This quasi-experimental study examined the effects of participation in a Supplemental Instruction (SI) program on student test performance in a second-level developmental mathematics class in a four-year university setting. This research deviated from past research on Supplemental Instruction in that it examined effects of the program at the end of each test block rather than at the end of the course only. The quasi-experimental design was precipitated by an inability to control factors of participation and limited sample size. Test data were analyzed using analysis of variance; final course grades were analyzed using chi-square.

To obtain information regarding the effects of two divergent thought processes used in a college mathematics course for prospective elementary school teachers, this study compared the effectiveness of an adaptation of the traditional, deductive teaching method with that of an inductive method reflecting the recommendations of the Committee on the Undergraduate Program in Mathematics. In the spring semester of 1973, two sections of Mathematics for Elementary Teachers I, at Cameron College, Lawton, Oklahoma, served as experimental groups to test the two adaptations. The course followed the Committee on the Undergraduate Program in Mathematics recommendations for a first course in mathematics for prospective elementary teachers.

This study is a description and analysis of the effect of criterion referenced test data on the acquisition of math skills and the mastery of selected objectives in fifth-grade students.The first chapter includes the introduction, statement of the problem, purposes of the study, statement of the hypotheses, background and significance., definition of terms, limitations, basic assumptions, and procedures for collecting data. The second chapter is a review of the literature pertaining to criterion-referenced testing and also includes a review of studies utilizing criterion-referenced test material. The third chapter describes the population being studied, the instruments used to measure achievement, and procedures for treatment of the data. The fourth chapter presents an analysis of the data collected for the study and a discussion of the findings. The fifth and final chapter presents a summary of the study, findings, conclusions, and recommendations pertaining to future research in the utilization of criterion- referenced testing. The subjects in this study were sixty, fifth-grade students attending Lakeland Elementary in the Lewisville Public School System who comprised the experimental group and sixty, fifth-grade students attending Central Elementary in the same district, who comprised the control group. The Comprehensive Test of Basic Skills (Form G Level 2), and the Prescriptive Mathematics Inventory (Aqua Level), were administered to both groups, with the pretest occurring in September, 1973 and the posttest being administered in April, 1974. Analysis of covariance and chi square goodness of fit were the techniques used to analyze the data statistically. Significant change was found to take place in the experimental group in mastering a greater proportion of the objectives selected for this study. The socio-economic level and educational background of the parents of the subjects in this study proved to be a significant factor in mastering the objectives selected for this study. The hypotheses utilizing the Comprehensive Test of Basic Skills, were all rejected. Two things may be assumed. The test may not have been sensitive enough to pick up changes that occurred during the year. Secondly, it might be assumed that the direction of the instructional program came from the 113 objectives selected by the teachers prior to the school year. These particular objectives were covered specifically in the Prescriptive Mathematics Inventory, but not in the Comprehensive Tests of Basic Skills.

Hersh (1986) states, "One's conception of what mathematics is affects one's conception of how it should be presented. One's manner of presenting it is an indication of what one believes to be most essential in it." In this research study, three hundred ninety-seven urban early childhood teachers were given a survey that examined their attitudes toward mathematics and mathematics teaching, their views of mathematics, views of teaching mathematics, and views of children learning mathematics. The purpose of this study was to identify the attitudes and beliefs of early childhood teachers in two urban school districts to determine if mathematics reform efforts made a difference in teachers' attitudes and beliefs about mathematics and its teaching. Questionnaires were mailed directly to teachers in one school district and principals distributed questionnaires in the other. Summary scores were calculated for parts of the instrument. The researcher performed descriptive statistics, comparative analysis, and conducted frequency distributions, t-tests, ANOVA, and Pearson Correlations. Findings revealed that teachers with 30 or more years of teaching experience had more positive attitudes toward mathematics than teachers with 1-3 years of experience. African American teachers had more positive attitudes toward mathematics and its teaching than other ethnic groups. Teachers who held a minor or major in mathematics had more positive attitudes toward mathematics and its teaching than teachers without a minor or major in mathematics. Teachers in District-A favored constructivist learning while teachers in District-B favored rote learning. Both school districts' teachers favored the problem-solving approach to teaching mathematics. If instruction is to be transformed, reformers need to understand teachers' beliefs about mathematics. Beliefs, which are essential for teachers' development, seldom change without significant intervention (Lappan and Theule-Lubienski, 1994). Therefore, school districts must be informed about the changes necessary for the reform of mathematics teaching and identify and implement through staff developments and other measures what they perceive mathematics to be and how it should be taught.

