Statistically skilled workers are highly demanded in today's world, which means we need high-quality statistics education. There has been a continuously increased enrollment of statistics students. At the college level, introductory statistics courses are typically taught by professors who often hold a strong qualification in mathematics but may lack formal training in statistics education and statistical analysis. Existing literature claims that a unique way of thinking--statistical thinking or reasoning--is essential when teaching statistics, especially at the introductory level. To elaborate and expand on the issue of statistical thinking, a qualitative study was conducted on 15 mathematics teachers from a local community college to discuss differences between statistics and mathematics as academic disciplines and exemplify two types of thinking--statistical thinking and mathematical thinking--among mathematics teachers who teach college-level introductory statistics. Additionally, the study also inspected mathematics teachers' pedagogical ideas influenced by each type of thinking, some of which were recognized as "pedagogically powerful ideas" that transcend students' conceptual understanding about statistics. The study consisted of two online questionnaires and one interview. In the two online questionnaires, participants explored and rated five technology options for teaching statistics and self-evaluated their technology, pedagogy, and content knowledge. During the interview, participants solved nine statistical problems designed to elicit statistical thinking and addressed pertinent pedagogical questions related to each problem's statistical concept. A framework that hypothesizes aspects of mathematics teachers' statistical thinking and mathematical thinking in statistics was created, summarizing the prominent differences in problem-solving, variability, context, data production, transnumeration, and probabilistic thinking. Select responses from participating mathematics teachers were provided as examples of each type of thinking. Furthermore, it was revealed that mathematics teachers with a different type of thinking tended to cover different statistical topics, deliver the same statistical concept in different ways, and assess students' knowledge with different emphases and standards. This study's results have implications: if statistics is to be taught by mathematics teachers, statistical thinking is required to implement pedagogically powerful ideas for furthering meaningful statistical learning and to unveil the differences between statistics and mathematics.

This action research study examined the effects of professional development on teaching for conceptual understanding in Algebra I. “Conceptual knowledge refers to knowledge of the underlying structure of mathematics - the relationships and interconnections of ideas that explain and give meaning to mathematical procedures” (Eisenhart et al., 1993). Conceptual knowledge is “explicit or implicit understanding of the principles that govern a domain and of the interrelations between pieces of knowledge in a domain” (Rittle-Johnson & Wagner, 1999). The study took place in a large metropolitan school district. The participants for the study were two Algebra I instructors with varying pedagogical experiences. Participant #1 is a novice teacher with seven months of classroom experience at the start of this study. The participant holds an undergraduate degree in mathematics and a professional mathematics teaching license. Participant #2 is a tenured teacher with five years of classroom experience at the start of this study. The participant does not hold an undergraduate degree in mathematics and is licensed in special education, not mathematics. The study was formulated in response to the growing difficulty in recruiting qualified mathematics teachers, and the increasing number of mathematics teachers with limited studies in mathematics. Concept-based instruction techniques were presented to participants through a series of six professional development workshops, the first three of which followed classroom observations, and the second three after a second round of observations. The study was qualitative in nature and the collected data were used to develop responses to two research questions. After classroom observations, a concept-based instruction checklist and scoring criteria was used to note evidence of concept-based instruction, as well as any changes to instructional strategies following professional development workshops. Student artifacts were also examined to note evidence of conceptual understanding. Study participants engaged in a semi-structured interview where they were asked to describe changes, if any, to their instructional practices as a result of participating in professional development on teaching for conceptual understanding. The research findings suggested that effective professional development positively affects pedagogical practices in mathematics. After participating in a series of professional development workshops, the researcher observed shifts in participant pedagogical practices that included emphasis on using appropriate math language and encouraging explanations and justifications through questioning as tools for fostering conceptual understanding. Responses to semi-structured interviews suggest that teachers most value professional development that leads to positive impacts on student performance. An analysis of student artifacts demonstrated growth in student written responses and problem-solving approaches. Participant #1 stated: “Participating in this research has allowed me to wonder about the misconceptions and problems within my classroom; I am able to go over student coursework and come up with a solution to better help students with common errors.”

