This study examined the relationship between levels of implementation of the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards and 5th Grade Louisiana Educational Assessment Program Math Scores with the effects of race of students accounted for. Secondary areas of interest were the relationship between LEAP mathematics scores with the effects of race of students accounted for and the teacher characteristics of years experience and educational attainment and of the relationship between level of implementation of the Standards and teacher characteristics. The population, from which a sample size of 250 was randomly drawn, was comprised of 1994-95 Louisiana public school teachers who taught in a regular 5th grade or departmentalized math class. Survey research was used to place the responding teachers at one of the five levels of implementation. Hierarchical Multiple Regression was used to analyze the question of primary interest. Race of the students was found to have accounted for nearly 9% of the variance in LEAP mathematics scores. This figure was statistically significant. The independent variable Level of Implementation of the Standards produced ambiguous results. Students of Level 1 (non-implementers) teachers were found to have statistically significantly higher LEAP scores than did students of Level 2 teachers. The Level 1 students had scores which were non-statistically significantly higher than did those of Level 3 and 5. Students of Level 4 teachers had scores which were significantly higher than those students whose teachers were at Level 2 and 5. No significant relationship was found to exist between student LEAP mathematics scores and teacher characteristics of years experience and educational attainment nor between levels of implementation of the Standards and the same two teacher characteristics. Despite these findings, in light of the amount of research pointing to their value, implementation of Standards is still highly recommended.

This investigation of twentieth century trends in mathematics education includes the survey of existing literature and questionnaires conducted with retired and active Texas teachers. Historical events, trends in curriculum, instruction, learning theories, and contradictions of twenty-year periods are delineated. Questionnaire responses are tabulated along the same periods and vignettes of typical classrooms are drawn from the data. Results of the survey show the impact of societal forces on mathematics curricula, a continued downward expansion of content into lower grades and expanding knowledge of learning processes. A unified mathematics curriculum, classroom-related learning theory research, and further development of team-teaching are postulated as future trends. Recommendations include further examination of trends through isolation of other variables such as region and ethnicity.

Based on the classification from quantitative studies, total six teachers, two in each category, were interviewed to construct six individual qualitative case studies. The results suggested that teacher professional knowledge about function and beliefs about mathematics had impacts on their teaching approaches. The teaching approaches can be classified into three categories, i.e, content-centered with performance focus, contentcentered with understanding focus and student-centered with cognitive focus, which constituted traditional content-centered and student-centered perspectives on teaching approaches. Emphasizing process or product is still dichotomy for teachers. / In conclusion, this study showed the significance of subject matter knowledge, pedagogical content knowledge and beliefs about mathematics to teaching approaches of mathematics teachers, which pave the way for future education researches in this field. This study has also provided some valuable experiences in applying hypothetical situations to education researches. In the future, further explorations can be conducted in finding the effect of contextual factors to teaching approaches and how teaching approaches influenced student learning. / In past 30 years, under the global trend of curriculum reform, new requirements on teacher professional knowledge and belief were put on teachers. Accordingly, the focus of research on teaching was shifted from finding effective teaching behavior to in search for teacher professional knowledge, beliefs and cognitions behinds their behaviors. Before, the literatures on teacher professional knowledge were mainly focused on what professional knowledge that teachers have and/or should have. Only few literatures were interested in the effect of teacher professional knowledge and beliefs to teaching approaches. / The main objective of this study is to fill in the missing pieces and investigate the effect of teacher professional knowledge and mathematics beliefs on teaching for inservices mathematics teachers. Mixed method was applied in this study in order to build up some comprehensive understandings to the effects. In quantitative part, this study has surveyed ninety one high school mathematics teachers in M city to find out the deepness of professional knowledge and mathematical beliefs that teachers held. For professional knowledge, the results showed that teachers had different levels of subject matter knowledge and pedagogical content knowledge. For beliefs about mathematics, the results echoed with Ernest's (1989) classification of teacher mathematical beliefs, i.e. instrumentalist, Platonist, and problem-solver. / 張侨平. / Adviser: Ngai-Ying Wong. / Source: Dissertation Abstracts International, Volume: 73-03, Section: A, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (p. 184-209). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in Chinese and English. / Zhang Qiaoping.

呈交日期: "1999年12月" / 論文(博士)--香港中文大學, 2000. / 參考文獻 (p. 128-138) / 中英文摘要. / Cheng jiao ri qi: "1999 nian 12 yue" / Available also through the Internet via Dissertations & theses @ Chinese University of Hong Kong. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Lun wen (Bo shi)--Xianggang Zhong wen da xue, 2000. / Can kao wen xian (p. 128-138) / Zhong Ying wen zhai yao.

