Typescript, etc. / Digitized by Kansas State University Libraries

This study assessed the relative effectiveness of verbal and non-verbal teaching methods in facilitating the learning of mathematics. The two treatments differed only in that nonverbal instruction did not permit oral communication or use of written words. Chalkboard instruction was characterized by complete silence in nonverbal classes. In verbal classes, new terminology was introduced by writing the terms on the board and using them thorughout the lesson. Four fourth-grade classes consisting of 88 students in one school were randomly assigned to treatment groups so that two were taught non-verbally, and two by the conventional verbal method. Two teachers were assigned one class of each type. Treatment and teacher factors were crossed in a pretest-posttest control group design. The demonstrated comparability of the two teaching methods not only points to nonverbal instruction as an alternate mode, but also seriously questions the effectiveness of conventional teacher talk in enhancing learning. Teachers with a creative bent should be encouraged to experiment with nonverbal instruction and design activities for all levels of development. The technique could be used effectively to break the routine of conventional instruction. The importance of nonverbal components should be stressed in methods courses for pre- and in-service teachers. Techniques of nonverbal instruction should be practiced in student teaching practices. / Typescript. / "August, 1973." / "Submitted to the Department of Mathematics Education in partial fulfillment of the requirements for the degree of Doctor of Philosophy." / Advisor: Eugene D. Nichols, Professor Directing Dissertation. / Vita. / Includes bibliographical references (leaves 141-142).

The current study examined how GeoGebra contributed to middle grade Algebra I students' conceptual understanding of functions. In order to gain a deeper understanding a case study approach was utilized. Vinner (1983), and Vinner and Dreyfus' (1989) concept definition and concept image framework was used to analyze the students' function definition. O'Callaghan's (1994) component of translating was used to analyze the students' comparison of different function representations, and his component of modeling and interpreting was used to analyze the students' use of functions to model relationships between quantities. The following results were derived from the analyses. Having more correct concept images of functions through GeoGebra could also bring about a more correct definition. The dependency upon the concept definition to verify if a given example was a function could not contribute to the concept image. In order to gain correct concept images more integration of technology into algebra instructions was crucial to explore and interact with more function models. GeoGebra was an ideal environment to perform a transition among the representations. All three cases were able to understand how the given real-world problems transformed to GeoGebra simulator and the reverse procedure. The role of instructor was very important to guide and facilitate the learning. The results indicated that verification and exploration of more functions on GeoGebra contributed to a better conceptual understanding of a function definition. The advantages of GeoGebra were obvious for the translating component. The real-world problem scenario could be better modeled and interpreted via a simulator on GeoGebra and the need for algebraic symbolic manipulations could disappear. / A Dissertation submitted to the School of Teacher Education in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester 2015. / November 10, 2015. / Algebra, Concept Image, Functions, GeoGebra, Technology / Includes bibliographical references. / Elizabeth Jakubowski, Professor Directing Dissertation; Frances Berry, University Representative; Diana Rice, Committee Member; Angela Davis, Committee Member.

"In general terms, the purposes of this study were two in number: (1) to suggest whether unique mental factors as identified by methods of factor analysis are correlated with success in usual school learning situations and (2) to suggest whether it is possible to design instructional materials in a way which would suit the learner's mental ability profile"--Introduction. / Typescript. / "June, 1967." / "Submitted to the Graduate School of Florida State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy." / Advisor: E. D. Nichols, Professor Directing Dissertation. / Includes bibliographical references.

by Cheng Fun Chung. / Bibliography: leaves 48-51 / Thesis (M.A.Ed.)--Chinese University of Hong Kong, 1983

This dissertation focuses on beginning mathematics teachers from alternative certification programs and their perceptions of what is required to be successful. A mixed - methods research study was completed with several goals in mind: (1) identifying how beginning mathematics teachers define success in the classroom during their earliest years, (2) identifying what important factors, attributes, or experiences helped them achieve this success, and (3) determining where these beginning mathematics teachers learned the necessary attributes, or experiences to become successful in the classroom. A sample of beginning mathematics teachers (n = 28) was selected from an alternative certification program in California for a quantitative survey. A subsample of teachers (n = 7) was then selected to participate further in a qualitative semi-structured interview. The results of the study revealed that beginning teachers defined success in their beginning years by their classroom learning environment, creating and implementing engaging lessons, and a belief in their own ability to grow professionally as educators. Mathematics content knowledge, classroom management, collaboration with colleagues and coaches, reflection, a belief in one's ability to grow professionally as a teacher, a belief in the ability to have a positive impact on students, personality, and previous leadership experiences were several of the factors, attributes, or experiences identified as most important by the participating teachers. The participating teachers also felt that before and after, but not during, their teacher preparation program were the stages of teacher development that best instilled the necessary factors, attributes, or experiences to become successful in a mathematics classroom.

