This study was conducted to determine if varying amounts of mathematics preparation and varying attitudes toward mathematics by teachers had a significant effect on the mathematics performance of their eighth grade students. Mathematics preparation was determined by the total number of college credits a teacher had accumulated and attitude toward mathematics was determined by a survey using the Revised Math Attitude Scale authored by Aiken and Dreger in 1961. In addition to mathematics preparation and attitude, the teacher characteristics of sex, age, years of experience, ethnicity, and type of certification were also observed and analyzed in relation to student performance. The sample population consisted of 30 eighth grade teachers from 10 middle schools in a large southwestern metropolitan school district and their 1,368 students. Student performance was measured by using the student math scores from the Iowa Test of Basic Skills. All variables in the study were tested at the .05 level of confidence using multiple regression and analysis of variance. None of the variables were significant predictors of student performance when the teachers were analyzed as an entire group. When divided into subgroups by student achievement levels, teachers with greater amounts of preparation had a significant effect at the .05 level of confidence with high achievement students; teachers with high attitudes toward mathematics had a significant effect at the .05 level of confidence for students of medium achievement. All other variables were insignificant for the subgroups. Conclusions were drawn that the individual teacher characteristics examined were not significant predictors of student performance unless students were grouped by achievement levels. This indicated that "more" in terms of math preparation for teachers or the concept of being a specialist at the middle school level was not a significant predictor of teacher effectiveness.

<p>The purpose of the study was to investigate prospective &lsquo / A&rsquo / level mathematics teachers&rsquo / knowledge of the concept of a function. The study was a case study of six prospective Zimbabwean teachers who were majoring in mathematics with the intention of completing a programme leading to certification as secondary mathematics teachers. At the time of the study the six prospective teachers were in their final year of study. Prospective teachers&rsquo / knowledge of the concept of a function was assessed through task-based interviews and reflective interviews. These interviews, which were done over a period of three months, were structured to capture the prospective teachers&rsquo / subject matter knowledge and pedagogical content knowledge for teaching the concept of a function. The interviews were also meant to capture the prospective teachers&rsquo / underlining pedagogical reasons for their choices of the examples, representations and teaching approaches when planning to teach the concept.</p> <p>As part of the study a theoretical framework for understanding prospective teachers&rsquo / knowledge of the concept of a function was developed. The framework, which was developed, was used as an analytical tool in analyzing prospective teachers knowledge of the concept of a function. The results of the study indicated that the prospective teachers had a process conception of a function although some of them had given a set-theoretic definition of a function in which a function is perceived as a mathematical object. They also confined the notion of a function to sets of real numbers. Functions defined on other mathematical objects (for example, the differential operator and the determinant function) were not considered as functions by five of the six prospective teachers.</p>

This study explores the nature of pre-service Mathematical Literacy teachers' problem solving with a focus on intra-mathematics and extra-mathematics connections, across two years (2011-2012). The pre-service teachers were enrolled into a new three-year Bachelor of Education course, Concepts and literacy in mathematics (CLM), at a large urban University in South Africa. The CLM course aimed specifically at developing the teachers' fundamental mathematical knowledge as well as contextual knowledge, which were believed to be key components in ML teaching. The fact that the course offered a new approach to professional teacher development in ML (pre-service), contrasting the old model (in-service) reported in ML-related literature in South Africa, where qualified teachers from other subjects were reskilled, coupled with the need to grow the pool of qualified ML teachers, provided a rationale for conducting this study. Data relating to the pre-service teachers' responses to assessment tasks within the course, and their school practicum periods focusing on classroom mathematical working, combined with pedagogical orientations, was collected. PISA's (OECD, 2010, 2013) dimensions of the mathematisation process provided the theoretical framework while Graven and Venkat's (2007a) pedagogic agendas were used to make sense of the pedagogic orientations in practice. The results relating to both learning and practice suggest that the teachers' knowledge relating to model formulation, an aspect of extramathematics connections, was weak across the two years. Nevertheless, improvements in ways in which the dimensions ofthe mathematisation process occurred were noted across the two years, with localised errors. In terms of pedagogic agendas foregrounded by the teachers in ML classrooms, results indicate that agenda 2 (content and context driven) and agenda 3 (mainly content driven) featured more than agenda 1 (context driven) which supports the rhetoric in the ML curriculum. Two implications to teacher training have been noted; first the need for a focus on correctly translating quantities from problem situations into mathematical models, and secondly, the need for promotion of provision of solution procedures with pedagogic links. This study offers two key contributions namely; extending knowledge relating to pre-service ML teacher training, and extending theory for understanding steps in problem solving to incorporate aspects of pedagogy.