Based on the findings above, it is recommended that the future study should explore further how teachers' problem schemas influence their teachings by means of classroom observation. The second recommendation is to study problem schema and other subject matter knowledge in one research to see a comprehensive view. It is also recommended that the development of teachers' problem schemas and subject matter knowledge should be strengthened in teacher education. / Teacher knowledge was an active research area in the last twenty years. It focuses on all kinds of knowledge that teacher knows related to teaching, The study explored subject matter knowledge in teacher knowledge. From the past researches on subject matter knowledge, we find that researchers often focus on teachers' understanding of mathematical concepts and procedures. This is the knowledge of "knowing that". The past researches on subject matter knowledge didn't touch on the knowledge of "knowing how". Based on the theory of problem schema in psychology, we studied teacher's problem schemas, which are related to problem solving. / The study shows that there are various types of problem schemas among secondary school mathematics teachers. They include: "schema organized by mathematics concept ", "schema organized by conclusion or unknown", "schema organized by basic figure ", "schema organized by mathematical structure", "schema organized by general mathematical problem solving strategies". Compared to non-expert teachers, expert teachers have a wider set of problem schemas. Expert teachers not only have the schemas non-expert teachers have, but also have the schemas non-expert teachers don't have. "Schema organized by mathematical structure", "schema organized by general mathematical problem solving strategies" are two of them. Generally speaking, expert teachers possess more profound problem schemas. Hence we see a relationship between problem schemas and teaching expertise. / To explore possible relationship between problem schema and teaching, we first identified the figure of schemas secondary school mathematics teachers have. Then we examined the differences between expert teachers and non-expert teachers to explore the relationship between teachers' problem schemas and their teaching context. In this study, secondary school mathematics teachers were chosen for case studies. Qualitative research methods, including questionnaire and interview were adopted to find out teacher's problem schemas. / 韓繼偉. / 論文(哲學博士)--香港中文大學, 2005. / 參考文獻(p. 154-169). / Adviser: Ngai-ying Wong. / Source: Dissertation Abstracts International, Volume: 67-01, Section: A, page: 0122. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in English. / School code: 1307. / Lun wen (Zhe xue bo shi)--Xianggang Zhong wen da xue, 2005. / Can kao wen xian (p. 154-169). / Han Jiwei.

李琼. / 论文(哲学博士)--香港中文大学, 2004. / 参考文献 (p. 218-233). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts also in English. / Li Qiong. / Lun wen (Zhe xue bo shi)--Xianggang Zhong wen da xue, 2004. / Can kao wen xian (p. 218-233).

孫旭花. / 論文(哲學博士)--香港中文大學, 2007. / 參考文獻(p. 185-194). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in Chinese and English. / Lun wen (zhe xue bo shi)--Xianggang Zhong wen da xue, 2007. / Can kao wen xian (p. 185-194). / Sun Xuhua.

A research report submitted to the Faculty of Science, in partial fulfilment of the requirements for the degree of Master of Science, University of the Witwatersrand, Johannesburg. December 2014. / The National Curriculum and Assessment Policy Statement document (CAPS) (Department of Basic Education, 2012: 4) outlines some of the salient skills related to the modelling of word problems that Mathematics learners are expected to acquire during the course of their learning. One such critical skill is the learners' ability to represent and describe situations in algebraic language, formulae and expressions. In line with this broad objective, the present study investigated learners' linguistic knowledge and skills in translating from word to linear algebraic representations. Particularly focussing on errors learners made during the translation process, a class of 40 Grade 11 learners at one school in Gauteng West District were selected and given a written test on word problems. To gain access to learner misunderstandings leading to the observed errors and their sources, five learners were selected for interviews that were audio recorded. A Mixed-method Sequential Explanatory Design was used in the study. The major finding of this present study was that learners committed more semantic errors than syntactic and schematic errors suggesting that they (learners) had challenges in understanding the language used in the word problems. The major sources of semantic errors were found to be learners' lack of vocabulary knowledge, inexperience in interacting with expository text structures and their lack of syntax awareness. In addition to the above finding, learners exhibited limited metacognitive skills essential in word problem solving as well as their inability to reflect on the appropriateness of their written algebraic representations for all categories of word problems. The study concludes by providing recommendations on how errors committed in word problem solving can be attended to

Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Humanities, School of Education, 2013 / Mathematics-for-teaching (MfT) is complex, multi-faceted and topic-specific. In this study, a Financial Mathematics course for pre-service secondary mathematics teachers provides a revelatory case for investigating MfT. The course was designed and taught by the author to a class of forty-two students at a university in South Africa. Eight students, forming a purposive sample, participated as members of two focus tutorial groups and took part in individual and group interviews. As an instance of insider research, the study makes use of a qualitative methodology that draws on a variety of data sources including lecture sessions and group tutorials, group and individual interviews, students’ journals, a test and a questionnaire. The thesis is structured in two parts. The first part explores revisiting of school mathematics with particular focus on compound interest and the related aspects of percentage change and exponential growth. Four cases are presented, in the form of analytic narrative vignettes which structure the analysis and provide insight into opportunities for learning MfT of compound interest. The evidence shows that opportunities may be provided to learn a range of aspects of MfT through revisiting school mathematics. The second part focuses on obstacles experienced by students in learning annuities, their time-related talk, as well as their use of mathematical resources such as timelines and spreadsheets. A range of obstacles are identified. Evidence shows that students use timelines in a range of non-standard ways but that this does not necessarily determine or reflect their success in solving annuities problems. Students’ use of spreadsheets reveals that spreadsheets are a powerful tool for working with annuities. A key finding with regard to teachers’ mathematical knowledge, and which cuts across both parts of the thesis, is the importance of being able to move between compressed and decompressed forms of mathematics. The study makes three key contributions. Firstly, a framework for MfT is proposed, building on existing frameworks in the literature. This framework is used as a conceptual tool to frame the study, and as an analytic tool to explore opportunities to learn MfT as well as the obstacles experienced by. A second contribution is the theoretical and empirical elaboration of the notion of revisiting. Thirdly, a range of theoretical constructs related to teaching and learning introductory financial mathematics are introduced. These include separate reference landscapes for the concepts of compound interest and annuities

This project explored the Concrete to Representational to Abstract instruction (CRA instruction) as a strategy to teach abstract math concepts for secondary students with learning disabilities. Through the review of literature, multiple researchers suggested that students with learning disabilities need to be exposed to a variety of instructional strategies to develop problem solving skills in algebra concepts.