This ethnographic study investigated teacher leadership and professional learning in a secondary mathematics department. Qualitative data were collected through in-depth face-to-face interviews, observations, and document analysis. It is the social aspect of the school environment and specifically, the subject department, which presents an opportunity for teachers to learn and share their expertise with one another in an informal setting and for teacher leaders to emerge using their expertise and close proximity to affect the learning of colleagues. Teachers were asked to share their thoughts on leadership and learning within their department. A narrative was written to give the reader a better understanding of the day-to-day practices, behaviors, and habits of the teachers in the department, creating a holistic picture of the culture studied. ... teacher leadership is experienced informally through teachers sharing and talking about their practice. Teacher leadership is also experienced outside the department when teachers have opportunities to lead school professional development seminars and to practice leadership through role modeling. Professional learning is experienced one-on-one, as well as formally and informally through colleagues and organized workshops. Implications for administrators, department and team leaders, and policy implementation are discussed. This study may contribute to the development of teacher leadership and professional learning, which ultimately may lead to improving student achievement. / by Christine Higgins. / Thesis (Ph.D.)--Florida Atlantic University, 2013. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.

Education plays a vital role in any society; so much so, that countries strive to have not only adequate, but excellent educators in their classrooms. The aim of this study was to understand how beginning secondary mathematics teachers define success and to what experiences they attribute that success. Specifically, the central research question addressed was, "To what degree were significant attributes or experiences, important to the success of the first year teaching, learned pre-teacher education program, during a program, or post-program?" The practical goal of filling classrooms with great educators needs to be informed by research on how best to recruit highly qualified candidates into the field of mathematics education and how best to facilitate the teacher preparation process. This study employed a mixed methodology, using a sample of beginning secondary mathematics teachers to gather both quantitative and qualitative data on when they reported gaining influential knowledge or experiences. In particular, input from those who have had some success as beginning mathematics teachers was desired. The interview protocol designed for these participants added depth to the survey responses. Emphasis was placed on the relative importance of the three stages, pre-, during, and post-program, in developing common attributes associated with good teaching. Two characteristics were generally discussed as developing pre-program: being a self-starting and hard-working individual, and holding a belief that every student can learn. Beginning teachers viewed these traits as important for their success. Participants also felt that they acquired both practical classroom tools and educational theory from their teacher education program; having program instructors model pedagogy and mathematical instruction, and having opportunities to practice incorporating theory into their teaching were also seen as important. These aspects distinguished particularly prominent roles that the teacher education program played in shaping its graduates. Classroom management and being flexible and adaptive to different contexts were the most notable qualities frequently reported as being learned post-program. The study's results have implications for informing the types of students a mathematics education program should try to attract or recruit and defining areas where practicum or internship components might be incorporated into the teacher education process.

What is good mathematics teaching? The answer depends on whom you are asking. Teachers, researchers, policymakers, administrators, and parents usually provide their own view on what they consider is good mathematics teaching and what is not. The purpose of this study was to determine how beginning teachers define good mathematics teaching and what they report as being the most important attributes at the secondary level. This research explored whether there was a relationship between the demographics of the participants and the attributes of good teaching. In addition, factors that influence the understanding of good mathematics teaching were explored. A mixed methodology was used to gather information from the research participants regarding their beliefs and classroom practices of good mathematics teaching. The two research instruments used in this study were the survey questionnaire and a semi-structured interview. Thirty-three respondents who had one to two years of classroom experience comprised the study sample. They had graduated from a school of education in an eastern state and had obtained their teacher certification upon completing their studies. The beginning mathematics teachers selected these four definitions of good teaching as their top choices: 1) have High Expectations that all students are capable of learning; 2) have strong content knowledge (Subject Matter Knowledge); 3) create a Learning Environment that fosters the development of mathematical power; and 4) bring Enthusiasm and excitement to classroom. The three most important attributes in good teaching were: Classroom Management, Motivation, and Strong in Content Knowledge. One interesting finding was the discovery of four groups of beginning teachers and how they were associated with specific attributes of good mathematics teaching according to their demographics. Beginning teachers selected Immediate Classroom Situation, Mathematical Beliefs, Pedagogical Content Knowledge, and Colleagues as the top four factors from the survey analysis that influenced their understanding of good mathematics teaching. The study's results have implications for informing the types of mathematical knowledge required for pre-service teachers that can be incorporated into teacher education programs and define important attributes of good mathematics teaching during practicum.