The often aggregated reports of academic excellence of Asian American students as a whole, compared to students from other ethnic groups offers compelling evidence that Asian Americans are more academically successful than their ethnic counterparts, particularly in the area of mathematics. These comparative data have generated many topics of discussion including the model minority stereotype: a misconception that all Asian Americans are high academic achievers. Research has shown that this seemingly positive stereotype produces negative effects in Asian students. The aim of this study is to examine differences in mathematics success levels and beliefs about the model minority stereotype among different generations of Asian American college students. This study focuses on comparing three different generations of Asian American students with respect to: (1) their success and confidence in mathematics, (2) their personal views on the factors that contribute to their success, (3) their perceptions of the model minority stereotype and (4) how they believe the stereotype affects them. In this mixed methods study, a sample of n = 117 Asian American college students participated in an online survey to collect quantitative data and a subsample of n = 9 students were able to participate in a semi-structured interview. The results of the study indicated that there were almost no differences in either the mathematics success and confidence level, or in the perceptions and perceived effects of the model minority stereotype across generations. Quantitative results showed that all generations of Asian Americans generally are confident in their mathematics abilities. Qualitative analysis showed that the students felt that there were three reasons for their level of success: parental influence, differences in the education system between the U.S. and their home country, and using mathematics and science to get ahead academically as their native English speaking peers tend to be ahead of them in the liberal arts due to language barriers. Though there were mixed feelings among the sample subjects about the validity of the model minority stereotype, all three generations of Asian American students felt peer pressure from the stereotype to excel in mathematics, more frequently in high school than in college.

Analysis of mathematical fiction with geometric themes is a study that connects the genre of mathematical fiction with informal learning. This study provides an analysis of 26 sources that include novels and short stories of mathematical fiction with regard to plot, geometric theme, cultural theme, and presentation. The authors' mathematical backgrounds are presented as they relate to both geometric and cultural themes. These backgrounds range from having little mathematical training to advance graduate work culminating in a Ph.D. in mathematics. This thesis demonstrated that regardless of background, the authors could write a mathematical fiction novel or short story with a dominant geometric theme. The authors' pedagogical approaches to delivering the geometric themes are also discussed. Applications from this study involve a pedagogical component that can be used in a classroom setting. All the sources analyzed in this study are fictional, but the geometric content is factual. Six categories of geometric topics were analyzed: plane geometry, solid geometry, projective geometry, axiomatics, topology, and the historical foundations of geometry. Geometry textbooks aligned with these categories were discussed with regard to mathematical fiction and formal learning. Cultural patterns were also analyzed for each source of mathematical fiction. There were also an analysis of the integration of cultural and geometric themes in the 26 sources of mathematical fiction; some of the cultural patterns discussed are gender bias, art, music, academia, mysticism, and social issues. On the basis of this discussion, recommendations for future studies involving the use of mathematical fiction were made.

Mathematicians have, historically, not been overly successful in their approach to teaching and much research has looked in to why this is so. Teaching mathematics is based on a solid understanding of the subject; however, instructors also need to be able to efficiently communicate the subject to their students. The purpose of this study was to establish common characteristics of excellent university lecturers in mathematics by applying Marsh's ten evaluation categories. This thesis sought to identify which of these areas were most consistently demonstrated by those university lecturers receiving the highest student ratings and whether there are any areas in which excellent lecturers received inconsistent ratings. The dissertation further used these observations to provide evidence of particular characteristics that are more important than others in the development of excellent university mathematics instructors. This study collected quantitative data in the shape of teacher evaluation forms from both Swedish and US mathematics institutions. The data suggests that instructors acknowledged to be excellent receive high ratings in areas concerning subject matter knowledge, explanatory ability, the fairness of examinations, and enthusiasm and commitment to students. Overall, items that explain a lecturer's persona, character and personality are generally more highly correlated with ratings for the instructor himself whereas categories which describe the preparation, organization and structure of the course, are generally more highly correlated with a student's overall learning experience and Overall Course rating.

Mathematical problem posing and creativity are important areas within mathematics education, and have been connected by mathematicians, mathematics educators, and creativity theorists. However, the relationship between the two remains unclear, which is complicated by the absence of a formal definition of creativity. For this study, the Consensual Assessment Technique (CAT) was used to investigate different raters' views of posed mathematical problems. The principal investigator recruited judges from three different groups: elementary school mathematics teachers, mathematicians who are professors or professors emeriti of mathematics, and psychologists who have conducted research in mathematics education. These judges were then asked to rate the creativity of mathematical problems posed by the principal investigator, all of which were based on the multiplication table. By using Cronbach's coefficient alpha and the intraclass correlation method, the investigator measured both within-group and among-group agreement for judges' ratings of creativity for the posed problems. Previous studies using CAT to measure judges' ratings of creativity in areas other than mathematics or mathematics education have generally found high levels of agreement; however, the main finding of this study is that agreement was high only when measured within-group for the psychologists. The study begins with a review of the literature on creativity and on mathematical problem posing, describes the procedure and results, provides points for further consideration, and concludes with implications of the study along with suggested avenues for future research.