The National Curriculum statement, or NCS for short, proposes significant shifts in the way that teachers carry out their work. Strategies, such as investigation and collaborative work were promoted as a reform model for effective teaching and learning. Thus, the intention of this research project is to determine how mathematics teachers are implementing the new reform in South Africa. Based on Sfard’s theory of commognitive development, a theoretical framework has been established and the focus specified in the following research questions: 1. How does a teacher mediate instruction during object-level & meta-level learning? 2. What enables and constrains her/his facilitative mediation in the case of Congruency in Grade 9? 3. What can we learn about the practical efficacy of Sfard’s discourse theory? In order to explore the actual teaching process the research project presents a case study constituted from two teaching practices on one topic, Congruency, at a College in Johannesburg. The purpose of observing and interviewing two teachers on the same lessons is to get a greater variety of conversation on object-level and meta-level learning. At the same time analysing their teaching process in-depth creates an opportunity to have different possibilities of mediating collaborative learning. The study addresses the three research questions through two related activities – non-participant observation and semi-structural interviews with teachers (in order to provide an opportunity for teachers to express their opinion). Two main findings can be summarized: Firstly, the way the teacher manages instruction originates from her/his teaching style. The data analysis clearly confirms that mediation of the two teachers on the topic Congruency does not differ according object-level and meta-level learning, but according to the teachers. The second finding is related with Sfard’s theoretical perspective: on the one hand the Department recommends investigative activities, whilst, on the other hand, Sfards’ theory states that reinvention by the learner is highly unlikely. Therefore the practical efficacy of Sfard’s theory is that in meta-level learning investigative activities are not appropriate and the role of the teacher should be dominant, not necessarily as facilitator. This research study is an empirical proof of the validity of Sfard’s theory and unspecified requirements of the Department of Education. KEYWORDS: object-level learning, meta-level learning, Congruency, Commognitive theory.

Orientador: Mara Sueli Simão Moraes / Banca: Nelson Antonio Pirola / Banca: Elizabeth Mattiazzo Cardia / Resumo: Um dos argumentos que impulsionam os atuais pesquisas relacionadas à educação e a formação continuada de professores são os resultados insatisfatórios apresentados pela escola pública nasavaliações em larga escala. A participação em duas pesquisas realizadas no Estado de São Paulo deu origem à presente dissertação. A primeira foi desenvolvida pelo grupo Pibid (Programa Institucional de Bolsa de Iniciação à Docência) da Capes, no ano de 2010, na qual foram investigados os possíveis problemas, relacionados ao ensinoo de ciências, enfrentados na escola pública. A segunda foi desenvolvida pelo grupo "Boas práticas Docentes no Ensino de Matemática" da Cesgranrio, em 2011, que se comparada com o primeira, apresentava um foco oposto, não apontando os problemas, mas evidenciando prática de ensino que estavam "dando certo" através da observação das aulas de 64 "bons professores" do Estado de São Paulo. Apesar de seres pesquisas diferentes, de grupos de pesquisa, distintos e realizadas em anos, também, diferentes, ambas preocuparam-se em analisar o desempenho dos alunos nas avaliações em larga escala. Partindo da experiência na primeira pesquisa, na qual identificamos alguns possíveis agravantes do ensino de matemática e ciências, e tendo observado o diferencial desses professores no ensino de matemática na segunda, a presente pesquisa segue uma ótica unificada. A Cesgranrio identificou 12 práticas de ensino que contribuem para um aprendizado de qualidade. Este trabalho, no entanto, tem por objetivo apontar os facilitadores e os agravantes que colaboram ou dificultam alcançar as boas práticas de ensino segundo os participantes da pesquisa da Cesgranrio, realizada em 2011. Para tanto, foi elaborado e aplicadoum questionário, com questões fechadas e abertas e 14 professores de Matemática do estado de São Paulo que participaram da pesquisa "Boas Práticas Docentes no Ensino de Matemática", que se prontificaram... / Abstract: One of the arguments which prompt current research related to education and the continuous training of teachers is the unsatisfactory results shown in public schools in wide scale assessments. This dissertation originated in the participation in two investigations carried out in the State of Sao Paulo. The first was carried out by Capes Pibid Program (ProgramaInstitutional de Bolsa de Iniciação à Docência - Institutional Program for the Initiation to Teaching Scholarship), in 2010, in which the possible problems faced by public shools related to the teaching of science were investigated. The second was developed by the Cesgranrio group "Good Teaching Practices in the Teaching of Mathematics" in 2011, which, if compared to the first, took the opposites slant, not pointing out the problems, but showing teaching practices which were "working out" through the observation of 64 classes taught by "good teachers" in the State of Sao Paulo. Although they were different investigations, of distinct research groups and carried out in different years, both took the trouble to analyze student performance in wide scale assessments. With the experience of the first investigation, in which we identified some possible aggravating factors in the teaching of mathematics and science as a stepping stone, and having observed the differences of the those teachers in the teaching of mathematics in the second, this research follows a joint approach. Cesgranrio identified 12 teaching practices which contribute to quality learning. This work, however, aims to point out the facilitators and the facilitators and aggravating factors which help towards or hinder good teaching practices in the Cesgranrio research, which took place in 2011. In order to do so, a questionnaire was elaborated and applied with open and closen questions put to 14 Sao Paulo Mathematics Teachers who took part in the research "Good Teaching Practices in the Teaching of Mathematics", who... / Mestre

