Thesis advisor: Diana C. Pullin / As district- and school-level leaders face increasing pressure from federal, state, and local accountability mandates there has been increased dependence on using and analyzing student data to help improve student performance. While the reporting of disaggregated data by student subgroup confirms that achievement gaps exist, it does not provide district- and school-level leaders with the diagnostic data needed to identify key factors inhibiting student performance. Identifying and understanding factors hindering student performance is critical knowledge for leaders to cultivate as they work to address elements within their school or district that may need to change if student learning is to improve. This research study examined specific ways district- and school-level leaders go about challenging and helping their community to face the problem of student performance disparities, as well as specific aspects of the situation that may be contributing to the community's collective capacity, to address student performance disparities. Without proper district-level leadership, effectively addressing operational conditions that may lead to disparities in student learning is unlikely. Yet, little is known about which structures and routines district- and school-level leaders perceive to be important when analyzing student data. This single case study presents the results of an examination of student data analysis structures and routines within a small diverse urban Massachusetts district designated by the state as low-performing based on state indicators. In order to further understand structures and routines, interview and document data were reviewed. Four primary findings identified the district leadership's response to educational inequities: (1) a mandate for using data war-rooms and student data walls; (2) a traveling cabinet to ensure uniform review of student data across the schools in the district; (3) a mandate for individual school improvement plans; and (4) the use of school-based instructional coaches. / Thesis (EdD) — Boston College, 2014. / Submitted to: Boston College. Lynch School of Education. / Discipline: Educational Leadership and Higher Education.

Esta Dissertação tem por objetivo realizar estudo empírico que possibilite compreender a distribuição das oportunidades de aprendizagem para alunos do 5º e 9º do Ensino Fundamental de diferentes grupos socioeconômico, étnico-raciais e residentes em distintos estados brasileiros. O referencial teórico da pesquisa está alicerçado i) no conceito de Opportunity to Learn (OTL) e ii) na discussão do papel dos fatores extra e intraescolares no aprendizado dos alunos. Dessa análise, concluiu-se que os fatores que mais influenciam a aprendizagem dos alunos são i) características observáveis dos professores; ii) professores preocupados com um ambiente de aprendizagem; iii) professores com altas expectativas e iv) gestão de sala de aula e abordagem pedagógica na disciplina de matemática que promovam a aprendizagem profunda nos alunos. Portanto, com base na importância nestes fatores de OTL, este trabalho utiliza os dados do SAEB 2015 e desenvolve dois modelos: i) regressão multivariada, para entender a correlação dos fatores de OTL e a proficiência dos alunos no SAEB 2015 e ii) modelo logit, para calcular a probabilidade dos alunos do 5º e 9º anos de diferentes grupos socioeconômicos, étnico-raciais e estados brasileiros terem acesso à oportunidade de aprender matemática. Os resultados da regressão multivariada apontam que, controlando as características pessoais dos alunos, há uma correlação positiva entre os fatores de OTL e a proficiência em matemática tanto no 5º EF quanto para o 9º EF. Além disso, dentre todos os fatores de OTL analisados, a magnitude do coeficiente é maior no caso de professores que cumprem mais de 80% do currículo e professores que acreditam que quase todos os alunos irão entrar na universidade. Os resultados do modelo logit para cada fator de OTL analisado mostram desafios diferentes para a educação brasileira. Os fatores da categoria características observáveis do professor não são um grande desafio, pois ou a probabilidade de acesso é alta para todos os subgrupos de alunos ou quando a