This study examines the relationship of student achievement in mathematics and factors purported to influence such achievement. The factors utilized in the study were selected from those contained in accountability reports issued by the state of Tennessee in 1995-96. The student achievement measures were based on four high school end-of-course mathematics tests. Student performance on these tests is examined both in terms of actual scores and value-added measures. This study organizes the available accountability measures in an Opportunity-to-Learn (OTL) framework for the purpose of determining relationships that can inform practice and give policy guidance. The study examined 65 (of 139) school systems in Tennessee in a research design of correlation and multiple regression analyses. Twenty-three independent variables were organized into three OTL categories (fiscal, educational process, and teacher quality) and an "external factors" category. Eight dependent variables represented actual and value-added results on the four tests. Results revealed a number of significant relationships; there were relatively fewer and weaker relationships involving value-added measures than actual measures of achievement. Conclusions emphasize the need for continued refinement of the accountability and research goals for the state. Specific recommendations are that the number of variables measured be increased and that the focus and specificity of the variables be increased.

Research has shown that the focus of mathematics student teaching programs is typically classroom management and non-mathematics specific teaching strategies. However, the redesigned BYU student teaching structure has proven to help facilitate a greater focus on mathematics-specific pedagogy and student mathematics during post-lesson reflection meeting conversations. This study analyzed what specific principles of NCTM’s standards of effective teaching were discussed in the reflection meetings of this redesigned structure. This study found that the student teachers extensively discussed seven of the eight principles NCTM considers to be necessary for effective mathematics teaching. Other pedagogical principles pertaining to student mathematical learning not included in NCTM’s standards of effecting teaching were also discussed, as well as the student teachers’ own understanding of mathematics. Behavior was discussed very little. This study also provides insights into how mathematics student teaching can be further restructured to assure that mathematics student teachers can leave their student teaching programs ready to implement the principles of effective teaching in their own classrooms.

The presence of outlying anchor items is an issue faced by many testing agencies. The decision to retain or remove an item is a difficult one, especially when the content representation of the anchor set becomes questionable by item removal decisions. Additionally, the reason for the aberrancy is not always clear, and if the performance of the item has changed due to improvements in instruction, then removing the anchor item may not be appropriate and might produce misleading conclusions about the proficiency of the examinees. This study is conducted in two parts consisting of both a simulation and empirical data analysis. In these studies, the effect on examinee classification was investigated when the decision was made to remove or retain aberrant anchor items. Three methods of detection were explored; (1) delta plot, (2) IRT b-parameter plots, and (3) the RPU method. In the simulation study, degree of aberrancy was manipulated as well as the ability distribution of examinees and five aberrant item schemes were employed. In the empirical data analysis, archived statewide science achievement data that was suspected to possess differential opportunity to learn between administrations was re-analyzed using the various item parameter drift detection methods. The results for both the simulation and empirical data study provide support for eliminating the use of flagged items for linking assessments when a matrix-sampling design is used and a large number of items are used within that anchor. While neither the delta nor the IRT b-parameter plot methods produced results that would overwhelmingly support their use, it is recommended that both methods be employed in practice until further research is conducted for alternative methods, such as the RPU method since classification accuracy increases when such methods are employed and items are removed and most often, growth is not misrepresented by doing so.

As contemporary federal education legislation requires schools to ensure that all students are prepared for college and careers upon graduation, the college and career readiness of ELs is an urgent matter requiring investigation. Within this policy context, career and technical education (CTE) has been presented as a potential pathway for ELs to achieve college and career readiness. This necessitates research examining ELs’ opportunities to participate in CTE programs as an alternative to traditional secondary schools. Thus, the purpose of this dissertation is (a) to examine the processes required to access CTE programs and the barriers ELs face when attempting to enroll in CTE, (b) to understand how institutional culture and the distribution of resources support ELs and instructors with ELs in their courses, and (c) to investigate ELs’ classroom experiences and opportunities to learn, as understood by the students, teachers, and administrators in a school dedicated to CTE programming. Drawing on ethnographic methodology, data were collected through fieldwork and classroom observations documented as fieldnotes; 36 in-depth interviews with teachers, administrators, ELs and former ELs; artifacts from classrooms; policy documents; student academic records; and state-level data from the Department of Education. The data analysis demonstrated that, overall, ELs did not experience equitable access to educational experiences leading to college and career readiness. First, ELs’ access to CTE programs that aligned with their career aspirations was restricted; administrators and counselors justified this practice through discourses of meritocracy and deficit framing of ELs. Second, despite the fact that ELs and instructors complained about the lack of support and resources, administrators drew upon race- and language-neutral ideologies to rationalize their failure to invest in programs and practices that would ensure equitable access and success for ELs. Finally, within this context of limited support, instructors expressed deficit views of ELs and relied on pedagogies that did not accommodate the linguistic needs of ELs. As a result, ELs believed that they did not receive adequate support, and many felt unprepared for college and careers. Interpreting these data from a critical race theory perspective, these findings suggest that CTE functions as a White educational space, operating under tacit White supremacist ideologies to justify inequitable treatment of ELs and privilege the cultural and linguistic practices of White students. This undermines CTE’s potential in providing equitable access to college and career readiness for ELs. / Teaching & Learning

