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The purpose of this research study is to describe and analyze the self-reported experiences of exemplary high school mathematics teachers who underwent personal and professional transformations in order to develop and use a standards-based, constructivist (SBC) teaching paradigm in their classrooms. These teachers were all past recipients of the Presidential Award for Excellence in Mathematics and Science Teaching (PAEMST), an award that required them to demonstrate that their mathematics instruction was rigorous in the manner described by the NCTM standards. The following research questions are addressed: (a) What are the paths SBC secondary mathematics teachers who received the PAEMST pursued to become highly effective?, (b) What obstacles and challenges did they encounter and how were these obstacles overcome?, and (c) What sustained them on their journeys? The research methodology used to be a narrative inquiry. Following a wide survey of PAEMST recipients, five volunteer participants were chosen for the study. Data were collected from each participant using a one-to-one interview and the written section of each participant's PAEMST application. A narrative was written for each participant describing the path they had followed to become a highly effective high school mathematics teacher. The narrative was sent to each participant, and a follow-up interview was conducted via telephone amending the narrative to reflect the participant's additions and deletions. From the five amended narratives, eight themes were identified: (a) influences; (b) education; (c) professional development; (d) NCTM standards; (e) teaching style: beginning, current, or end of a career; (f) obstacles; (g) personality traits and personal beliefs; and (h) student influence. Several of the themes were supported by previous research. However, this research study discovered two new findings. First, the five participants had common characteristics and beliefs: (a) belief in their students, (b) persistence, (c) belief that professional development is vital for teacher growth, and (d) passion about mathematics and about conveying that passion to their students. The second research finding pertained to the influence that their own students had on all of the five participants. All the participants purposely sought out their students' thoughts about the classroom curriculum and about the instruction they received. The teachers considered their students part of the classroom learning community, and they honored and acted on their input. Finally, in addition to describing the trajectory of five PAEMST winning teachers, this study offers recommendations for students studying to become high school mathematics teachers, teacher educators, and educational researchers. For these students, their teaching preparation courses need to be taught adhering to the four principles of learning: activity, reflection, collaboration and community. According to this research, the model of teacher preparation courses that emphasize the teaching of the above four principles using a traditional teacher-directed method does not prepare future mathematics teachers for the use of SBC teaching in their classrooms. Suggestions about further research are addressed.

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.

published_or_final_version / Education / Master / Master of Education

The major focus of this study is to explore, using the 1990 British Columbia Mathematics Assessment data at the Grade 7 level, gender differences in mathematics teachers' beliefs. As well, this study compared these differences to gender differences of students' beliefs found in the same data. The theoretical rationale for this study is based on a model devised by this researcher, namely the Modified Cognitively Guided Instruction (CGI) Research Model, which is the combination of the Cognitively Guided Instruction Research Model (Fennema, Carpenter, and Peterson, 1989) and the Autonomous Learning Behavior (ALB) Model (Fennema & Peterson, 1985). Two way ANOVA as well as planned comparisons (t-test) were used to investigate gender differences within and across a random sample of two status groups (teachers and students). The analysis of the data suggested several conclusions. First, male and female teachers are more similar than different with respect to their beliefs regarding the importance and difficulty of selected mathematics topics. And, Numbers and Operations was the only topic under study in which male and female teachers differed significantly. Male teachers rated Numbers and Operations more important than female teachers. Second, gender differences existed only in students' beliefs about the difficulty of Geometry, and Numbers and Operations. Female students, compared to male students, believe Geometry and Numbers and Operations more difficult. Third, the findings of this study show that the gender differences within each status group are similar. In addition, significant gender difference was found only in overall male's and female's (regardless of their status) beliefs about the importance of Numbers and Operations. Males rated Numbers and Operations significantly more important than females. Further research which directly investigates gender differences in teachers' beliefs and students' beliefs is suggested, as well as further research into relationships between gender differences in teachers' and students' beliefs.

The major focus of this study is to explore, using the 1990 British Columbia Mathematics Assessment data at the Grade 7 level, gender differences in mathematics teachers' beliefs. As well, this study compared these differences to gender differences of students' beliefs found in the same data. The theoretical rationale for this study is based on a model devised by this researcher, namely the Modified Cognitively Guided Instruction (CGI) Research Model, which is the combination of the Cognitively Guided Instruction Research Model (Fennema, Carpenter, and Peterson, 1989) and the Autonomous Learning Behavior (ALB) Model (Fennema & Peterson, 1985). Two way ANOVA as well as planned comparisons (t-test) were used to investigate gender differences within and across a random sample of two status groups (teachers and students). The analysis of the data suggested several conclusions. First, male and female teachers are more similar than different with respect to their beliefs regarding the importance and difficulty of selected mathematics topics. And, Numbers and Operations was the only topic under study in which male and female teachers differed significantly. Male teachers rated Numbers and Operations more important than female teachers. Second, gender differences existed only in students' beliefs about the difficulty of Geometry, and Numbers and Operations. Female students, compared to male students, believe Geometry and Numbers and Operations more difficult. Third, the findings of this study show that the gender differences within each status group are similar. In addition, significant gender difference was found only in overall male's and female's (regardless of their status) beliefs about the importance of Numbers and Operations. Males rated Numbers and Operations significantly more important than females. Further research which directly investigates gender differences in teachers' beliefs and students' beliefs is suggested, as well as further research into relationships between gender differences in teachers' and students' beliefs. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate

The purpose of this project was to determine if there was a correlation between teachers' scores on fractions items on project assessments and the percentage of participation time in professional development activities.

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education