probabilidade não é tão alta, praticamente não existe desigualdade entre os níveis socioeconômicos e os grupos étnico-raciais. Já os fatores da categoria professores com alta expectativa são um desafio tanto em termos de aumento da probabilidade de acesso quanto de diminuição da desigualdade. Na categoria professores comprometidos com um ambiente de aprendizagem é preciso diminuir as desigualdades entre os subgrupos de estudantes e aumentar a probabilidade de acesso para todas as subpopulações, mesmo as mais privilegiadas. Por fim, na categoria gestão de sala de aula e abordagem pedagógica na disciplina de matemática é necessário aumentar a probabilidade de acesso a fatores que aumentam as OTL e diminuir a probabilidade de acesso a fatores que diminuem as OTL para todos os níveis socioeconômicos, inclusive para os alunos mais privilegiados. Portanto, é essencial investir em políticas educacionais que foquem suas ações nos de fatores de OTL, principalemente, os diretamente relacionados a sala de aula, a fim de aumentar as oportunidades de aprendizagem dos alunos brasileiros e reduzir as desigualdades existentes entre as subpopulações de estudantes. / This paper aims to conduct an empirical study that allows to understand the distribution of learning opportunities for 5th and 9th grade students from different socioeconomic, ethnic-racial and resident groups in different Brazilian states. The theoretical framework of research is based on i) the concept of Opportunity to Learn (OTL) and ii) the discussion concerning the role of intra and extra-school factors in students\' learning. From this analysis, it was concluded that the factors that most influence students\' learning are i) observable characteristics of teachers; ii) teachers committed to a learning environment; iii) teachers with high expectations and iv) teachers classroom management and pedagogical approach in mathematics. Therefore, based on the importance of these OTL factors, this paper uses SAEB 2015 data and develops two models: i) multivariate regression to understand the correlation of OTL factors and student proficiency in SAEB 2015 and ii) logit model, to calculate the probability of 5th and 9th grade students from different socioeconomic, ethnic-racial, and Brazilian states having access to the opportunity to learn mathematics. The results of the multivariate regression indicate that, by controlling the personal characteristics of the students, there is a positive correlation between the OTL factors and the mathematics proficiency in both the 5th EF and the 9th EF. In addition, among all OTL factors analyzed, the magnitude of the coefficient is higher in the case of \"teachers declare that they teach more than 80% of the curriculum\" and \"teachers declare that they believe that almost all of them students will enter the university\". The results of the logit model for each OTL factor analyzed show different challenges for Brazilian education. The factors of the category \"observable teacher characteristics\" are not a great challenge because either the probability of access is high for all subgroups of students or when the probability is not so high, there is practically no inequality between socioeconomic levels and groups ethnic-racial relations. On the other hand, the factors of the category \"teachers with high expectations\" are challenging both in terms of increasing access probability and decreasing inequality. In the category \"teachers committed to a learning environment\" is necessary to reduce the inequalities between the subgroups of students and increase the probability of access for all subpopulations, even the most privileged ones. Finally, in the category \"classroom management and pedagogical approach in mathematics\" is necessary to increase the probability of access to factors that increase OTL and decrease the probability of access to factors that decrease OTL for all socioeconomic levels, including for the most privileged students. Therefore, it is essential to invest in educational policies that focus their actions on OTL factors, mainly those directly related to the classroom, in order to increase the learning opportunities of Brazilian students and reduce the existing inequalities among subpopulations of students.

