Using fonts as a context, we will analyze symmetry of fi gures. Diff erent letters and numbers will be measured, and participants will describe items that possess vertical, horizontal, and rotational symmetry. Our discussion and activity will focus on the mathematics of fonts and the presence and absence of symmetry in their design.

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Explore fun nonfiction texts and resources for teaching bioluminescence and how animals use the light they produce to find prey, communicate, and defend themselves.

abstract: Researchers have described two fundamental conceptualizations for division, known as partitive and quotitive division. Partitive division is the conceptualization of a÷b as the amount of something per copy such that b copies of this amount yield the amount a. Quotitive division is the conceptualization of a÷b as the number of copies of the amount b that yield the amount a. Researchers have identified many cognitive obstacles that have inhibited the development of robust meanings for division involving non-whole values, while other researchers have commented on the challenges related to such development. Regarding division with fractions, much research has been devoted to quotitive conceptualizations of division, or on symbolic manipulation of variables. Research and curricular activities have largely avoided the study and development of partitive conceptualizations involving fractions, as well as their connection to the invert-and-multiply algorithm. In this dissertation study, I investigated six middle school mathematics teachers’ meanings related to partitive conceptualizations of division over the positive rational numbers. I also investigated the impact of an intervention that I designed with the intent of advancing one of these teachers’ meanings. My findings suggested that the primary cognitive obstacles were difficulties with maintaining multiple levels of units, weak quantitative meanings for fractional multipliers, and an unawareness of (and confusion due to) the two quantitative conceptualizations of division. As a product of this study, I developed a framework for characterizing robust meanings for division, indicated directions for future research, and shared implications for curriculum and instruction. / Dissertation/Thesis / Doctoral Dissertation Mathematics Education 2019

Kindergarten, first and second grade teachers play an important role in the development of a student's understanding of mathematics. Consequently, in order to improve student achievement in mathematics, it is important to investigate the relationships that may exist among primary teachers' math profile, math teaching efficacy, and math pedagogy and content knowledge. Participants completed an online survey that included the Math Teaching Efficacy Belief Instrument (MTEBI) and Math Knowledge for Teaching (MKT) items. Participants provided math profile data through academic demographic questions.;Two-hundred seven respondents completed the survey. Analysis of the data included descriptive statistics, chi-square test of independence, and Spearman rho correlations. The descriptive statistics of this sample population indicated varied math professional learning experiences, reserved mathematic teaching efficacy and little expertise in the knowledge of third grade mathematics. Relationships between frequency of math professional learning and math teaching efficacy emerged as statistically significant and merit further investigation. Additional statistically significant relationships occurred between math content knowledge and math teaching efficacy. The strength of these relationships was moderate and warrant further investigation.

The purpose of this study was to determine what relationship existed between preservice science (biology) teacher education and the reforms in secondary school biology that occurred between 1950 and 1975. Research questions were generated which dealt with the collaboration of the various sectors of education as well as if the prospective teachers were being trained to teach the reform curricula through their college science and teacher education coursework.;Content analysis of textbooks was utilized to determine the content of textbooks on the secondary and higher education level. The secondary texts contrasted were Modern Biology and the BSCS Blue and Green series. A variety of textbooks were analyzed for higher education biology including those authored by Villee and Weisz. Teacher education methods textbooks which covered science education or biology teaching were also analyzed. Five topics were analyzed in each of the textbooks: the scientific method, classification, amphibians, heredity, and ecology. The evaluation instrument was adapted from the Curriculum Materials Analysis System for Science (Haussler & Pittman, 1973) and the Virginia Department of Education Science Textbook Evaluation Instrument.;It was hypothesized that the analyses would reveal that innovations and reforms in high school biology textbooks preceded reforms in higher education teacher education programs which would indicate that prospective teachers were not being taught the necessary skills, behaviors, or methods in their required coursework to adequately institute the reforms on the secondary level. It was also hypothesized that the analyses would reveal an inordinately long period of time before prospective teachers were being instructed in the methods necessary for them to function effectively in secondary classrooms with the reform curricula.;It was concluded that there was generally very little collaboration between the various sectors of education during 1950 and 1975. The first hypothesis was confirmed and the second hypothesis supported but not totally confirmed due to the lack of information on how textbooks were actually used in the teacher education classrooms. Further research is needed in this area.;Additional findings of the study indicate that textbooks from the recent past are difficult to locate and thus a significant portion of the history of education is disappearing.

Research has established that motivation is an important factor of student achievement. Many researchers in the field of gifted education consider motivation to be a crucial component of giftedness, yet the literature base for motivation and math talent development within gifted populations is scarce. This descriptive study used a within-group design to measure the math motivation, math achievement, and goal orientation of high-ability 5 th grade math students to elucidate the relationships among motivation, achievement, goal orientation, and gender. Findings indicated that math achievement, math motivation, and goal orientation were similar for both genders; students had high math achievement yet low math motivation; and a high number of students had a performance goal orientation. Ideas for future math motivation research for the gifted are shared.;Keywords: gifted math students, math achievement, math motivation, goal orientation.

The purpose of this study was to examine theories of organizational culture typically applied to the university level of organization and their applicability to the academic department. Chaffee and Tierney's (1988) theory of organizational culture, dimensions of culture, and leadership strategies became the basis for a qualitative case study of a Department of Biological Sciences in a metropolitan university.;Interviews of current faculty members, current and former deans, and other administrators were conducted. Observations were made of faculty meetings and retreats and of departmental governance committee meetings. Extensive review of documents and correspondence covering more that twenty years provided additional data.;Interview and observation transcripts and documents were analyzed in terms of Chaffee and Tierney's (1988) concepts of the structural, environmental, and values dimensions of the department. Linear, adaptive, and interpretive strategies of faculty members and the department chair were identified.;The department was found to have what Clark (1972) refers to as strong organizational saga, or a sense of unique accomplishment which serves to maintain and perpetuate the integrity of the culture. Central to the value system of the Department of Biological Sciences is the shared sense that the department is unique in the degree to which faculty members work together cooperatively for the good of the department. These strong values were rooted in an earlier era when the department was experiencing growth and development of its research programs under adverse circumstances.;The primary usefulness of the results of this study go far beyond the particular findings for this individual academic department. Most important is the demonstration of the value of using this method of organizational analysis to understand the role of culture in shaping and perpetuating the organization. Administrators, department chairs, and faculty members can enhance their understanding of the departmental organization by applying concepts of organizational culture.;Further study and analysis are needed to evaluate disciplinary and institutional similarities and differences in departmental culture and to expand the existing theory to accommodate the variety of academic departments in colleges and universities.