This study focused on the mathematical content knowledge of prospective teachers in Iceland. The sample was 38 students in the School of Education at the University of Iceland, both graduate and undergraduate students. All of the participants in the study completed a questionnaire survey and 10 were interviewed. The choice of ways to measure the mathematical content knowledge of prospective teachers was grounded in the work of Ball and the research team at the University of Michigan (Delaney, Ball, Hill, Schilling, and Zopf, 2008; Hill, Ball, and Schilling, 2008; Hill, Schilling, and Ball, 2004), and their definition of common content knowledge (knowledge held by people outside the teaching profession) and specialized content knowledge (knowledge used in teaching) (Ball, Thames, and Phelps, 2008). This study employed a mixed methods approach, including both a questionnaire survey and interviews to assess prospective teachers' mathematical knowledge on the mathematical topics numbers and operations and patterns, functions, and algebra. Findings, both from the questionnaire survey and the interviews, indicated that prospective teachers' knowledge was procedural and related to the "standard algorithms" they had learned in elementary school. Also, findings indicated that prospective teachers had difficulties evaluating alternative solution methods, and a common denominator for a difficult topic within both knowledge domains, common content knowledge and specialized content knowledge, was fractions. During the interviews, the most common answer for why a certain way was chosen to solve a problem or a certain step was taken in the solution process, was "because that is the way I learned to do it." Prospective teachers' age did neither significantly influence their test scores, nor their approach to solving problems during the interviews. Supplementary analysis revealed that number of mathematics courses completed prior to entering the teacher education program significantly predicted prospective teachers' outcome on the questionnaire survey.Comparison of the findings from this study to findings from similar studies carried out in the US indicated that there was a wide gap in prospective teachers' ability in mathematics in both countries, and that they struggled with similar topics within mathematics. In general, the results from this study were in line with prior findings, showing, that prospective elementary teachers relied on memory for particular rules in mathematics, their knowledge was procedural and they did not have an underlying understanding of mathematical concepts or procedures (Ball, 1990; Tirosh and Graeber, 1989; Tirosh and Graeber, 1990; Simon, 1993; Mewborn, 2003; Hill, Sleep, Lewis, and Ball, 2007). The findings of this study highlight the need for a more in-depth mathematics education for prospective teachers in the School of Education at the University of Iceland. It is not enough to offer a variety of courses to those specializing in the field of mathematics education. It is also important to offer in-depth mathematics education for those prospective teachers focusing on general education. If those prospective teachers teach mathematics, they will do so in elementary school where students are forming their identity as mathematics students.