Esta Dissertação tem por objetivo realizar estudo empírico que possibilite compreender a distribuição das oportunidades de aprendizagem para alunos do 5º e 9º do Ensino Fundamental de diferentes grupos socioeconômico, étnico-raciais e residentes em distintos estados brasileiros. O referencial teórico da pesquisa está alicerçado i) no conceito de Opportunity to Learn (OTL) e ii) na discussão do papel dos fatores extra e intraescolares no aprendizado dos alunos. Dessa análise, concluiu-se que os fatores que mais influenciam a aprendizagem dos alunos são i) características observáveis dos professores; ii) professores preocupados com um ambiente de aprendizagem; iii) professores com altas expectativas e iv) gestão de sala de aula e abordagem pedagógica na disciplina de matemática que promovam a aprendizagem profunda nos alunos. Portanto, com base na importância nestes fatores de OTL, este trabalho utiliza os dados do SAEB 2015 e desenvolve dois modelos: i) regressão multivariada, para entender a correlação dos fatores de OTL e a proficiência dos alunos no SAEB 2015 e ii) modelo logit, para calcular a probabilidade dos alunos do 5º e 9º anos de diferentes grupos socioeconômicos, étnico-raciais e estados brasileiros terem acesso à oportunidade de aprender matemática. Os resultados da regressão multivariada apontam que, controlando as características pessoais dos alunos, há uma correlação positiva entre os fatores de OTL e a proficiência em matemática tanto no 5º EF quanto para o 9º EF. Além disso, dentre todos os fatores de OTL analisados, a magnitude do coeficiente é maior no caso de professores que cumprem mais de 80% do currículo e professores que acreditam que quase todos os alunos irão entrar na universidade. Os resultados do modelo logit para cada fator de OTL analisado mostram desafios diferentes para a educação brasileira. Os fatores da categoria características observáveis do professor não são um grande desafio, pois ou a probabilidade de acesso é alta para todos os subgrupos de alunos ou quando a probabilidade não é tão alta, praticamente não existe desigualdade entre os níveis socioeconômicos e os grupos étnico-raciais. Já os fatores da categoria professores com alta expectativa são um desafio tanto em termos de aumento da probabilidade de acesso quanto de diminuição da desigualdade. Na categoria professores comprometidos com um ambiente de aprendizagem é preciso diminuir as desigualdades entre os subgrupos de estudantes e aumentar a probabilidade de acesso para todas as subpopulações, mesmo as mais privilegiadas. Por fim, na categoria gestão de sala de aula e abordagem pedagógica na disciplina de matemática é necessário aumentar a probabilidade de acesso a fatores que aumentam as OTL e diminuir a probabilidade de acesso a fatores que diminuem as OTL para todos os níveis socioeconômicos, inclusive para os alunos mais privilegiados. Portanto, é essencial investir em políticas educacionais que foquem suas ações nos de fatores de OTL, principalemente, os diretamente relacionados a sala de aula, a fim de aumentar as oportunidades de aprendizagem dos alunos brasileiros e reduzir as desigualdades existentes entre as subpopulações de estudantes. / This paper aims to conduct an empirical study that allows to understand the distribution of learning opportunities for 5th and 9th grade students from different socioeconomic, ethnic-racial and resident groups in different Brazilian states. The theoretical framework of research is based on i) the concept of Opportunity to Learn (OTL) and ii) the discussion concerning the role of intra and extra-school factors in students\' learning. From this analysis, it was concluded that the factors that most influence students\' learning are i) observable characteristics of teachers; ii) teachers committed to a learning environment; iii) teachers with high expectations and iv) teachers classroom management and pedagogical approach in mathematics. Therefore, based on the importance of these OTL factors, this paper uses SAEB 2015 data and develops two models: i) multivariate regression to understand the correlation of OTL factors and student proficiency in SAEB 2015 and ii) logit model, to calculate the probability of 5th and 9th grade students from different socioeconomic, ethnic-racial, and Brazilian states having access to the opportunity to learn mathematics. The results of the multivariate regression indicate that, by controlling the personal characteristics of the students, there is a positive correlation between the OTL factors and the mathematics proficiency in both the 5th EF and the 9th EF. In addition, among all OTL factors analyzed, the magnitude of the coefficient is higher in the case of \"teachers declare that they teach more than 80% of the curriculum\" and \"teachers declare that they believe that almost all of them students will enter the university\". The results of the logit model for each OTL factor analyzed show different challenges for Brazilian education. The factors of the category \"observable teacher characteristics\" are not a great challenge because either the probability of access is high for all subgroups of students or when the probability is not so high, there is practically no inequality between socioeconomic levels and groups ethnic-racial relations. On the other hand, the factors of the category \"teachers with high expectations\" are challenging both in terms of increasing access probability and decreasing inequality. In the category \"teachers committed to a learning environment\" is necessary to reduce the inequalities between the subgroups of students and increase the probability of access for all subpopulations, even the most privileged ones. Finally, in the category \"classroom management and pedagogical approach in mathematics\" is necessary to increase the probability of access to factors that increase OTL and decrease the probability of access to factors that decrease OTL for all socioeconomic levels, including for the most privileged students. Therefore, it is essential to invest in educational policies that focus their actions on OTL factors, mainly those directly related to the classroom, in order to increase the learning opportunities of Brazilian students and reduce the existing inequalities among subpopulations of students.

