The purpose of this study was to investigate differences between native and community college transfer students and identify factors that predicted upper-level biology course grade-point average and final overall grade-point average at a four-year institution in biological sciences. The results of this study indicated four-year institution persistence was not significantly related to gender, high school grade-point average, or ACT composite score. Persistence was significantly related to transfer status; whether the student was a native or community college transfer student with native students persisting at a higher rate at the four-year institution than community college transfer students. Furthermore, ACT composite score, high school grade-point average, final overall grade-point average, and upper level biology course grade-point average were significantly related to transfer status. Multiple regression analyses indicated high school grade-point average and ACT composite score were significantly predictive of upper-level biology course grade-point average while high school grade-point average, ACT composite score, and Pell eligibility were significantly predictive of final overall grade-point average.

Graphing is a fundamental topic in algebra that is notoriously difficult for students. Much of the past research has focused on conceptions and misconceptions. This study extends past research by looking at the mathematical practices of a practitioner, specifically one instructor of a function-based covariation-focused algebra class in the linear functions unit. Considering practices in addition to conception adds dramatically to our understanding of mathematical activity because it leads to explicit descriptions of normative purposes that are connected to particular situations or problems and also specifies how tools and symbols are coordinated to achieve these purposes. The results of this study are three levels of empirically proven practices associated with the conception of one advanced level of covariational reasoning, chunky continuous covariation. This study not only describes how practices may be described at different levels of complexity, but also demonstrates how smaller practices may be combined to form larger, more complex practices. These practices can be used to guide instruction of those who want to participate in and become practitioners in the community of teachers of function-based covariation-focused algebra curricula.

How do teachers talk about the productiveness of teacher's in-the-moment responses to student mathematical thinking? This is a question current research does not fully answer as most research on teacher moves is focused on what teacher moves researchers have noticed teachers do rather than on what teachers think about these teacher moves. To fill the gap in the research and to answer the question, a group of 13 teachers were given ten classroom situations to compare and contrast for productivity. I analyzed (a) the content of the teachers' discussions by drawing on Teacher Response Coding (TRC) language, and (b) the extent to which the teachers' discussions align with theorized productive responses to student mathematical thinking, or building. From the teachers' group conversations, I articulated principles of productivity— articulations of the main ideas and conclusions of the teachers' conversations with regards to productivity. Focusing on the principles of productivity, I highlighted what teacher moves the teachers said were productive or not productive with respect to teacher's in-the-moment responses to student mathematical thinking. In analyzing the list of unique principles of productivity, I noticed three main themes that the principles were focused around: student mathematics, teacher moves, and mathematics, which reflected some of the ideas in research for productive teacher moves. Additionally, I analyzed the principles for alignment with the practice of building, which led to the conclusion that the ideas of orchestrating discussion and making explicit are the most salient of the sub-practices of building to the teachers. These results based on teachers' discussions around the productivity of teacher moves can help inform teacher education and professional development.

Questions have been shown to aid in student understanding of mathematics, particularly "novel" questions (Mesa, Celis, & Lande, 2013) that do not have a predetermined answer. However, students do not always understand what is intended by questions posed by teachers, particularly those students who come from different cultural and lingual backgrounds than those dominant in the classroom discourse. This project investigated the relationship between how a mathematics teacher acknowledged students funds of knowledge in her questions and how Latina/o students responded. It shows some research based questioning techniques that allow Latina/o students greater opportunity to participate in the mathematical problem-solving process and how resulting classroom experience shows evidence of progression toward a hybrid space, as well as factors that limited progression toward a hybrid space. These results yield implications for English-speaking teachers instructing students who are bilingual in English and Spanish at varying degrees of proficiency.

After recognizing the need for a more thorough concentration of statistics at the seventh grade level, the author concluded that it would be a good idea to include statistics that cover both seventh and eighth grade Virginia Standards of Learning. Many years of administering the SOL mathematics test at the eighth grade level led the author to the understanding that some of the more advanced seventh graders would be missing some key concepts taught in eighth grade because those advanced students would be taking algebra in the eighth grade. In this thesis, the author has developed four units that she feels are appropriate for this level and will fill the gap.

