The focus of this research was to use the computer to examine certain cognitive factors of 134 eighth grade mathematics students. The program, "Trace and Find," was designed and written for the Apple II+ or IIe to identify the field-dependent-independent cognitive styles, the reflective-impulsive cognitive styles, and the trial and error strategy. Student behaviors were evaluated, timed, and counted by the computer to measure students' cognitive behaviors. Alpha was set at .05, beta was set at .05, and the effect size was set at + or - .30. Significant relationships were found among mathematics achievement, field dependence/independence, and reflective-impulsive cognitive styles. The results of the stepwise analysis found the field-dependent-independent cognitive styles and the reflective-impulsive cognitive styles accounted for 40% of the total variance of mathematics achievement with a multiple correlation of .64. Other significant relationships were established between mathematics achievement and the field-dependence-independence variable (r = .56), mathematics achievement and one of the reflective-impulsive variables (r = -.41), and the field-dependent-independent variable and this same reflective-impulsive variable (r = -.34). No significant relationships were found between or among males and females or the use of trial and error. I concluded that high mathematics achievers tend to be field independent and more impulsive than lower mathematics achievers. Low mathematics achievers tend to be field dependent and reflective. These results demonstrated that the computer can be used as a research and diagnostic tool for studying and evaluating cognitive behaviors. / Source: Dissertation Abstracts International, Volume: 46-09, Section: A, page: 2605. / Thesis (Ph.D.)--The Florida State University, 1985.

No description available.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Education." Includes bibliographical references (219-225).

This dissertation takes a qualitative look at the understanding of mathematical statements and proofs held by college students enrolled in a transitional course, a course designed to teach students how to write proofs in mathematics. I address the following three research questions: (1) What are students' understandings of the structure of mathematical statements? (2) What are students' understandings of the structure of mathematical proofs? (3) What concerns with the nature of proof do students express when writing proofs? Three individual interviews were held with each of the six participants of the study during the final month of the semester. The first interview was used to gain information about the students' mathematical backgrounds and their thoughts and beliefs about mathematics and proofs. The second and third interviews were task-based, in which the students were asked to write and evaluate proofs. In this dissertation, I document the students' attempts and verbal thoughts while proving mathematical statements and evaluating proofs. The results of this study show that the students often had difficulties interpreting conditional statements and quantified statements of the form, "There exists...for all..." These students also struggled with understanding the structure of proofs by contradiction and induction proofs. Symbolic logic, however, appeared to be a useful tool for interpreting statements and proof structures for those students who chose to use it. When writing proofs, the students tended to emphasize the need for symbolic manipulation. Furthermore, these students expressed concerns with what needs to be justified within a proof, what amount of justification is needed, and the role personal conviction plays within formal mathematical proof. I conclude with a discussion connecting these students' difficulties and concerns with the social nature of mathematical proof by extending the theoretical framework of the Emergent Perspective (Cobb & Yackel, 1996) to also include social norms, sociomathematical norms, and the mathematical practices of the mathematics community.

The results of the change in Calculus instruction at the University of Arizona in 1991, 1992, and 1993 were examined using three complementary methods. A survey of students (45) who took calculus during this period was administered, and analyzed for attitudinal differences between those who took traditional and those who took reform calculus. There were no statistically significant differences in reported attitude. Volunteers (14) were solicited from those who had been freshmen during the change to participate in interviews. These interviews included students taught by each method, and were analyzed by using concept maps to determine if there is a difference in retained knowledge. Although consortium (reform) students showed slightly improved retention, the differences were not statistically significant. University computerized grade records were used to determine if there was a difference between students who took consortium calculus and those who took the traditional course. Both retention and grades in subsequent calculus-dependent mathematics, science, and engineering courses were examined. A pattern of comparisons emerged which showed that consortium students somewhat outperformed traditional students. The patterns were indicative of better teaching and cannot be directly attributed to the materials. There is good evidence that the consortium students were not at a disadvantage in subsequent course work. This research should be of interest to teachers of calculus, and those involved in calculus reform. The techniques and computer programs for analysis of large data sets for performance differences in subsequent (dependent) course work can be useful for comparing different instructors, procedures, or materials in large institutions.

The purpose of this research is to examine possible causes of gender differences in mathematics and to investigate potential methods for lessening their effect on adolescent girls. Throughout a six week, summer school mathematics course, the participants were exposed to various activities and instructional methods thought to positively impact adolescent girls' self-esteem, self-efficacy and future mathematics course taking plans. Data collected included pretest - posttest measures as well as interview and observational data. The results indicate that along with a statistically significant improvement in mathematical skills, the participants showed an increase in self-confidence related to learning mathematics. The amount of mathematics courses the participants planned to take increased considerably by the end of the study. Suggestions for future research are also discussed.