Complex systems abound on this planet, in the composition of the human body, in ecosystems, in social interaction, in political decision-making, and more. Analytical methods allowing us to better understand how these systems operate and, consequently, to have a chance to intervene and change the undesirable behavior of some of the more pernicious systems have developed and continue to be enhanced via quickly changing technology. Some of these analytical methods are accessible by pre-college students, but have not been widely used at that level of education. Jay Forrester, the founder of one of the methodologies, System Dynamics (SD), used to study complex system behavior involving feedback, laments the lack of understanding of complex systems evident in short-sited decisions made by legislators -- global climate change and fiscal policies being cases in point. In order to better prepare future decision makers with tools that could allow them to make more informed decisions about issues involving complex systems efforts have been underway to increase pre-college teacher understanding of the SD method. The research described in this dissertation introduces the mathematics education community to the value of System Dynamics modeling in pre-college algebra classes, indicates a path by which a traditional mathematics curriculum could be enhanced to include small SD models as a new representation for elementary functions studied in algebra classes, and provides an empirical study regarding conceptual understanding of functions by students. Chapter 2 indicates the numerous beneficial learning outcomes that empirical studies have shown accompany model-building activities. Chapter 3 indicates the need for students to become familiar with complex systems analysis, how SD modeling (one method of complex systems analysis) aligns with the Common Core State Standards in Mathematics, and the work that has transpired over the past two decades using SD in K-12. Chapter 4 focuses on the importance of the concept of function in high school mathematics, some limitations of exclusive reliance on the closed form equation representation for mathematizing problems and the SD stock/flow representations of some of the elementary functions that are studied in algebra classes. Chapter 5 looks at the issues affecting two traditional teachers and the challenges they faced when trying to reintroduce SD modeling into their algebra classes. Chapter 6 explains the student component of the classroom experiment that was conducted by the teachers who are highlighted in Chapter 5. The analysis of the results of student model-building activities in the two classroom studies that are part of the third paper did not indicate a statistical difference between the two experimental groups and the two control groups. Many environmental and scheduling issues conspired to adversely affect the experiment. However, positive outcomes were evident from the two pairs of students who were videotaped while they built the final multi-function drug model, the final student lesson in the experiment. Research focused on student outcomes is needed to further assess the strengths and weakness of the SD approach for student learning in mathematics.

In view of the National Plan for Higher Education (Department of Education, 2001) that calls for an increased throughput of students at higher education institutions within South Africa, a quantitative study was undertaken at a particular higher education institution during 2005 to identify factors associated with achievement in mathematics at entry level to tertiary studies. Factors considered in this study pertained specifically to those that may facilitate the introduction of intervention aimed at assisting students enrolled for mathematics at tertiary level and who are at risk of failing. Students admitted to either a degree or extended degree programme in science, engineering and technology (SET) in 2005 at the higher education institution constituted the target population. A survey was conducted at the onset of the academic year among students in the target population providing written consent to participate in the study. Three pen-and-paper questionnaires were administered, i.e. a background questionnaire, a newly developed cognitive instrument for the measurement of basic mathematical skills, including mathematics language proficiency, and an adapted instrument, based on an existing standardised instrument, the Study Orientation in Mathematics (SOM) instrument (Maree, Prinsloo & Claassen, 1997), for the measurement of the affective and behavioural domains related to the studying of mathematics. Information regarding student achievement at the end of their first semester of study was obtained from student academic records. Background variables, in particular being an English second language (ESL) student and having received home language tuition at school were shown to be associated with the initial preparedness of students, i.e. their Grade 12 achievement. These variables did not, however, directly contribute towards the prediction of achievement at entry level to the institution. The extent to which students have acquired basic mathematical skills, particularly mathematical language proficiency (not necessarily reflected in their Grade 12 results) was shown to contribute significantly towards the prediction of achievement in mathematics at entry level. In addition, anxiety and attitude towards mathematics and the utilisation of effective study behaviour were also shown to be associated with achievement; the latter contributing significantly towards the prediction of achievement at entry level for both degree and extended degree programme students. The findings culminated in recommendations for tertiary institutions, educators and those embarking on future research relating to the theme in question. The issue of measuring basic mathematical skills, including mathematical language proficiency and study strategies of students studying towards careers in SET at the onset of their studies and providing support to improve these, is emphasised. / Prof. J. Strauss

M.Ed. (Didactics Mathematics) / Mathematical literacy is essential for functioning effectively in a technological society. Many occupations which may appeal to young people require mathematical ability as a prerequisite. By establishing factors which contribute to a pupil's difficulties within a subject, teachers are better able to assist these pupils ...

