Svetlana Fortner-Henderson grew up experiencing abuse, sexual assault, and drug and alcohol abuse within the home. She suffered hearing loss as a child, which impacted her education. She went to college, attended graduate school, and worked in the field of environmental toxicology and regulatory compliance. She volunteered in many capacities that influenced her calling to become an educator. She agreed to teach were she was ‘called,’ as she considers that as the implementation of ministry of social justice through science education. She teaches in a high-trauma, deep inner-city setting, where students have experienced similar types of trauma that she experienced. She follows the lives of three students that derive from various backgrounds. These backgrounds contribute to the assets, strengths, and opportunities for growth socially and academically for these students. Svetlana is able to use the tools inherent and applied to educate the three students to benefit other students that have similar opportunities for educational and social/emotional growth. Svetlana deeply reflects on the impact she has made with her students and opportunities she sees for continued personal development within the profession. During her ethography, she modifies and massages her techniques in order to extact quality and usable content, as she seeks to be an effective teacher within a high trauma and high risk school and community. She also modifies her techniques as she believes in continuous improvement of herself and the students she has chosen to work with.

It is well documented that undergraduate students struggle with the more formal and abstract concepts of vector space theory in a first course on linear algebra. Some of these students continue on to classes in abstract algebra, where they learn about algebraic structures such as groups. It is clear to the seasoned mathematician that vector spaces are in fact groups, and so linear transformations are group homomorphisms with extra restrictions. This study explores the question of whether or not students see this connection as well. In addition, I probe the ways in which students’ stated understandings are the same or different across contexts, and how these differences may help or hinder connection making across domains. Students’ understandings are also briefly compared to those of mathematics professors in order to highlight similarities and discrepancies between reality and idealistic expectations. The data for this study primarily comes from clinical interviews with ten undergraduates and three professors. The clinical interviews contained multiple card sorts in which students expressed the connections they saw within and across the domains of linear algebra and abstract algebra, with an emphasis specifically on linear transformations and group homomorphisms. Qualitative data was analyzed using abductive reasoning through multiple rounds of coding and generating themes. Overall, I found that students ranged from having very few connections, to beginning to form connections once placed in the interview setting, to already having a well-integrated morphism schema across domains. A considerable portion of this paper explores the many and varied ways in which students succeeded and failed in making mathematically correct connections, using the language of research on analogical reasoning to frame the discussion. Of particular interest were the ways in which isomorphisms did or did not play a role in understanding both morphisms, how students did not regularly connect the concepts of matrices and linear transformations, and how vector spaces were not fully aligned with groups as algebraic structures.

Informal learning experiences have become increasingly effective in enhancing self-efficacy and interest in the fields of science, technology, engineering, and mathematics (STEM).This study investigated the impact of access to informal STEM learning experiences on student self-efficacy and interest in STEM before and after participating in the 2018 See Blue See STEM Summer Experience. Pre-survey results indicated that middle school students who had previous access to informal STEM learning experiences are 3.21 times as likely to demonstrate high self-efficacy in STEM as those who had no previous access. After engaging in the 2018 summer experience, post-survey results showed a statistically significant increase in student self-efficacy in STEM and indicated that students who had previous access to informal STEM learning experiences are 4.13 times as likely to manifest interest in STEM as those who had no previous access. These results suggest that increasing exposure to informal STEM learning experiences enhances both self-efficacy and interest in STEM.

For most of the twentieth and all the twenty-first century, there has been a great debate over educational reform for teaching mathematics. From these debates have come a critical look at how to properly instruct students so they can actively learn in the classroom, yet still retain the information for use in their later life. These questions are rooted in the larger debate between philosophical and psychological dimensions of human growth and development. Some educators, therefore, believe structuring their instruction around some philosophies such as idealism, realism, pragmatism, or existentialism was the key to success for their students. Others took the psychological approach and featured behaviorist or cognitive ideas in their teaching. Most feel that the approaches to psychology reflect these philosophical and psychological theories. These positions have resulted in the emergence of specific suggested teaching strategies that each proponent believes provide the solutions to the dilemma of how to best educate today’s students. This study examines what effect two different instructional strategies have on student acquisition of mathematical concepts and procedures.

Public education is a continually evolving field, with new research, policies, and practices explored by professionals who are driven to provide America’s youth with high-quality education. Research literature since 2000 has highlighted the importance of disciplinary literacy and its unfortunate neglect in a majority of secondary classrooms (Shanahan & Shanahan, 2008). Students who are literate in a particular discipline, such as math, view themselves as fluent in the language of mathematics, comfortable with reading, discussing, and practicing complex mathematical concepts while using appropriate vocabulary (Buehl, 2017). As seasoned professionals and novice educators consider the role of disciplinary literacy in their own classrooms, it is necessary to ponder the practices that are implemented within classrooms. Do they align with current research on the matter? What role do motivation and culture play in the process of becoming mathematically literate? How do these ideas influence classroom literacy practices? These are the central questions that have guided the construction of this research study, which will seek to examine the phenomena that occur within a classroom as teachers implement practices which promote and teach mathematical literacy. The exploratory nature of this study dictates that no judgement on the effectiveness of observed and discussed instructional strategies is considered, rather, a comparison of the latter with those strategies recommended by current educational researchers and literature. Interviews and classroom observations will work in tandem with a review of the current publications that address the areas of motivation, mathematical literacy, and culture.