This dissertation explored how a professional developer, using the Center’s Professional Development Model for Innovating Instruction, supported two teachers’ acquisition of the knowledge needed for their mathematics instruction. Through analysis of detailed field notes and semi-structured interviews of two experienced elementary school teachers working in an urban, high-need school, this dissertation studied how the design and situate components of the Center’s Professional Development Model for Innovating Instruction can lead to multiple ways of supporting teachers’ instruction depending on the teachers’ needs and interests. Findings from these two case studies suggest that there is a need for teacher education mathematics programs—In-service and pre-service—to provide teachers with the knowledge for innovative mathematics instruction needed to create demanding learning experiences in their classrooms. This dissertation elaborates on these results, discusses connections with other research, and ends with implications of these results, in terms of their immediate application and the need for future research.

The new mathematical modeling standard found in the Common Core State Standards for Mathematics in 2010 immediately created a gap between teachers’ knowledge and the new curriculum. Mathematical modeling is a way of doing mathematics with which many teachers are not familiar. The trilogy of Teachers College Mathematical Modeling Handbooks (Handbooks) were created with this in mind and made to be used as a tool for teachers of mathematical modeling. This study utilized a professional development program to determine teachers’ perceptions of these Handbooks. This study used the qualitative case study approach with two active middle school teachers. Data were collected through researcher observations, journal entries of the two participants, and exit interviews. The data from this study show the two teachers found creating and working on their own models was the most useful activity in preparing to teach mathematical modeling. The teachers also reported positive perceptions toward reading background literature and being provided time to adapt the lesson modules from the Handbooks for their own classrooms. While the teachers did not utilize the theoretical structure provided in the third Handbook, they found the Handbooks, overall, to be an effective tool.

The purpose of this study was to determine the modes of acquisition of Shanghai elementary mathematics teachers’ pedagogical content knowledge within their communities of practice. This study uses the qualitative multiple-case study with a survey research approach with two teachers in two public elementary schools, one each from an urban and a suburban district of Shanghai. In total, forty-four teachers, four teaching research coordinators in the two districts and city, one university professor, and four school administrators were involved in the study. The study shows that Shanghai elementary mathematics teachers acquire and develop their pedagogical content knowledge through positive mentorship; active participation in Teaching Research Group activities in the schools, districts, and city; and informal and formal communications with their colleagues in their school communities. The teaching research coordinators help teachers to better understand the elementary mathematics curriculum, topics, and teaching materials, and students’ learning of mathematics. School policies encourage, support, and ensure that teachers’ professional learning and development occur through their participation within teacher-supported communities of practice. This study has implications for the teachers’ communities of practice, in that policy makers and school administrators should enable teachers to share their teaching practices to improve their mathematics pedagogical content knowledge, and therefore improve students’ learning of mathematics.

The goal of this study was to investigate whether mathematics teachers in Brazil had implicit gender biases, and if that potential bias was related to students' confidence and interest. The literature shows that there is a significant gender gap in mathematics achievement favoring boys, and Brazil is a special case in that it has one of the largest divergences in the world. This study investigated whether mathematics teachers in Brazil had implicit gender biases, if that bias was related to their students' confidence and interest in mathematics, and in what ways teachers' bias could be observed in conversations about teaching. For this study I surveyed 40 teachers, along with the students in one of each instructor’s mathematics classes. Teachers were asked to respond to a demographic questionnaire and implicit association test (IAT), while students were asked to respond to a questionnaire measuring their self-assessed confidence and interest in mathematics. At a later date, 10 teachers were selected to be interviewed, based on their IAT scores. The results show that mathematics teachers in Brazil had implicit gender biases regarding mathematics, but that their respective biases varied significantly. Male teachers were significantly biased in favor of boys, while female teachers were not. Teachers' implicit biases also varied depending on their educational levels. Students' confidence and interest in mathematics were shown not to be related to their teacher's measure of bias. However, confidence and interest did vary based on whether students attended public or private schools – with private schools having a significantly larger gender gap in both of these factors, and students' grade -- with the gap being wider among older students. Students' interest in mathematics also proved to be related to teachers' educational level, but their confidence in mathematics was not. Teachers in Brazil believe overall that girls and boys behave differently from each other in school; furthermore, they believe that these differences are due to societal and parental pressures and expectations regarding gender. Teachers who associated mathematics with boys did not appear to be aware of that implicit bias, and in conversation often referred to gender differences in a way that indicated they thought girls had advantages in school that boys did not.