This research introduces, develops and applies the concept of using student perceptions to measure opportunity-to-learn, in order to evaluate regular and special educational provision. A qualitative investigation into services for the education of learners with vision impairment identified the common aim of giving students equal access to the curriculum as their sighted peers. It also elicited potential determinants of need that affect caseload allocation decisions. Opportunity-to-learn was identified as a concept in the research literature, which has evolved from a measure of content coverage into a potential indicator of school effectiveness, measured almost exclusively from the teachers' perception. This research drew on the growing body of research that asks the students, to shift the focus from the teacher to the students themselves. An instrument was developed, based on the Essential Skills of the New Zealand curriculum, that measures opportunity-to-learn from the perspective of the students. This was used to collect baseline data on 1300 students, with no identified special needs, from twenty secondary schools throughout New Zealand. Analysis of the baseline data demonstrated the validity of the approach, and its potential to aid in research on the educational process, using this set of intermediate indicators. Results showed differences between schools and between girls and boys. The mean index scores for the schools were not strongly related to the socio-economic background of the schools, but did reflect independent measures of school quality. The instrument was then used to measure opportunity-to-learn for fifty learners with vision impairment in regular high schools. Comprehensive data on these learners was gathered from regular and specialist teachers, parents, schools and the individuals themselves. This data was analysed to evaluate the services and the opportunity-to-learn for the learners with vision impairment. Results showed that on average these students had opportunity-to-learn at least as good as for their sighted peers. Areas of weakness and strength within the service were identified. The instrument proved effective in the evaluation process.

Poor mathematics performance in South African schools is a major concern (Reddy et al., 2014) and learners’ opportunity to learn is one of the concepts that needs to be explored in schools (Dowd, Friedlander & Guajardo, 2014). Several authors (Gür, 2009; Ebert, 2017; Rohimah & Prabawanto, 2019) state that learners believe that trigonometry is difficult and abstract compared with the other topics of mathematics. Opportunity to learn (OTL) is defined as the degree to which learners during instruction get exposed to the content of the mathematics intended curriculum (Reeves & Muller, 2005). The term “mathematical tasks” refers to classwork problems, homework problems, projects, investigations and assignments. These tasks play a vital role in effective teaching and learning. Learners’ OTL was explored according to the types and nature of tasks selected by the teacher, and the pedagogical approach and strategies used by teachers and the influence of these two aspects on the time spent on tasks and learner engagement. This study therefore aimed to answer the research question about the extent to which mathematics tasks provided Grade 10 learners an opportunity to learn trigonometry. A two-part conceptual framework was used: the first part focused on the task selection in terms of its nature and cognitive demand and the second part focused on the teacher-specific factors such as teachers’ approaches and strategies. The influence of these two parts on the implementation of the tasks by the learners in terms of time-on-task and learner engagement was then described. A qualitative approach was followed, and a descriptive case study was conducted with two Grade 10 mathematics teachers from two formerly disadvantaged public schools in Gauteng Province. A qualitative research approach was used in which document analysis and classroom observations served as data collection techniques. A deductive analysis approach was implemented. The study revealed that teachers mainly gave learners recall-type and routine procedure questions involving pure mathematics, which according to CAPS’ cognitive demands, are classified as lower order thinking tasks. There was a lack of higher order mathematics tasks that could have provided the learners with and OTL trigonometry effectively. The study further revealed that both teachers’ approaches were dominated by a teacher-centred approach where the focus was on the teachers and where teachers mainly used direct teaching as teaching strategy where learners were directed to learn through