<p> The mathematical concept of function has been revisited and further developed with regularity since its introduction in ancient Babylonia (Kleiner, 1989). The difficulty of the concept of a function contributes to complications when students learn of functions and their graphs (Leinhardt, Zaslavsky, &amp; Stein, 1990). To understand the concept of a function, students must understand the sub-concepts, such as correspondence, domain, and range. A function's domain and range are critical to understanding the graph of that function. </p><p> Through a review of the literature, it is apparent that many researchers have studied students' concepts of functions. However, no study has focused on how students understand the graphical representation of a function's domain and range. In this research, I explored students' transitional conceptions (often referred to by those with different theoretical framings as "misconceptions") of the domain and range of a graphical representation of a function. The research questions are as follows: 1. Which conceptions and strategies are evident when students consider the domain and range of a graphical representation of a function? 2. How do students' use of strategies and their understanding of concepts and representations impact their understanding of the domain and range of a graphical representation of a function? </p><p> The findings of this study exposed that many students have diverse transitional strategies and conceptions. Twenty-two strategies and conceptions were discovered. These were categorized as (a) projecting graphs to the x-axis or y-axis, (b) following or tracing graphs, (c) working with horizontal lines and discontinuous functions, and (d) representing with interval notation. Among the 22 strategies and conceptions, four are grouped as the fully developed strategies and the other four are the partially transitional strategies and conceptions, while the remaining 14 are the transitional strategies and conceptions. </p><p> Among transitional strategies and conceptions, three strategies and conceptions were predominantly used by the majority of the interviewees: (a) difficulty with the notation in representing the range of horizontal lines, (b) belief that a horizontal line or segment of a line has no range, and (c) tracing or chasing the graph from left to right. In addition, most transitional strategies and conceptions stem from measuring the range of a graph, not the domain. This implies the need for more instructional focus on measuring the range as well as for additional study on the matter.</p>

<p> This investigation was a confidential case study that explored the qualities of the mathematics program in a Catholic all-girls academic high school, also known as an academy, and how those qualities changed over time. National interest in students' persistence and achievement in mathematics and the national priority of equitable opportunity for all students to be successful in mathematics support the need for this study. Catholic academies were part of the alternative paradigms of Catholic and of single-sex schooling that were studied and debated in educational and political circles during the latter 20th century as possible models for improving student achievement in American public education. Although such schools have been embedded in large-scale and qualitative research studies, Catholic all-girls high schools have been underrepresented in studies of learning communities in mathematics education within sociocultural research. </p><p> Through the qualitative methodology of portraiture, past and current mathematics teachers and alumnae shared their perceptions of teaching and learning mathematics. Learning experiences inside and outside the classroom affected students' persistence, engagement, and self-efficacy regarding mathematics. Semi-structured interviews with ten mathematics teachers and eleven mathematically successful alumnae formed a portrait of learning that was focused, rigorous, and respectful. More than 1,400 alumnae responses to an online survey that explored their high school mathematics experiences and the impact on their mathematical lives further shaped the portrait by quantifying high engagement and lifelong confidence, regardless of socio-economic status. Further evidence was gathered through the examination of school, congregational, diocesan, and state education artifacts to corroborate perceptions. </p><p> The school's mission of <i>the More</i>, which reflected its sponsoring congregation's Jesuit roots, was realized within the mathematics program through high expectations and expanded opportunities for students to experience mathematics in deep and varied ways. Strong teacher content knowledge and supportive, problem-solving pedagogy elicited continued student persistence and engagement. Weak pedagogies that utilized memorization and were exclusionary negatively impacted student learning and self-efficacy. </p><p> Findings suggest topics for further research within mathematics education as well as other social science fields.</p>

<p>This study examined the relationship between beliefs found using the Integrated Mathematics and Pedagogy (IMAP) project beliefs survey and the beliefs found in math stories of eight novice (less than two years teaching) elementary school teachers. The stories were coded for the same beliefs used in the IMAP survey. As in the IMAP survey, the strength of evidence of the belief was assigned numerical values, zero through three, indicating virtually no evidence to very strong evidence respectively. Results showed that specific beliefs could be found in math stories, yet not always at the same level of strength as the IMAP survey. This indicates that each conveys differing views on the teachers' beliefs, and thus provides more detailed pictures of the teachers' beliefs. The details include a sense of the trajectory of development of teachers' beliefs from student to teacher that the IMAP survey does not. The math stories also provide evidence of the role of emotion in the formation and entrenchment of beliefs.

Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2007. / Title from PDF t.p. (viewed Nov. 19, 2008). Source: Dissertation Abstracts International, Volume: 68-02, Section: A, page: 0500. Adviser: Frank K. Lester.