A renewed focus to produce college and career ready graduates capable of thriving in science, technology, engineering, and mathematics (STEM) and other career and technical education professions has made access to advanced mathematics and science courses for all students a priority in K-12 education. Previous research on achievement has indicated that Black and Latino students are underrepresented in advanced mathematics and science courses and are lagging behind their peers in academic performance. Some researchers have suggested that these disparities in participation and achievement result from unequal access to educational opportunities. This purpose of this study was to examine student access to advanced mathematics and sciences courses in Virginia public high schools as an indicator of college and career readiness. This study employed secondary data analysis of school level data from the Virginia Department of Education. Regression analyses, simple and multiple, were used to examine access to advanced mathematics (Algebra II and higher) and advanced science (Chemistry and higher) course offerings by school characteristics, including school size, economically disadvantaged percentage, the percentage of minority students, and urbanicity locale. The results of this study indicated that student access to advanced mathematics and science course offerings, excluding and including AP mathematics and science courses, as in indicator of college and career readiness, differed based upon school size, economically disadvantaged percentage, and urbanicity locale. These findings, consistent with national statistics and other research, suggested that students who attend public high schools in the Commonwealth of Virginia do not have equal access to advanced mathematics and science course offerings, including AP mathematics and science courses, when school size, economically disadvantaged, and urbanicity locales are considered. Other findings related to access based on the percentage of minority students were inconsistent with prior research, as there was no significant difference in the number of advanced mathematics and science course offerings, excluding and including AP mathematics and science courses, based on the percentage of Black and Latino students enrolled in Virginia public high schools. / Ed. D.

After implementing a statewide standardized testing program in 1998, the Virginia Department of Education realized that some schools were making great gains in student achievement while other schools continued to struggle. The Department conducted a study to identify the practices used by schools showing improvement. Six effective practice domains were identified. The current study was a follow-up to the research conducted by the Virginia Department of Education. A questionnaire measuring the six effective practice domains: (a) curriculum alignment, (b) time and scheduling, (c) use of data, (d) professional development, (e) school culture, and (f) leadership was administered to teachers in 148 schools in Virginia; 80 schools participated. Two questions guided the study: (1) How frequently do schools use the Virginia Department of Education effective practices, and (2) what is the relationship between the use of the effective practices and school pass rates on the 3rd grade 2005 Standards of Learning (SOL) reading test? Descriptive statistics, linear regression, and discriminant function analysis were applied to explore the relationships between the predictor variables (percentage of students receiving free or reduced-price lunch and the use of the effective practices) and the criterion variable (school pass rate on the 2005 SOL 3rd grade reading test). Academic culture and the percentage of students receiving free or reduced-price lunch accounted for significant amounts of the variance in school pass rates. The remaining five effective practice measures were not related to school pass rates. The measures may have affected the results. In most cases, one person was used as the proxy for the school, and this person may have provided a biased assessment of what was happening in the school. / Ed. D.

Achieving equitable opportunities to learn has been recognized as an important issue in multilingual content classrooms. However, partially because mathematics is conceptualized as a language-free subject, there is limited research examining linguistic minority students’ opportunities to learn in mathematics classrooms. The purpose of this research is to identify linguistic minority students’ opportunities to learn in mathematics classrooms in a Canadian multilingual urban elementary school, where English was the main instructional language. Drawing on cultural historical activity theory, this study focuses on two aspects of learning: externalization, which emphasizes learners’ creation of new cultural artifacts and new contexts to apply the given artifacts, and internalization, which emphasizes learners’ acquisition of preexisting cultural artifacts. In this ethnographic study, I examined the activity systems of participatory action research (PAR) with the activity system of regular mathematics lessons. Within these activity systems, I focused on newly-arrived English language learners’ (ELLs) participation. Specifically, I examined the range of opportunities to learn afforded to students in the two activity systems and identified how focal ELLs accessed these opportunities to learn. In the activity system of PAR, which emphasized externalization, students conducted research and presented their conclusions in order to implement changes in their school environment. All students, however, did not participate equally. Specifically, the focal ELLs were not able to access these opportunities to learn as a result of group dynamics, marginalized social identities, and other students’ perceptions of their linguistic ability. In the activity system of regular mathematics lessons, which emphasized internalization, the teacher organized lessons in ways that allowed focal ELLs to receive extra support and resources to reach the curriculum expectations. These mathematics lessons allowed focal ELLs to increase their participation through mathematical reasoning, problem solving, and explanations with a variety of resources including visual representations. A critical examination of the interactions revealed that focal ELLs’ opportunities to learn were expanded or limited depending upon classroom configurations. Furthermore, this research suggests that students’ social identities serve as both a medium and a product of learning. These results have valuable implications for developing inclusive classroom practices and curriculum in multilingual content classrooms.