memorisation and recitation techniques. Although, due to the small sample, the study’s results cannot be generalised, I believe that the findings will contribute to pre- and in-service teacher training, where teachers come to realise the importance of appropriate mathematics tasks to contribute to learners’ OTL. Moreover, the study’s findings highlight the need to engage the four cognitive levels, namely knowledge (20%), routine procedures (35%), complex procedures (30%), and problem solving (15%) in the types of tasks. The value of teachers’ choices regarding the teaching approaches and strategies used should never be under-estimated. Future research could possibly build on this study by examining the implementation of tasks to enhance learners’ in-depth understanding of trigonometry. / Dissertation (MEd)--University of Pretoria, 2021. / Science, Mathematics and Technology Education / MEd / Unrestricted

This study examined the relationships between opportunity to learn (OTL), science engagement, and science achievement in students' middle school level. This study used the Trends in International Mathematics and Science Study (TIMSS) data from the 2003 wave. The data were analyzed using structuring equation modeling and hierarchical linear modeling. It was hypothesized that students' engagement in science is a mediator between opportunity to learn and science achievement. Moreover, class and school level variability was also examined since the organization of the data was nested. The study examined the effects of OTL on students' emotional, cognitive, and behavioral engagement in science and subsequently on science achievement controlling for family socioeconomics status. The results of structural equation modeling supported some theoretical formulations of the conceptual model, and showed significant effect of OTL factors on students' science engagement, especially the behavioral engagement. Furthermore, science emotional and cognitive engagement showed positive effects on science achievement, but the effect of behavioral engagement on science achievement was complex. Detailed exploration and discussions were included in this study. The findings from hierarchical linear models suggested that students' science achievement was not only related to students' engagement, but also varied by class and school level OTL factors. The study had both theoretical and practical significances, providing valuable insights for the pedagogy of science. / Ph. D.

Thesis advisor: Diana C. Pullin / This dissertation examines how district- and school-level leaders' understanding of achievement gaps influences the work of leadership in addressing educational inequities and broadening students' opportunity to learn. While the reporting of disaggregated data by student subgroup confirms that achievement gaps exist, reports from high-stakes testing fail to provide district- and school-level leaders with the diagnostic data needed to identify key factors inhibiting student performance. Yet, identifying and understanding factors hindering student performance is critical knowledge for leaders to cultivate as they work to address elements within their school or district that may need to change if student learning is to improve. Results from this single case study in a diverse urban district illuminate how district- and school-level leaders can challenge and support their community as they work collectively to confront and address issues related to disparities in student performance. Drawing on previous research, which introduced the cognitive shift as a unit of analysis for studying the work of leadership, this study identifies shifts in thinking that district- and school-level leaders attempted to prompt in others, as well as the framing strategies district- and school-level leaders used in their attempts to prompt identified shifts in thinking. The study found that district- and school-level leaders attempted to prompt a common set of cognitive shifts using a range of framing strategies. Furthermore, the study found a correlation between leaders' use of a particular of framing strategy and their level of leadership (i.e., district or school), with common patterns of strategy use unique to each level of leadership. Additionally, distinct patterns of strategy use also emerged for the leaders of the district's top performing schools which differed from the patterns of strategy use that emerged for the leaders of the district's lower performing schools. These findings suggest that certain framing strategies may be more effective than others. / Thesis (EdD) — Boston College, 2014. / Submitted to: Boston College. Lynch School of Education. / Discipline: Educational Leadership and Higher Education.

