be influenced by their beliefs about the nature of geometry as a discipline. Teachers were also influenced by whether they viewed the process of becoming an effective teacher as a life-long process. For four of the teachers, reform agendas were influential as another source of curriculum ideas. / Graduation date: 1997

Thesis (Ph. D.)--Oregon State University, 2007. / Printout. Includes bibliographical references (leaves 160-168). Also available on the World Wide Web.

Organizations leading education reform of the 1980's have challenged teacher education programs at colleges and universities across the nation to improve the subject matter content preparation of teachers. Past methods of program development and techniques to assess teacher's knowledge competence have been one-sided in their approach. New research studies on expert vs novice teachers show that expert teachers are more efficient in carrying out standard patterns of instruction. This nation's mathematics community has engaged in a revitalization of mathematics curricula. Traditional mathematics is being transformed to become a powerful science. Using the growing body of research, the National Council of Teachers of Mathematics have developed standards for improving the teaching and learning of mathematics. Oregon's Department of Education has also established standards to meet the needs of a changing mathematics curricula and the challenges of a changing society. This study identified the specific content knowledge taught in the mathematics curricula within colleges and universities which offer four, five or fifth year teacher education programs. It then compared these findings against teacher identified origins of elementary, middle and high school teachers' mathematics content knowledge relative to the Essential Learning Skills of Oregon. It was found that teachers' content knowledge of the Essential Learning Skills of Oregon was not directly related to their preparation as teachers; at the elementary and high school levels, there was no direct relationship found between teachers' degrees and their teaching assignment; there was no apparent relationship between teachers' knowledge of the Essential Learning Skills of Oregon and graduation from an Oregon college or university; there was no apparent relationship between teachers' lack of knowledge of the Essential Learning Skills of Oregon and graduation from a non-Oregon college or university. / Graduation date: 1990

The purpose of this study was to investigate the effect of teachers' behaviors and characteristics upon the development of student mathematical critical thinking skills. From a pool of 20 teachers, whose students had been pre- and post-tested for a measure of critical thinking skills, 10 middle level teachers were selected to complete extensive questionnaires on their backgrounds and experiences, submit videotaped records of classroom activity, and to maintain detailed data on their classroom actions. The teachers were ranked in accordance with their respective classes' mean gain scores on the assessment tool. From the pool of 20 teachers, the top-ranked 25% (five teachers) and the bottom-ranked 25% (five teachers) were selected for the study. Extremes of the ranking order were used to increase the probability of determining potential differences in teacher behaviors and characteristics between the two groups. The two extremes were thus placed in two groups to identify those variables which contributed to differences between the groups. Identified variables from pairwise comparisons of the teachers within each group were analyzed, following corroboration from a minimum of three data sources, to generate groups profiles. A 5 x 5 matrix was constructed for each potential group variable. Comparisons were conducted between all pairs of teachers within each group, and the differences between the two groups were compiled in the form of group profiles. The five top-ranked teachers, based upon student performances, were distinguished from the lowest-ranked five teachers by greater use of small group instruction, math manipulatives, and warmup activities; as well as by provision for teaching higher-order thinking skills, frequency of transitions between classroom activities, and the use of activities which required the application of concepts. The lowest-ranked teachers were characterized by the greater frequency of teacher-directed instruction, a higher amount of computer usage, assignment of individual student work, highly structured classes, and extensive reliance on textbooks as the primary source of instructional materials. / Graduation date: 1993

The goal of the research project was to assess the effect of a written intervention on the state anxiety of new mathematics teachers. Twenty-eight beginning mathematics teachers in Washington, Oregon, and California were randomly assigned to treatment or control groups. Treatment was a survival guide, Green Broke, carefully designed to meet the needs of beginning mathematics teachers. A Delphi panel determined topics for the guide, beginning with suggestions from the literature. The panel included mathematics teachers in grades 7 to 12 from all three Pacific states, and both urban and rural areas. School administration and college mathematics education were also represented on the panel. A subset of the panel and a writer edited the guide. Trait anxiety of subjects was determined prior to the 1989-90 school year using the trait anxiety portion of Spielberger's State-Trait Anxiety Inventory. The state anxiety inventory was administered at that same time and again three times during the school year. All subjects also completed a teacher report twice during the year regarding their teaching experiences. In addition, the treatment group was asked to complete two questionnaires regarding the effectiveness of Green Broke. Subjects perceived that they were part of two studies, one involving the guide and one involving anxiety inventories. Analysis of covariance for repeated measures was used to assess differences between groups in state anxiety, using trait anxiety as covariate. Level of significance was set at .05. There was no significant main effect, but a significant interaction effect was found. The nearly linear relationship between state and trait anxiety found in the control group disappeared for the group having the guide. Mini case studies, using responses to the teacher reports, were done for seven subjects, including those with very high state anxiety. In addition, a subgroup of the treatment group, for which a linear relationship between state and trait anxiety did exist, was examined for common characteristics. Locus of control was hypothesized to be a variable that would differentiate this group. Other suggestions for further study include use of audio-visual forms of the survival guide, extension to other subject areas, and replication of the study. / Graduation date: 1991

The purpose of this study was to investigate the knowledge base and instructional practices of two highly qualified experienced secondary mathematics teachers within the context of their classrooms during a unit in a geometry class. Data collected from interviews, classroom observations, pre and post-observation questionnaires, and detailed analyses of several lesson segments were used to create case studies for each teacher, which were compared to reveal any patterns in their instructional practices. The theoretical framework used for this study was Schoenfeld's (1998) model of teaching-in-context that included three factors that affected teachers' decisions during instruction: beliefs, goals, and their knowledge bases. The supporting questions that were investigated in this study dealt with teachers' conceptions of mathematics and teaching and learning mathematics, instructional goals, instructional strategies and curricular materials used during the unit, and any modifications made to instruction. Both teachers in this study used a more traditional lecture and discussion style of instruction that closely followed an explicit model of teaching instead of a more reform-based style of teaching. The teachers incorporated the processes of mathematics such as proof and reasoning and representation into their instruction through modeling instead of incorporating activities into instruction designed to engage students in the processes. Although both teachers were aware of and had used reform-based methods, they perceived that the traditional instructional methods were more efficient and effective. Contextual factors played a dominant role in the decisions the teachers made about their instruction. The contextual factor that had the greatest effect on instruction for these two teachers was the pressure to teach all of the topics in the required curriculum to prepare their students for the state standardized high stakes test. Other contextual factors were large class sizes, limited physical space, and limited access to technology. The results of this study indicated that although the teachers had strong content knowledge and knowledge of both traditional and reform-based pedagogy, they chose a more traditional instructional style and this decision was affected by contextual factors such as high stakes testing, a required curriculum, and the demands of their jobs. / Graduation date: 2006

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (leaves 109-113).