Achieving equitable opportunities to learn has been recognized as an important issue in multilingual content classrooms. However, partially because mathematics is conceptualized as a language-free subject, there is limited research examining linguistic minority students’ opportunities to learn in mathematics classrooms. The purpose of this research is to identify linguistic minority students’ opportunities to learn in mathematics classrooms in a Canadian multilingual urban elementary school, where English was the main instructional language. Drawing on cultural historical activity theory, this study focuses on two aspects of learning: externalization, which emphasizes learners’ creation of new cultural artifacts and new contexts to apply the given artifacts, and internalization, which emphasizes learners’ acquisition of preexisting cultural artifacts. In this ethnographic study, I examined the activity systems of participatory action research (PAR) with the activity system of regular mathematics lessons. Within these activity systems, I focused on newly-arrived English language learners’ (ELLs) participation. Specifically, I examined the range of opportunities to learn afforded to students in the two activity systems and identified how focal ELLs accessed these opportunities to learn. In the activity system of PAR, which emphasized externalization, students conducted research and presented their conclusions in order to implement changes in their school environment. All students, however, did not participate equally. Specifically, the focal ELLs were not able to access these opportunities to learn as a result of group dynamics, marginalized social identities, and other students’ perceptions of their linguistic ability. In the activity system of regular mathematics lessons, which emphasized internalization, the teacher organized lessons in ways that allowed focal ELLs to receive extra support and resources to reach the curriculum expectations. These mathematics lessons allowed focal ELLs to increase their participation through mathematical reasoning, problem solving, and explanations with a variety of resources including visual representations. A critical examination of the interactions revealed that focal ELLs’ opportunities to learn were expanded or limited depending upon classroom configurations. Furthermore, this research suggests that students’ social identities serve as both a medium and a product of learning. These results have valuable implications for developing inclusive classroom practices and curriculum in multilingual content classrooms.

The study examined the opportunities to learn Mathematics that are accorded to secondary school students with visual impairment in Zimbabwe. The study focused on form one and form two students who are completely without sight, but are learning in inclusive settings, together with their Mathematics teachers. The study examined how teachers interacted with the subject matter, how the teachers interacted with the visually impaired students and how these students interacted with partially sighted students in the teaching and learning process. The study adopted the case study approach under the qualitative inquiry. Data was collected using document analysis, lesson observations, personal interviews with teachers and focus group interviews with students who were purposive sampled. The study established that visually impaired students were not accorded adequate opportunities to learn mathematics at secondary level. The reasons for this deficit are (1) visually impaired students learnt the same curriculum as sighted students when they could not access some topics on the syllabus, (2) the teachers were professionally qualified but they lacked the necessary specialist training for teaching students without sight, (3) teachers used the same teaching methods as those used with sighted students, (4) a lot of time was spent on task though not much ground was covered, (5) the schools were not adequately resourced with appropriate teaching and learning materials for use by visually impaired students, culminating in lost opportunities to learn mathematics. The study recommends that appropriately qualified teachers be deployed to teach at schools for the visually impaired, that all secondary teachers learn the basic modules in Special Needs Education during training. The study also recommends for the government to assist the schools for the visually impaired students to import the much needed teaching and learning equipment. The study has provided some knowledge about the learning of mathematics by visually impaired students in Zimbabwe in the areas of lesson delivery, materials provision, and programme adjustments at secondary teacher training colleges and universities. It has also provided curriculum planners with an insight on the prevailing situation with regard to the teaching and learning of mathematics by visually impaired students. This knowledge could be used when formulating future mathematics curriculum and training policies to do with non-sighted students in Zimbabwe and other countries in Africa. / Curriculum and Instructional Studies / D. Ed. (Curriculum Studies)