This thesis addresses adult education in a museum setting and measures adult learning during and after a museum visit. While a number of studies have investigated the impact of museum visits on children’s learning, there are few studies on adult learners. This thesis is an initial effort to fill that gap. Qualitative data were gathered through interviews with 24 adult visitors at the Victor Valley Museum in Apple Valley, California. The objective was to determine which exhibits were found to be of greatest interest to the visitor. Follow-up interviews were conducted four weeks later to measure retention. The qualitative data were grouped by responses and compared to the demographic data to reveal any relationships. The study found that while adult visitors may initially learn new information during their museum visit, the information is not retained; learning must be reinforced. The solutions offered to achieve this reinforcement are reflection, follow-up interviews, and additional museum visits.

This literature review was conducted after it was noticed that an active instruction approach in teaching mathematics was becoming more of a standard approach. This literature review aims to analyze and synthesize existing research regarding active and direct instruction, as well as examine how these instructional strategies support the promotion of flexible thinking in students, including their promotion of the Standards of Mathematical Practice related to flexibility in thinking. This review defines both active instruction and direct instruction, as well as compares the two strategies, particularly in terms of how well they promote flexible thinking in students. It was discovered that there exists an abundance of research regarding active instruction, including its promotion of flexible thinking, yet it was difficult to find articles advocating for direct instruction. From the research conducted, it appears that a more active approach is more conducive to the learning of mathematics for students in that it encourages flexible thinking, which is a necessary component of a successful mathematician. More research is needed to determine under which conditions these instructional strategies yield optimal results.

This study describes the partnership between an urban community college and seven high schools from its inception. The purpose of the partnership was to increase the number of high school seniors transitioning into college-level math courses through the college math readiness program, an existing community college intermediate algebra course. In addition to archival records and documents, college math faculty, high school math teachers, administrators and staff, and college students were interviewed for this study. Four major challenges were identified in the following areas: student recruitment process, data management, lack of information to students, and collaboration among math faculty and math teachers. Despite all challenges, the partnership and the college math readiness program was perceived by stakeholders to be a successful program for the students and the institutions involved.

In the United States students have traditionally struggled with mathematics. Many students leave the educational system with limited mathematical literacy that can adversely affect their success as a college student, a consumer and citizen. In turn, lack of mathematical literacy affects their socioeconomic status. Through improving their mathematical literacy, students can be more successful not only in mathematics but, it seems in many aspects of their lives. Many researchers have defined mathematical literacy; yet, we need to understand more about how mathematical literacy develops. This study explores a model that identifies four key components that seem to be associated with the development and sustainability of mathematical literacy. When mathematical capital is viewed through the theoretical frame of reciprocal determinism, the nonlinear effects may contribute to the development of mathematical capital leading to a solid foundation for mathematical literacy. The purpose of this study was to describe and explain in what ways successful mathematics high school student attributes, abilities and experiences contribute to the development of mathematical capital that seems to be a foundation for mathematical literacy. The participants were a representative sample of seven diverse freshman high school students from an urban high school in the Pacific Northwest United States who are successful in mathematics as determined by grades in first term freshman mathematics courses and standardized test scores. Data collected included a survey, an achievement test, and interviews. Results from the mixed methods case study seemed to indicate that successful mathematics students have the four components of the proposed model of mathematical capital. The four proposed components are: (a) a positive mathematical self-esteem, (b) a working toolkit of mathematical skills and content knowledge and the application of that knowledge, (c) a problem-solving mindset, and (d) access to a support network. Implications for mathematics instruction are included. Future research needs to address how the four components interact so that more students can experience success in mathematics and become mathematically literate.

This dissertation is a case study of a school district in the Pacific Northwest that developed three-year high school science curricula using a Physics First course sequence (Physics, Chemistry, Biology), with the crosscutting concept Patterns as the central theme of the courses. The purpose of the study was to examine the impact of the implementation of the 9th grade course, Patterns Physics, on teacher practice and beliefs about science teaching and determine whether this new approach facilitated teacher classroom practices and beliefs congruent with those expressed in A Framework for K-12 Science Education (NRC, 2012) and the Next Generation Science Standards (NGSS Lead States, 2013). Results from this study indicate that the implementation of Patterns Physics positively impacted teacher confidence in teaching the NGSS science and engineering practices. Professional development that provided teachers multiple opportunities to engage with the curriculum--in the role of a student, in professional discussions with colleagues, and over several years were critical to support a change in practice consistent with three-dimensional (3D) teaching called for by the Framework and NGSS. Teacher participants viewed the Patterns PCB (Physics, Chemistry, and Biology) sequence as an appropriate course sequence, with strong agreement that a 9th grade physics course needs to be tailored to the needs of students, such as added support for students with minimal mathematics skills. The NGSS, with an emphasis on 3D learning (science content knowledge, crosscutting concepts, and science and engineering practices), had a significant positive impact on instructional practice.