The purpose of this study is to investigate the relationship of elementary teachers' use of manipulative materials for mathematics instruction with teachers' hands-on training in the use of manipulative materials, their attitude toward mathematics and using manipulatives and school climate. The study was undertaken to predict what variables contribute to teachers' use of manipulative materials. / Research shows that mathematics educators recognize the importance of using manipulative materials in teaching elementary school mathematics. However, many teachers do not use them, and many pupils do not understand the meaning behind the mathematics they are being taught. / The researcher predicted that teacher variables (the amount and recency of hands-on mathematics training with active involvement with manipulative materials, teacher attitudes toward mathematics and manipulatives, grade level and teaching experience) and school variables (principal attitudes, district policy, school climate, and number of years at a school) will account for a significant amount of the variance in teacher's use of manipulative materials for mathematics instruction. / A random sample of 172 teachers, 15 assistant principals and 15 principals from fifteen schools were chosen from three Florida counties to answer questionnaires concerning their own attitudes, school climate and district policy toward using manipulatives. The researcher visited classrooms of all participating teachers with a checklist, to observe the presence of manipulative materials, where materials were placed and evidence of children's products that showed understanding through active involvement with materials. / Pearson correlations and multiple regression were used to analyze the data. All tests required a significance level of.05. Recency of training, attitude toward using manipulatives, attitude toward mathematics, grade level and district policy were significant in the regression model. Recency and amount of training correlated highly and were believed to measure the same characteristics. / Findings indicate that of the variables studied, recent training in the use of manipulatives contributes significantly to classroom use of manipulative materials. This study lends support for ongoing inservice training or University training with hands-on instruction in the use of manipulatives for teachers at all elementary levels. / Source: Dissertation Abstracts International, Volume: 49-10, Section: A, page: 2927. / Major Professor: Kathryn Scott. / Thesis (Ph.D.)--The Florida State University, 1988.

The purpose of this study was to investigate in-depth visually handicapped children's understanding of the length measurement concept. The concept was investigated using four assessment devices that included the Transitivity of Length, Conservation of Length, Written Length Assessment, and Functional Length Assessment. Both quantitative and qualitative data were obtained on all the assessments. Twenty-four children participated in the study, 7 braille readers, 7 large print readers, and 10 regular print readers who were included for purposes of comparison. / The data were analyzed to determine if there was a difference between the three vision groups on each of the four assessments. The vision groups were then divided into high and low scorers on each of the four assessments to determine if there was any difference between high and low scorers by vision group on each of the four assessments. Overall, regular print readers had the least difficulty with the tasks and large print readers the most difficulty. Vision seemed to account for the differences rather than age. / Source: Dissertation Abstracts International, Volume: 51-12, Section: A, page: 4083. / Major Professor: Pearl E. Tait. / Thesis (Ph.D.)--The Florida State University, 1990.

Source: Dissertation Abstracts International, Volume: 37-10, Section: A, page: 6327. / Thesis (Ph.D.)--The Florida State University, 1976.

Spatial ability has been the subject of mathematics education research because of the implications it has in the areas of problem solving, student cognition, and success in learning mathematics. This study investigated two questions related to student spatial ability: (1) What are the differences in reasoning between students with high spatial abilities and those with low spatial abilities, and what differences in these reasoning processes can be inferred using student interactions with a three-dimensional computer graphics program? (2) What are the differences in spatial strategies of the students as they engage in the three-dimensional graphing activities? / The subjects were third year college students in a teacher education program, and were enrolled in a mathematics teacher education course at the time. They were observed during lessons in three-dimensional graphing using a program, named Jellyfish Logo, which was created by myself. They attempted tasks such as representation of a rectangular solid, a tetrahedron, and a triangular prism. In addition to these representations they completed a series of lessons designed to test both their spatial and their problem solving abilities. These lessons included area and volume estimations and the location of both two- and three-dimensional objects in space. / There were several observable results from this study. One of these was that there is, in an environment such as this, a forced integration of verbal/symbolic and graphic representations. It was necessary for the subject to have verbal/symbolic skills in order to construct the desired graphic representations. Another result of this study is that there is a direct relationship between the amount of anticipation/reflection and student success in completing a task. The results of this study indicate that it is imperative that educators emphasize the importance of anticipation and reflection in problem solving. / Source: Dissertation Abstracts International, Volume: 53-03, Section: A, page: 0747. / Major Professor: Janice Flake. / Thesis (Ph.D.)--The Florida State University, 1992.

A case study approach was used to explore second-chance mathematics through two larger courses and one individual study program. A different teaching approach, by committed experienced teachers, was used in each course. In evaluating their effectiveness, I focused on affective change in the students, relating this to their achievement. This study contributes to research on understanding good teaching of mathematics to adults. Qualitative and quantitative data were collected over several years. Methods included: a questionnaire (including mathematics attitude and belief scales as well as demographic and open questions); interviews with students to gather more affective data and explore their reactions to the course approach; and the individual supervised study course was audio-taped for six months. Teachers of the larger courses were also interviewed about their goals for, and experiences with, the students. These multiple strands of evidence provide a complex overall picture of three, largely successful, teaching approaches. Each measure had its own contribution to make, and taken together they illuminated the ways in which affective change was related to ackevement in the three contexts. The higher achieving groups in each of the two larger courses entered the courses with more positive attitudes and beliefs than the lower achieving groups and subsequent affective changes reinforced these differences. The lower achieving groups completed the courses affectively worse off than when they started, Students' reactions to these approaches were compared and found to reflect the nature of the approach. In addition to this finding, successhl students' beliefs about mathematics changed in two of the courses. In the one-to-one course the teacher focused initially on understanding the students' fear of mathematics and early mathematical experiences. The student-focused teaching approach trusted and encouraged the growth of ths student's mathematical thinking. Six months later the student felt empowered and had come to believe that mathematics as a creative and enjoyable process of discovering patterns. The second course focused on the mathematization of realistic situations. Successful students came to regard mathematics as useful, interesting, relating to real life. Successful students in the third course appreciated the carefully structured reintroduction to mathematics and were pleased they could finally do the mathematics they hadn't been able to understand at high school.