Over the last few decades school accountability for student performance has become an issue at the forefront of education. The federal No Child Left Behind Act of 2001 (NCLB) and various regulations by individual states have set standards for student performance at both the district and individual public and charter school levels, and certain consequences apply if the performance of students in an institution is deemed unsatisfactory. Conversely, rewards come to districts or schools that perform especially well or make a certain degree of improvement over their earlier results. Albeit with certain conditions, the federal government makes additional education money available to the states under NCLB. While testing is nothing new in American public education, the concept of district/school accountability for performance is at least relatively so. In New York City, where New York State Regents Examinations (NYSRE) have been a measure of student performance for many years, scores on these tests are low, often preventing students from receiving course credit, which in turn results in failure to graduate on schedule. In addition, rates of graduation from public high schools are low. The city and state have kept data on student performance broken out by a number of factors including socioeconomic status, ethnicity, attendance, and gender which point to an achievement gap among different groups. This study investigates a series of those factors associated with the mastery of high school Algebra, Geometry, and Trigonometry. This study concerns itself specifically with the effect that gender, socioeconomic status, attendance, and ethnicity may have on student achievement in a mathematics course and on standardized tests, specifically the NYSRE, an annual rite of passage for students in grades 9 through 11. This research considered and ran tests on data gathered from a single large New York City high school. In this study, a 12 two-way (between-groups) univariate analyses of variance (ANOVAs) were conducted to assess whether there were differences in students' mathematics achievement scores by gender, ethnicity, attendance, and family socio-economic status (SES). In addition, three Pearson correlation analyses were conducted to determine whether there was a correlation among Integrated Algebra, Geometry, and Algebra II/Trigonometry unit examination scores and Regents scores. Nine Pearson correlation analyses were conducted to determine whether there was a correlation between Regents scores and mathematics achievement unit examination scores. A correlation was run between each mathematics achievement score with the Regents score from each subject. Six two-way (between-groups) ANOVA were also conducted to assess whether there were difference in students' mathematics achievement among Black males, Black females, Hispanic males, and Hispanic females. Data were gathered, merged, and transferred into a Statistical Package for the Social Sciences (SPSS) 19.0 (IBM, 2010) for analysis. The findings indicate that attendance and family SES have a meaningful relationship to mathematics achievement in the New York City public high school which was the subject of this investigation. On the other hand, gender and ethnicity showed no relationship to students' mathematics achievement. As an implication of this research, school policies must focus more on the achievement gap of students from low-SES families and must encourage students to maintain good attendance. Students should have access to different forms of academic interventions that go beyond after-school or Saturday tutoring; academic intervention services; community counseling or mediation; or peer intervention or peer counseling through which students learn basic mathematics skills from each other to achieve college readiness.

The release of the Common Core State Standards for Mathematics in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by teachers about mathematical models and modeling in order to aid in the development of teacher education and professional development programs. The study used a mixed methods approach. Quantitative data were collected through an online survey of a large sample of practicing and prospective secondary teachers of mathematics in the United States. The purpose of this was to gain an understanding of the conceptions held by the general population of United States secondary mathematics teachers. In particular, basic concepts of mathematical models, mathematical modeling, and mathematical modeling in education were analyzed. Qualitative data were obtained from case studies of a small group of mathematics teachers who had enrolled in professional development which had mathematical models or modeling as a focus. The purpose of these case studies was to give an illustrative view of teachers regarding modeling, as well as to gain some understanding of how participating in professional development affects teachers' conceptions. The data showed that US secondary mathematics teachers hold several misconceptions about models and modeling, particularly regarding aspects of the mathematical modeling process. Specifically, the majority of teachers do not understand that the mathematical modeling process always requires making choices and assumptions, and that mathematical modeling situations must come from real-world scenarios. A large minority of teachers have misconceptions about various other characteristics of mathematical models and the mathematical modeling process.

