Thesis (M. Ed.)--Kutztown State College. / Source: Masters Abstracts International, Volume: 45-06, page: 2787. Typescript. Includes bibliographical references (leaves 33-35).

University-based initial teacher education aims at instilling in teacher candidates the idea of the interconnectedness of content, pedagogical and educational research knowledge by allowing meaningful interaction between teacher candidates and teacher educators. The theory-practice divide is presented in the literature as barrier to achieving this goal. This mixed methods research study re-conceptualizes the theory-practice divide from a problem into an opportunity. Secondary school teacher candidates can use contradictions and tensions, surrounding the theory-practice divide, for synthesizing diverse perspectives on content, pedagogical and educational research knowledge. They can integrate this perspective in their practice teaching. The study examined secondary school teacher candidates’ perspectives on the interaction of their content, pedagogical and educational research knowledge in practice teaching as well as factors contributing to these perspectives. The study found that participants’ different perspectives on their research pedagogical and content knowledge (RPACK) were associated with the different levels of their reform-mindedness in mathematics education as measured by a survey. The low, medium and high reform minded participants placed as the first priority pedagogical knowledge, content knowledge and educational research knowledge, respectively.

University-based initial teacher education aims at instilling in teacher candidates the idea of the interconnectedness of content, pedagogical and educational research knowledge by allowing meaningful interaction between teacher candidates and teacher educators. The theory-practice divide is presented in the literature as barrier to achieving this goal. This mixed methods research study re-conceptualizes the theory-practice divide from a problem into an opportunity. Secondary school teacher candidates can use contradictions and tensions, surrounding the theory-practice divide, for synthesizing diverse perspectives on content, pedagogical and educational research knowledge. They can integrate this perspective in their practice teaching. The study examined secondary school teacher candidates’ perspectives on the interaction of their content, pedagogical and educational research knowledge in practice teaching as well as factors contributing to these perspectives. The study found that participants’ different perspectives on their research pedagogical and content knowledge (RPACK) were associated with the different levels of their reform-mindedness in mathematics education as measured by a survey. The low, medium and high reform minded participants placed as the first priority pedagogical knowledge, content knowledge and educational research knowledge, respectively.

The goal of this paper is to evaluate commonly held criticisms of the practice of ability tracking in high school mathematics. To do so, I employ data from the National Education Longitudinal Study of 1988 and follow-ups to model classroom selection and education production. This paper will focus only on the causes and effects of tracking on students who were tracked as low-ability in eighth grade. From this, we can see how many students, if any, switched out of the low-ability track by tenth grade and how various switches have affected their test scores in mathematics. I find that students exercise mobility between ability-tracks as late as tenth grade and that ability-track placement is largely determined by test scores. In addition, I find evidence that there would be minimal, if any, test score improvement among low-ability students if they were all moved to a class of heterogeneous ability. / Master of Science

The purpose of this research was to examine the possible associations between the perceived classroom environment of high school students, the level of mathematics anxiety that they possess, and their attitudes towards mathematics. This marks the first time that these three fields of research have been simultaneously combined. Data were gathered from 745 high school mathematics students in 34 classes in high schools in the Southern California area using three instruments: the What is Happening In this Class? (WIHIC) learning environment survey created by Fraser, McRobbie, and Fisher (1996), an updated version of Plake and Parker's (1982) Revised Mathematics Anxiety Ratings Scale WRS), and a mathematics version of selected scales from Fraser's (1981) Test of Science-Related Attitudes (TOSRA). This revised attitude instrument was called the Test of Mathematics-Related Attitudes (TOMRA). Using statistical methods, the three instruments were checked for internal consistency reliability, factor structure, and discriminant validity. The RMARS and WIHIC were both found to exhibit good reliability and factorial validity in mathematics classrooms in Southern California, while the TOMRA yielded two scales of the four a priori scales, Enjoyment of Mathematics Lessons and Normality of Mathematicians, which met reliability and factorial validity standards. Within-class gender differences were analysed using paired t-tests combined with a modified Bonferroni procedure and effect sizes. Between- student gender difference were investigated using MANOVA. Simple correlation and multiple regression analyses were performed to identify possible associations between the learning environment and anxiety/attitudes scales. Qualitative data were collected from interviews and inductive analysis was performed in order to refute or corroborate the quantitative findings. / Significant within-class gender differences were found in four areas of the learning environment (Student Cohesiveness, Task Orientation, Cooperation, and Equity), but no gender differences in attitudes were found. All four learning environment areas were perceived in a more favourable light by females than by males. Individual gender differences were similar, with a significant difference also being found in Teacher Support, as well as both types of mathematics anxiety, namely, Learning Mathematics Anxiety and Mathematics Evaluation Anxiety. In order to carefully identify the relationships between the classroom learning environment and mathematics anxiety, analyses were conducted for both factors of mathematics anxiety. While no association between the learning environment and Mathematics Evaluation Anxiety was found, there were significant associations between Learning Mathematics Anxiety and three areas of the learning environment: Student Cohesiveness, Task Orientation, and Investigation. Significant associations between the Normality of Mathematicians attitude scale and the learning environment scales Equity and Involvement were identified, while three areas of the learning environment (Investigation, Task Orientation, and Cooperation) had a significant relationship with Enjoyment of Mathematics Lessons. Qualitative data analyses confirmed relationships between anxiety, attitudes, and classroom learning environments. The data also suggest that the structure of the mathematical content is linked with the level of anxiety that high school students feel.