A variety of factors influence what teaching strategies an educator uses. I analyze survey responses from algebra teachers in Scotland and Appalachia America to discover how a teacher's perception of these factors, particularly their view of mathematics itself, determines the pedagogical strategies employed in the classroom.

This study examines the effectiveness of two common tutoring program delivery models by analyzing tutored and nontutored students' grades and semester grade point averages in three subject areas. The effects of gender, age (if 25 years or older), course, duration of tutoring, tutoring contacts, and contacts per week are also measured. The approach to the ex post facto study is quantitative and utilizes data from the Student Information System at Appalachian State University and from tutoring contact sheets. Areas of data presentation include analysis of covariance results for experimental group, gender, age (if 25 years or older), and course; and correlational results for duration of tutoring, tutoring contacts, and contacts per week. Statistical results from this research rejected 10 of the 72 null hypotheses at the $p < .05$ level, and four of the rejected hypotheses were directly linked to the effect of experimental group. Findings showed that students who received tutoring in labs in mathematics and accounting had the highest semester grade point averages, and females earned higher course grades in mathematics and accounting, regardless of whether they were tutored or not. Results also showed that students 25 years or older who were enrolled in a physics course earned higher semester grade point averages as compared to younger students, regardless of whether they were tutored or not. Conclusions of this study emphasize the need for additional research with more students in the subject area of physics and for qualitative approaches to answer the questions of why specific variables were significant. Results and conclusions have applicability for tutoring program administrators in other settings.

Every year thousands of students graduate from high school and move on to higher education, but many of them are not yet prepared for college level courses. The Tennessee Board of Regents does not currently allow 4-year institutions to teach courses that are below college level, so many institutions are using programs such as learning support courses to assist a growing population of underprepared students. The purpose of this study was to determine if the 1-term and 2-term retention rates for students with the same ACT mathematics subsection scores were different between students who took a regular section of Probability and Statistics and students who took a learning support section of the course. The subjects of this study were students who enrolled in a Probability and Statistics class (either regular sections or learning support sections) at a 4-year institution from the 2013 summer semester through the 2014 fall semester. The criteria used for selecting subjects included: (1) enrolled in a section of Probability and Statistics, (2) had a valid ACT mathematics subsection score on file with the institution, and (3) recorded a final grade in the course. Students were then grouped by ACT mathematics subsection score and type of course (learning support or regular). When students were grouped by matching ACT mathematics subscores there were no real significant differences in 1-term retention, 2-term retention, or final course grade between students who took a 4-hour learning support section of probability and statistics and students who opted to take a regular 3-hour version of the same course, with one exception. Of students who scored a 17 on the ACT mathematics subsection, the students enrolled in a regular course had a 1-term retention rate that was significantly higher than the learning support course.

The complementary prism GG of a graph G is formed from the disjoint union of G and its complement G by adding the edges of a perfect match- ing between the corresponding vertices of G and G. A Roman dominating function on a graph G = (V,E) is a labeling f : V(G) → {0,1,2} such that every vertex with label 0 is adjacent to a vertex with label 2. The Roman domination number γR(G) of G is the minimum f(V ) = Σv∈V f(v) over all such functions of G. We study the Roman domination number of complementary prisms. Our main results show that γR(GG) takes on a limited number of values in terms of the domination number of GG and the Roman domination numbers of G and G.

The use of kits in elementary science classes is a growing trend in some countries. Kits provide materials and inquiry lessons in a ready-to-teach format for teachers to use in their science instruction. This study examined elementary teachers' instructional strategies, classroom practices, and assessment types in relation to the frequency of science kit use. A total of 503 elementary teachers from an urban school district received professional development, implemented kits in their classrooms for a year, and then completed a survey about science kit use and teaching practices. Despite similarities in demographic characteristics (gender, ethnicity, certification/educational level), there were significant differences in teachers' use of inquiry-based teaching and assessment practices by kit use. Teachers who reported using kits the most often were significantly more likely to report that their students designed and implemented laboratory investigations as well recorded, represented, and analyzed data. In addition, the high kit users indicated that they were more likely to use student groups, require students to use evidence to support claims, and use alternative assessments of student work including portfolios, notebooks, and long-term projects than those teachers who used kits less frequently. Those teachers who reported using kits the least often were significantly more likely to report having students practice for standardized tests. The role of kits in promoting reform-based teaching practices is discussed.