This study analyzed the mathematical problem solving behavior of mathematically gifted students. It focused on a specific fourth step of Polya's (1945) problem solving process, namely, looking back to find alternative approaches to solve the same problem. Specifically, this study explored problem solving using many different approaches. It examined the relationships between students' past mathematical experiences and the number of approaches and the kind of mathematics topics they used to solve three non-standard mathematics problems. It also analyzed the aesthetic of students' approaches from the perspective of expert mathematicians and the aesthetic of these experts' preferred approaches from the perspective of the students. Fifty-four students from a specialized high school were selected to participate in this study that began with the analysis of their past mathematical experiences by means of a preliminary survey. Nine of the 54 students took a test requiring them to solve three non-standard mathematics problems using many different approaches. A panel of three research mathematicians was consulted to evaluate the mathematical aesthetic of those approaches. Then, these nine students were interviewed. Also, all 54 students took a second survey to support inferences made while observing the problem solving behavior of the nine students. This study showed that students generally were not familiar with the practice of looking back. Indeed, students generally chose to supply only one workable, yet mechanistic approach as long as they obtained a correct answer to the problem. The findings of this study suggested that, to some extent, students' past mathematical experiences were connected with the number of approaches they used when solving non-standard mathematics problems. In particular, the findings revealed that students' most recent exposure of their then-AP Calculus course played an important role in their decisions on selecting approaches for solution. In addition, the findings showed that students' problem solving approaches were considered to be the least "beautiful" by the panel of experts and were often associated with standard approaches taught by secondary school mathematics teachers. The findings confirmed the results of previous studies that there is no direct connection between the experts' and students' views of "beauty" in mathematics.

Given the impact of computers and computing on almost every aspect of society, the ability to develop, analyze, and implement algorithms is gaining more focus. Algorithms are increasingly important in theoretical mathematics, in applications of mathematics, in computer science, as well as in many areas outside of mathematics. In high school, however, algorithms are usually restricted to computer science courses and as a result, the important relationship between mathematics and computer science is often overlooked (Henderson, 1997). The mathematical ideas behind the design, construction and analysis of algorithms, are important for students' mathematical education. In addition, exploring algorithms can help students see mathematics as a meaningful and creative subject. This study provides a review of the history of algorithms and algorithmic complexity, as well as a technical monograph that illustrates the mathematical aspects of algorithmic complexity in a form that is accessible to mathematics instructors at the high school level. The historical component of this study is broken down into two parts. The first part covers the history of algorithms with an emphasis on how the concept has evolved from 3000 BC through the Middle Ages to the present day. The second part focuses on the history of algorithmic complexity, dating back to the text of Ibn al-majdi, a fourteenth century Egyptian astronomer, through the 20th century. In particular, it highlights the contributions of a group of mathematicians including Alan Turing, Michael Rabin, Juris Hartmanis, Richard Stearns and Alan Cobham, whose work in computability theory and complexity measures was critical to the development of the field of algorithmic complexity. The technical monograph which follows describes how the complexity of an algorithm can be measured and analyzes different types of algorithms. It includes divide-and-conquer algorithms, search and sort algorithms, greedy algorithms, algorithms for matching, and geometric algorithms. The methods used to analyze the complexity of these algorithms is done without the use of a programming language in order to focus on the mathematical aspects of the algorithms, and to provide knowledge and skills of value that are independent of specific computers or programming languages. In addition, the study assesses the appropriateness of these topics for use by high school teachers by submitting it for independent review to a panel of experts. The panel, which consists of mathematics and computer science faculty in high school and colleges around the United States, found the material to be interesting and felt that using a pre-programming approach to teaching algorithmic complexity has a great deal of merit. There was some concern, however, that portions of the material may be too advanced for high school mathematics instructors. Additionally, they thought that the material would only appeal to the strongest students. As per the reviewers' suggestions, the monograph was revised to its current form.