Making the transition from calculus to advanced calculus/real analysis can be challenging for undergraduate students. Part of this challenge lies in the shift in the focus of student activity, from a focus on algorithms and computational techniques to activities focused around definitions, theorems, and proofs. The goal of Realistic Mathematics Education (RME) is to support students in making this transition by building on and formalizing their informal knowledge. There are a growing number of projects in this vein at the undergraduate level, in the areas of abstract algebra (TAAFU: Larsen, 2013; Larsen & Lockwood, 2013), differential equations (IO-DE: Rasmussen & Kwon, 2007), geometry (Zandieh & Rasmussen, 2010), and linear algebra (IOLA: Wawro, et al., 2012). This project represents the first steps in a similar RME-based, inquiry-oriented instructional design project aimed at advanced calculus. The results of this project are presented as three journal articles. In the first article I describe the development of a local instructional theory (LIT) for supporting the reinvention of formal conceptions of sequence convergence, the completeness property of the real numbers, and continuity of real functions. This LIT was inspired by Cauchy's proof of the Intermediate Value Theorem, and has been developed and refined using the instructional design heuristics of RME through the course of two teaching experiments. I found that a proof of the Intermediate Value Theorem was a powerful context for supporting the reinvention of a number of the core concepts of advanced calculus. The second article reports on two students' reinventions of formal conceptions of sequence convergence and the completeness property of the real numbers in the context of developing a proof of the Intermediate Value Theorem (IVT). Over the course of ten, hour-long sessions I worked with two students in a clinical setting, as these students collaborated on a sequence of tasks designed to support them in producing a proof of the IVT. Along the way, these students conjectured and developed a proof of the Monotone Convergence Theorem. Through this development I found that student conceptions of completeness were based on the geometric representation of the real numbers as a number line, and that the development of formal conceptions of sequence convergence and completeness were inextricably intertwined and supported one another in powerful ways. The third and final article takes the findings from the two aforementioned papers and translates them for use in an advanced calculus classroom. Specifically, Cauchy's proof of the Intermediate Value Theorem is used as an inspiration and touchstone for developing some of the core concepts of advanced calculus/real analysis: namely, sequence convergence, the completeness property of the real numbers, and continuous functions. These are presented as a succession of student investigations, within the context of students developing their own formal proof of the Intermediate Value Theorem.

Orientador: Marcus Vinicius Maltempi / Banca: Idania Blanca Peña Grass / Banca: Rosana Giaretta Sguerra Miskulin / Resumo: Esta pesquisa tem por objetivo compreender e investigar as inter-relações do uso das Tecnologias de Informação e Comunicação e alguns conceitos da teoria de Vasili Davydov, que propõe o desenvolvimento do pensamento teórico de um determinado conteúdo/fenômeno em estudo. Este pensamento caracteriza-se por priorizar a essência dos conteúdos/fenômenos por meio da análise das condições de sua origem e desenvolvimento. A pesquisa, que é de cunho bibliográfico, procura compreender a proposta do autor para o ensino de Matemática. Para alcançarmos o objetivo da pesquisa nos propomos a desenvolver exemplos que mostram a possibilidade de desenvolver um trabalho voltando o olhar para a essência de conceitos por meio do uso de tecnologias, em especial, o computador com software. Destacamos a importância do papel do professor como mediador dos processos de ensino e aprendizagem pautados na teoria de Davydov, conduzindo e proporcionando o desenvolvimento dos conceitos científicos por meio de atividades de ensino orientadas para a observação da essência dos conceitos / Abstract: This research aims to understand and investigate the interrelationships of the use of Information and Communication Technologies and some concepts of the theory of Vasili Davydov, which proposes the development of theoretical thinking of a particular content/phenomenon under study. This thought is characterized by prioritizing the essence of the contents/phenomena through the analysis of the conditions of its origin and development. The research, which is a bibliographical nature, the proposal seeks to understand the author for teaching mathematics. To achieve the research objective, we propose to develop examples that show the possibility of developing a job turning his gaze to the essence of concepts through the use of technology, in particular computer with software. We stress the importance of the teacher's role as mediator of the teaching and learning guided theory of Davydov, leading and encouraging the development of scientific concepts through targeted education activities to observe the essence of concepts / Mestre

Orientador: Renata Zotin Gomes de Oliveira / Banca: Suzete Maria Silva Afonso / Banca: Wladimir Seixas / Resumo: A Matemática Financeira está presente na vida de todos os cidadãos e grande parte deles não tem conhecimento necessário para ter um controle financeiro, tomar decisões como comprar à prazo ou guardar dinheiro para comprar à vista. O objetivo desse trabalho é ressaltar a importância do estudo da Matemática Financeira no Ensino Médio, trazendo uma proposta de ensino para tratar desse assunto através do uso de um software educacional livre. Espera-se com isso motivar e despertar o interesse dos alunos para esse assunto que é de extrema importância e que vai refletir no cotidiano deles e de seus familiares / Abstract: Financial Mathematics is present in the life of all citizens and most of them do not have the necessary knowledge to have a financial control, making decisions about how to pay on installments or save money for payment in cash. The objective of this study is to highlight the importance of the Financial Mathematics study in high school, bringing a teaching proposal to address this issue through the use of a free educational software. It is expected, therefore, motivate and arouse the interest of students to this issue that is of utmost importance and that will reflect in the daily lives of them and their families / Mestre