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Over the past decade there has been a growing investment in professional development (PD) programs for K-12 mathematics teachers. Researchers and policy makers often inquire about the effect of professional development programs and whether they are having a positive impact on students' learning, and which type of programs aid in students ' academic improvements. In view of the continued concern about the low achievement of U.S. students in mathematics there is a strong need to better understand the effect of PD on student learning and more specifically, which components of PD are more beneficial and are likely to enhance students' math learning. This study offers evidence in an effort fill the gap in the literature by examining the relationship between professional development and student achievement. A meta-analysis methodology was used to synthesize quantitatively and aggregate the results of the prior studies that have used scientific methods and reported numerical results. The time period for the selection of studies is from 2003 to 2014. Findings in this study confirm earlier literature and offers guidance about three effective components (duration, content, and intervention modality) in professional development programs that have been found to have a positive relationship with students' achievement. The results also highlighted the importance of content focus, sufficient duration and multiple modalities of professional development programs aiding teachers in their ability to become more effective in the classroom leading to increased students' achievement in math. / Ph. D.

The exploratory study sought to elicit and document mathematics teachers‟ views on how they enacted the process of transition between contexts and mathematics. The study pursued to understand teachers‟ beliefs and knowledge of mathematics. A mixed methods sequential explanatory research design was employed where a quantitative phase was followed by the connecting phase and concluded through a qualitative phase involving three case studies. A purposive sample of 165 practicing teachers who had registered for a professional advancement developmental course at a university participated in the study by voluntarily completing a survey questionnaire. From this sample, three cases of individual teachers were pursued. The first two cases involved conducting in-depth interviews with the teacher who had rated sentences in the questionnaire differently while the last case involved the recording of an interview of one individual using field notes. The questionnaire sought teachers‟ biographical details (section A), their views on contexts and mathematics (section B) and their rating of sentences in a passage with regard to the mathematics embedded in the sentences (section C). Semi-structured interviews were conducted in the qualitative phase to elicit in-depth views of the teachers‟ regarding the research problem. All the instruments were tested for validity and reliability. Quantitative data gathered was analysed using frequencies, percentages, cross tabulations, bar charts and pie charts as well as the calculation of Pearson chi-square tests (Cohen, Manion & Morrison, 2011). Descriptive and inferential statistics were used to collate teachers‟ views from which themes were drawn and related to make inferences. It was found that teachers‟ positive views about contexts and mathematics did not translate into them recognising mathematics in some mathematics potent contexts as captured in their ratings in section C of the questionnaire. Statistically significant associations were recorded to support this. The study also conceptualised a mathematical participation model (MP-model) as a tool to describe and analyse participation that involves the use of real world data in the teaching and learning of mathematics. The MP-model involves four components, viz. the community of practice (CoP), real world data, mathematics and a model in which members of the CoP tap into the real world data and mathematics to model their participation. The study recommends the MP-model as tool for description and enactment of full mathematical participation. / Mathematical Sciences / D.Litt.et. Phil. (Mathematics Education)

This quasi-experimental study, utilizing quantitative and qualitative descriptive methods, examined the sex-egalitarian attitudes of secondary mathematics teachers from the Ft. Worth Independent School District. A video tape, Women in the Workplace, was used as a training intervention to test the effectiveness of professional development training in altering the mathematics teachers' sex-egalitarian attitudes towards female employment. Information on the video presented seven jobs that provide opportunities for female students in the science, engineering, and technology fields that are considered nontraditional jobs for females. Subjects completed 19 Employment Role domain questions on the King and King (1993) Sex-Role Egalitarianism Scale. A one-way ANOVA was applied to the data to test for a significant difference in the means of the control group, who did not see the video, and the experimental group that viewed the video. Findings concluded that there was no significant difference in the sex equalitarian mean scores of the control group and the experimental group. The research indicated that it takes an intensive and prolonged training period to produce a significant change in people's attitudes. This study supports the research on length of training needed to change sex egalitarian attitudes of classroom teachers. There were data collected on four demographic areas that included gender, age, ethnicity, and years of teaching experience. A two-way ANOVA was applied to four demographic variables to test for interaction and main effect. A significant difference was found between the sex-egalitarian attitudes of male and female mathematics teachers' responses. There were no significant differences found in the sex egalitarian attitudes of secondary mathematics teachers when categorized by levels of age, ethnicity, and years of teaching experience. The information in this study should interest and benefit teachers, parents, students, administrators, and industry leaders.

Thesis (M.Ed.)--University of Hong Kong, 1979. / Includes bibliographical references (leaf 91) Also available in print.