I conducted a content analysis to examine the treatment of the surface area and volume concepts within four published middle-grades mathematics textbook series. In particular, I examined the treatment of the surface area and volume concepts in terms of the location of surface area and volume lessons in the textbook and the number of pages and lessons devoted to these concepts. I also investigated the sequence of the instructional blocks of surface area and volume lessons. In addition, I evaluated the tasks included in these lessons in regards to the performance expectations of students, the types of visual representations of 3D objects, and the level of mathematical complexity. At last, I examined the extent to which the content of surface area and volume lessons address the Common Core Content Standards (CCCS) for 6-8 geometry that are aligned with these topics. I used content analysis to analyze relevant content in a total of twelve middle-grades student edition mathematics textbooks from two popular textbook series, Go Math!(GM) and Glencoe Math (GMC); and two alternative textbook series, Connected Mathematics 3 (CM) and University of Chicago School Project (UCSMP). First, I used Flanders’ (1994) counting method to examine the physical characteristics of textbooks, such as the location of the surface area and volume lessons in the textbook, the number of pages and lessons devoted to these concepts. Second, I analyzed the sequence of the instructional blocks of surface area and volume lessons by using content analysis. Third, I adapted the Trends in International Mathematics and Science Study [TIMSS] (2002) Performance Expectations for Mathematics Framework to examine the performance expectations of students within tasks. Fourth, I developed and used the Visual Representations of 3D Objects Framework to examine the types of visual representations of 3D objects included in the tasks. Fifth, I employed the Mathematics Framework for the 2007 National Assessment of Educational Progress (NAEP) to examine the level of mathematical complexity of tasks. Finally, I created the CCCS for 6-8 Geometry Components guideline to examine to what extend the surface area and volume lessons address the geometry content standards. Results indicated that the majority of textbooks place the concepts of surface area and volume towards the end of the textbook. Small percentages of instructional pages and lessons are devoted to these concepts in all textbooks. Findings also revealed great similarities among the instructional blocks of lessons within three textbook series (GM, GMC, and UCSMP). The majority of tasks within all textbook series contain miniscule amounts of important performance expectations such as justifying and proving and visual representations of 3D objects such as nets and pictures. A significant amount of tasks are of moderate complexity across all textbook series. Analysis also showed that the CM textbook series offers the greatest opportunity for students to generate visual representations of 3D objects and contains the largest amount of high complexity tasks. At last, nearly all lessons address the appropriate geometry content standard among all textbook series. Limitations of the study, implications for mathematics education, as well as recommendations for future research are also presented.

abstract: This action research study (a) explored how institutionally labeled “at-risk” Latina/o students described their experiences in an opportunity to learn environment within an academic intervention program, (b) examined how these students experienced caring relationships with their teachers in an opportunity to learn environment when compared to their other core academic classes, and (c) investigated how school leaders created conditions to further support these students’ academic success on a larger scale. This action research study utilized a sequential phenomenological qualitative approach. Critical Race Theory, Critical Pedagogy, and Care theory served as the theoretical frameworks for this study. The blending of these theories worked to push Latina/o students’ narrative reflections to emerge as constitutive and instructive voices speaking back against the inequalities in the educational setting, and offered counterstories about the caring dynamics of Latina/o students in the classroom. Participants included high school students identified as “at-risk” and in an academic intervention class / Dissertation/Thesis / Doctoral Dissertation Leadership and Innovation 2016

Thesis advisor: Lauri Johnson / Student discipline practices evolved significantly in recent decades, yet pervasive use of out of school suspension persists. Such exclusionary discipline practice negatively influences students’ opportunity to learn and restricts inclusion within the school environment. Wide belief and extensive research speaks to the benefit of alternative practices, yet a gap in research remains specific to what leadership practices influence such opportunities. The purpose of this individual study nested in a larger case study focused on leadership for inclusive practices, was an examination of leadership perceptions of how student discipline decisions can support a student’s opportunity to learn. This study, conducted in a diverse urban school district in Massachusetts, Northside Public Schools, included interview data from fourteen district and school leaders as well as examination of publicly available and locally provided documents as data for analysis. Findings indicate that fostering relationships between school, student, family, and community members is integral to inclusive practices as a whole, specifically when related to discipline situations and pivotal to effective implementation of alternatives to suspensions, such as Positive Behavior Interventions and Supports and Restorative Practices. Recommendations include intentional tiered systems development and implementation of instructional interventions as alternative to exclusionary discipline through a culturally responsive perspective. / Thesis (EdD) — Boston College, 2020. / Submitted to: Boston College. Lynch School of Education. / Discipline: Educational Leadership and Higher Education.