The research reported in this study examined statistical relations in black adolescents’ identity and self-efficacy beliefs in mathematics. Data for this research study were drawn from the High School Longitudinal Study of 2009 (HSLS:09; Ingels, Dalton, Holder, Lauff, & Burns, 2011) and the study’s first follow-up (Ingels & Dalton, 2013); additional measures were taken from the National Center for Education Statistics’ Common Core of Data (CCD). Data were analyzed using quantitative methods on a nationally representative sample of secondary school students (N = 1,362) across 944 schools in the United States. Although there has been an increase in qualitative research on mathematics identity and mathematics identity development, few researchers have utilized quantitative methods to empirically examine the relationships existing between identity and self-efficacy. Fewer researchers have used panel (longitudinal) data in their investigations. Findings from this study confirmed the literature in that mathematics identity development pathways are informed by students’ mathematics self-efficacy beliefs. Sex differences were also noted. Specifically, males and females experienced divergence in their mathematics identity and mathematics self-efficacy beliefs during high school; however, the returns of these beliefs on a measure of Algebraic proficiency for females were significantly greater than they were for males, although females maintained less positive beliefs over the course of the study. School belonging and engagement significantly predicted shifts in students’ mathematics identity development pathways and were moderated by self-efficacy beliefs, supporting theories that measures of perceived differentiation (e.g., belongingness) are key factors in student motivation and subsequent outcomes. Additional findings underscored the ongoing need for empirical research on students’ peer networks and mathematics teacher’s classroom practices. Overall, results of this study indicated that variations in identity development and self-efficacy beliefs among adolescents extend beyond many theoretical considerations in both their complexity and measured effects when accounting for a host of contextual and psychosocial factors.

The purpose of this research was to identify if 1) there is a difference in student achievement between students who use the GeoLeg manipulative tool and students who use a traditional compass, protractor, and ruler on the same geometry unit; 2) there is a difference in student achievement between the genders between those who use the GeoLeg manipulative tool and those students who do not; and 3) there is a relationship between identified learning styles and student achievement on a geometry unit posttest after using the GeoLeg manipulative tool. There were 317 students in the study. The research found that students using the GeoLeg manipulative tool produced significantly better student performance on a posttest in this particular school setting. Although these results cannot be generalized to other school sites, it is plausible that these results could generalize to school sites whose demographics are similar. The research findings revealed that there was no statistically significant difference between male and female students within the treatment group. The significant finding is that the GeoLeg manipulative tool appears to work equally well with both genders. None of the learning styles, as identified by the Honey and Mumford Learning Styles Questionnaire, were correlated with student posttest score achievement on the tested geometry unit. In addition, there was no evidence to suggest that a student's learning style moderates the effectiveness of the use of the GeoLeg manipulative tool. There is no evidence to suggest that the effectiveness of the GeoLeg manipulative tool is any different depending upon the student's gender or learning style. The results of this research provide strong support for the use of the GeoLeg manipulative tool for improving student performance. Further research is needed to confirm these results in similar and different populations. / by Phyllis Pacilli. / Thesis (Ed.D.)--Florida Atlantic University, 2010. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2010. Mode of access: World Wide Web.

In the United States students have traditionally struggled with mathematics. Many students leave the educational system with limited mathematical literacy that can adversely affect their success as a college student, a consumer and citizen. In turn, lack of mathematical literacy affects their socioeconomic status. Through improving their mathematical literacy, students can be more successful not only in mathematics but, it seems in many aspects of their lives. Many researchers have defined mathematical literacy; yet, we need to understand more about how mathematical literacy develops. This study explores a model that identifies four key components that seem to be associated with the development and sustainability of mathematical literacy. When mathematical capital is viewed through the theoretical frame of reciprocal determinism, the nonlinear effects may contribute to the development of mathematical capital leading to a solid foundation for mathematical literacy. The purpose of this study was to describe and explain in what ways successful mathematics high school student attributes, abilities and experiences contribute to the development of mathematical capital that seems to be a foundation for mathematical literacy. The participants were a representative sample of seven diverse freshman high school students from an urban high school in the Pacific Northwest United States who are successful in mathematics as determined by grades in first term freshman mathematics courses and standardized test scores. Data collected included a survey, an achievement test, and interviews. Results from the mixed methods case study seemed to indicate that successful mathematics students have the four components of the proposed model of mathematical capital. The four proposed components are: (a) a positive mathematical self-esteem, (b) a working toolkit of mathematical skills and content knowledge and the application of that knowledge, (c) a problem-solving mindset, and (d) access to a support network. Implications for mathematics instruction are included. Future research needs to address how the four components interact so that more students can experience success in mathematics and become mathematically literate.