<p>This thesis investigates grade seven learners perceived experiences in learning algebra.Things that learners do and say during algebra lessons and about algebra were investigated. The study was done at one of the previously disadvantaged schools in Cape Town, South Africa.The data were collected through observations, a questionnaire and interviews. Observations were made from the day the topic was started in two grade seven classes. Two different teachers taught the two classes. Focus group interviews were conducted, two group of learners, ten learners from each of the two classes were interviewed. Learners devised a number of strategies for solving problems related to sums and differences. The principal learning difficulties experienced by learners in algebra related to the transition from arithmetic conventions to those of algebra, the meaning of literal symbols and the recoginition of structures. It became obvious then that developing algebraic thinking is not necessarily dependent upon algebraic notation and that the presence of algebraic notation says little about the level of problem solving.</p>

This thesis is focused on the utilization of simplified functional equations in logarithm exercise. The goal of this work is to assess the degree of formalism in the logarithm knowledge of high school students. The first part attends to the origin and development on the term logarithm and logarithmic tables. These findings are subsequently put into the context of present day logarithm teaching extracted from contemporary high school textbooks. The second part describes an experiment which was conducted for the purpose of this thesis. The final part contains the results of the thesis and the evaluation of their relevance for logarithm tuition. Keywords: logarithm, logarithm tables, textbook analysis, functional equations.

This study uses a discourse analysis from the perspectives of James Paul Gee (2005; 1999) in order to establish a socio-situated view of why grade 10 students often experience difficulties in representing mathematical word problems into appropriate equations and expressions that enable a solution to the problems. A discursive methodology was used to throw light on the difficulties that students experience that was different from the perspectives adopted previously, viz. from a view of the structure of the problems, from a pedagogic point of view and a cognitive understanding. An initial case study in one school in which four students were selected revealed that a master model existed that students were enacting when doing and talking about their experiences with word problems, viz. that word problems are obfuscatory. This master model rendered the students relatively mathematically helpless within a Discourse of school mathematics word problems. In order to more fully understand these findings an extended study was set up in which the methodology and analytic framework were refined. This extended study saw four students at each of three different sites selected to participate. The findings of this extended study were that the students enacting a situated Discourse model were more enabled within the Discourse of school mathematics word problems, whilst those enacting a deficit Discourse model were either peripheral or outside of that Discourse. This study contributes in that the constructs for the phenomena and the analytic tools within the context of school mathematics needed to be pioneered, adapted and refined over a period of time to address aspects particular to school mathematics. This resulted in a view from a socio-situated perspective which saw a shift in seeing what students do with the problem to what students do in the social setting associated with the problem. From this shift in focus came a new understanding of student difficulties with word problems that gave rise to a sub-Discourse within the Discourse surrounding school mathematics word problems, and students finding themselves in this sub-Discourse becoming marginalised through enacting a deficit Discourse model because they are unable to ascribe to the success model, or situated Discourse model.

The rationale behind this study concerns the issues school administrators and teachers of expatriate students face over the progress and placement of the growing number of these students in mathematics classrooms in various countries brought about by the demographical changes occurring in this globalization era. This study aimed to present a method of examining lower secondary school mathematics textbooks with the purpose of evaluating students' expected past learning and comparing students' expected mathematics learning across the different curricula. It is anticipated that such an investigation will be of value to those responsible for the correct level of placement of these students.Six sets of textbooks from four countries on the Asia-Pacific rim, namely Australia, Brunei, China and Singapore, were selected for this study. The textbook content of each country was analyzed in terms of strand weighting and content details, and then coupled with information gained from interviews with teachers. This led to the findings which addressed the various issues raised.The findings facilitated a comparison of the learning paths offered by the various textbooks, fleshed out the differences and similarities of the various curricula and made available detailed comparisons of the textbooks' content in terms of topics covered. The analytical procedure of the examination of text content as presented in this study is itself a diagnostic technique for assessment of the students' past learning, which addressed the main objective of the study.The findings will be of interest to all who are interested in the mathematics taught in the countries involved. / Outcomes will be particularly useful to curriculum planners and textbook writers as well as the administrators and teachers of International Schools and other schools enrolling expatriate students from these countries. The study offers a 'simplistic' way of evaluating textbooks to assess students' learning progress, and highlights the traits of the countries' curricula to provide a general idea of the mathematics ability expected from the expatriate students residing in these countries.

Achievement and the experiences of women in secondary school mathematics have been well documented in the research literature (e.g., Benbow & Stanley, 1980, 1983; Tartre & Fennema, 1995; Sherman, 1982; Ryckman & Peckham, 1987; Keller & Dauenheimer, 2003). With respect to achievement, the research literature primarily focuses on how women are deficient to men (e.g., Benbow & Stanley, 1980, 1983) and the roles affective attributes (e.g., Sherman, 1982; Fennema, Petersen, Carpenter & Lubinski, 1990) and stereotype threat (e.g., Quinn & Spencer, 2001; Steele & Aronson, 1995) have played in women’s deficiencies. Despite the perspective and nature of this research, there are, however, women who have achieved at extraordinarily high levels in the secondary mathematics classroom. It is important to examine this historical research as it has impacted the views of teachers, researchers, and media with regard to female mathematics students’ opportunities. By reflecting upon the research literature and its far reaching impacts, high-achieving women in mathematics can begin to reverse the perceptions that limit their opportunities. Thus, the purpose of this study was to explore, through the experiences and stories relayed by the study’s participants, how young women might negotiate the (historic all male) mathematics domain. Employing a qualitative research designed within a phenomenological framework and analyzed through a combination of postmodern and standpoint feminisms, I examined the stories of four undergraduate female students who were identified as being high-achieving in secondary school mathematics. These young women, by reflecting upon their secondary school experiences, and by reflecting upon their experiences within the context of the existing research literature, not only identified the aspects of their lives they felt had the greatest impact upon their opportunities but also examined their personal definitions of success and the impacts their gender had on their (socially defined) achievements within secondary school mathematics.