A case study approach was used to explore second-chance mathematics through two larger courses and one individual study program. A different teaching approach, by committed experienced teachers, was used in each course. In evaluating their effectiveness, I focused on affective change in the students, relating this to their achievement. This study contributes to research on understanding good teaching of mathematics to adults. Qualitative and quantitative data were collected over several years. Methods included: a questionnaire (including mathematics attitude and belief scales as well as demographic and open questions); interviews with students to gather more affective data and explore their reactions to the course approach; and the individual supervised study course was audio-taped for six months. Teachers of the larger courses were also interviewed about their goals for, and experiences with, the students. These multiple strands of evidence provide a complex overall picture of three, largely successful, teaching approaches. Each measure had its own contribution to make, and taken together they illuminated the ways in which affective change was related to ackevement in the three contexts. The higher achieving groups in each of the two larger courses entered the courses with more positive attitudes and beliefs than the lower achieving groups and subsequent affective changes reinforced these differences. The lower achieving groups completed the courses affectively worse off than when they started, Students' reactions to these approaches were compared and found to reflect the nature of the approach. In addition to this finding, successhl students' beliefs about mathematics changed in two of the courses. In the one-to-one course the teacher focused initially on understanding the students' fear of mathematics and early mathematical experiences. The student-focused teaching approach trusted and encouraged the growth of ths student's mathematical thinking. Six months later the student felt empowered and had come to believe that mathematics as a creative and enjoyable process of discovering patterns. The second course focused on the mathematization of realistic situations. Successful students came to regard mathematics as useful, interesting, relating to real life. Successful students in the third course appreciated the carefully structured reintroduction to mathematics and were pleased they could finally do the mathematics they hadn't been able to understand at high school.

Thesis (Ph. D.)--University of Oregon, 2003. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 81-86). Also available for download via the World Wide Web; free to University of Oregon users.

This quasi-experimental study examined student engaged time as a function of the gender composition of the classroom. Three levels of single sex and coeducational mathematics classes were compared. An analysis of variance found that class environment (single sex or coeducational), and class level (Algebra 1/2, Geometry 3/4, or Algebra 5/6) were significant factors. A significant interaction effect was also found. Algebra and Geometry students were more engaged in a coeducational environment and female Algebra 5/6 students were more engaged in a single sex environment.

This study is a comparative case study of what three college calculus teachers did in their classrooms and what their students understood about the concept of derivatives. The teachers were solicited on the basis of peer, supervisor and student recommendations as being good teachers; several volunteer student subjects were selected from each class. Using a naturalistic participant-observer paradigm, the data were collected primarily via extensive classroom observations and in-depth interviews with the teachers and students. Examination of written work, such as student exams, was employed for additional confirmation of hypotheses generated in the field. This study contributes to the bodies of knowledge on pedagogy, effective teaching, classroom dynamics, student understanding and teacher beliefs. The results should be of interest to teachers, teacher educators, mathematics text authors and people interested in how students learn and think about mathematics at the collegiate level. The study of these three classrooms reveals that there is a variety of effective teaching models for undergraduate calculus classrooms. There were, however, important commonalties among these models, the examination of which leads to some characterization of effective teaching practices. These teachers kept the focus on what their students were learning, rather than on covering material. In three different ways, these teachers each gave their students the opportunity to interact with the mathematics before the lesson ended. All three teachers displayed a willingness to grow and learn as teachers. Calculus students do not always learn what their teachers think they have taught. The students in this study displayed a variety of mistaken ideas about the concept of derivative and about other mathematical topics. For example, many students had trouble distinguishing between properties of the function and properties of the derivative. Some students believed that the derivative at a point was a line, rather than the numerical value associated with the slope of a line. Students and teachers disagreed about the correct definition of the derivative, with students attributing little importance to the idea of limits.

The conceptions of congruence of integers of six above-average-performing undergraduate mathematics students enrolled in a third-year introductory number theory course at a large state university in the southwestern US were examined using an exploratory case study design. Data collected include interviews, written questionnaires, and videotapes of class sessions. There were four major findings concerning these six students' conceptions of congruence. In general, the students (1) invented and used a pseudo-definition for congruence, (2) avoided working in what they called the "mod world," (3) developed an increasingly operational view of congruence (several students' relational views of congruence were heavily de-ephasized or disappeared), and (4) did not view congruences as analogous to equations. In addition, the students appropriated a strategy used to solve linear Diophantine equations in order to solve linear congruences, disregarding the method used by the instructor in class, and in the process reversed an important heuristic for solving mathematical problems. A framework was developed for analyzing the degree to which these students were employing advanced mathematical thinking. This framework represents an attempt to synthesize multiple perspectives on the nature of advanced mathematical thinking currently present in the field. In addition, the notion of classroom mathematical practices from the emergent perspective (Cobb and Yackel, 1996) was used to examine the development of the class's understanding of congruence. The development of the four interpretations described above coincided with the development of five classroom mathematical practices. The individuals' conceptions at various points in time can be viewed as "consequences" of these practices, and can be seen in turn as influencing the development of other practices. This study found many similarities between these undergraduates' conceptions of linear congruences and students' documented difficulties solving equations in algebra. The students in the study were primarily prospective secondary mathematics teachers, and since the topics studied in this type of course are closely related to those of high school mathematics, this study has implications for teacher education as well.