This study characterizes the mathematical knowledge upon which secondary school algebra teachers draw when pondering problem situations that could arise in the teaching and learning of solving algebraic equations, as well as examines the potential connections between teachers' knowledge and their academic backgrounds and teaching experiences. Seventy-two middle school and high school algebra teachers in Texas participated in the study by completing an academic background questionnaire and a written-response assessment instrument. Eight participants were then invited for followup semi-structured interviews. The results revealed three topic areas in equation solving in which teachers' mathematical subject matter understanding should be strengthened: (a) the balancing method, (b) the concept of equivalent equations, and (c) the properties of linear equations in their general forms. The participants provided a wide range of instances of student misconceptions and difficulties in learning how to solve linear and quadratic equations, as well as a variety of strategies for helping students to improve their understanding. Teachers' subject matter knowledge played a central or prerequisite role in their reasoning and decision-making in specific contexts. When the problem contexts became broader or more general, teachers drew from across the three basic domains of mathematical knowledge for teaching (knowledge of the mathematical subject matter, knowledge of learners' conceptions, and knowledge of didactic representations) and showed individual preferences. Overall, teachers tended to rely more heavily upon their knowledge of students' specific or general learning characteristics. Statistical analyses suggest that teachers who majored in mathematics and who had the most experience in teaching first-year or more advanced algebra courses performed significantly higher on the assessment than their counterparts, and there is a linear relationship between teachers' performance and the number of advanced mathematics course they have taken. Neither course-taking in mathematics education nor number of years of algebra teaching made a significant difference in their performance. Results are either unclear or inconsistent about the role of teachers' (a) use of algebra textbooks, (b) prior experience with a method or a manipulative, and (c) participation in professional development activities. Teachers also rated (a) collaborating with and learning from colleagues and (b) dealing with student conceptions and questions as highly influential on their professional knowledge growth.

A thesis submitted to the Wits School of Education, Faculty of Humanities, University of the Witwatersrand in fulfilment of the requirements for the degree of Doctor of Philosophy May, 2016 / This study investigates how primary school mathematics in-service teachers respond to learners’ offers, over time, during classroom interactions. The study was a follow-up to a one-year long in-service ‘maths for teaching’ professional development course in which 33 teachers participated in 2012. Four teachers from that course were tracked in this follow-up study. Data sources within this study consisted of two cycles of observations of lessons taught by the four teachers in 2013 and 2014, and an interim video-stimulated recall (VSR) interview with each teacher, with reflections guided by the structure of Rowland et al.’s ‘knowledge quartet’. A total of 18 lessons from the four teachers were video-recorded across the 2013 and 2014 observations. The notion of ‘elaboration’ was used in this study as an interpretive lens to examine and characterise responsive teaching actions in the South African context, with the focus narrowing over the course of the PhD to contingency situations within the knowledge quartet framework, focused on responses to learner offers. In the South African literature, the terrain of elaboration is characterised by extensive gaps in teachers’ mathematical knowledge, incoherent talk, and frequent lack of evaluation of learners’ offers in the classroom. Using a grounded theory approach, I propose an ‘elaboration’ framework with three situations of responsive teaching (breakdown, sophistication and individuation/ collectivisation), which can be used as a tool to support the development of more responsive teaching in the South African context (and perhaps in other contexts where similar problems prevail). In this way, the study has contributed in terms of identifying some important ‘stages of implementation’ (Schweisfurth, 2011) that might be required to move towards the ideals of more responsive teaching that are described in the international literature, and yet remain distant from the realities of South African schooling. Using the three markers of shifts (extent, breadth and quality) in elaboration recruited in this study, drawn from the ways in which the dimensions of responsive teaching were conceptualised, I report on the different patterns of shifts in elaboration by the four teachers. The results of this analysis indicated that all four teachers made shifts in their responses to learners’ offers from 2013 to 2014 lessons in at least one or more dimensions of responsive teaching, in relation to extent, breadth and quality of elaborations. Findings from VSR interviews indicated associations between shifts in teachers’ reflective awareness, and shifts in responsive teaching actions. Theoretically, the study contributes through characterising responsive teaching actions in contexts of evidence of limited evaluation within the elaboration framework, with a language of description for identifying and developing more responsive teaching actions in a resource constrained context

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.