A current trend in social justice oriented education research is the promotion of certain intellectual virtues that support epistemic responsibility, or differently put, the dispositions necessary to be a good knower. On the surface, the proposition of epistemically responsible teaching, or teaching students to be responsible knowers is innocuous, even banal. In the mathematics classroom, however, it is patently at odds with current practice and with the stated goals of mathematics education. This dissertation begins by detailing the extant paradigm in mathematics education, which characterizes mathematics as a body of skills to be mastered, and which rewards ways of thinking that are highly procedural and mechanistic. It then argues, relying on a wide range of educational thinkers including John Dewey, Maxine Greene, Miranda Fricker, and a collection of scholars of white privilege, that an important element in social justice education is the eradication of such process-oriented thinking, and the promotion of such intellectual virtues as courage and humility. Because the dominant paradigm is supported by an ideology and mythology of mathematics, however, changing that paradigm necessitates engaging with the underlying conceptions of mathematics that support it. The dissertation turns to naturalist philosophers of education make clear that the nature of mathematics practice and the growth of mathematical knowledge are not characterized by mechanistic and procedural thinking at all. In these accounts, we can see that good mathematical thinking relies on many of the same habits and dispositions that the social justice educators recommend. In articulating an isomorphism between good mathematical thinking and socially responsive thinking, the dissertation aims to offer a framework for thinking about mathematics education in and for a democratic society. It aims to cast the goals of mathematically rigorous education and socially responsible teaching not only as not in conflict, but also overlapping in meaningful ways.

The Florida Legislature passed a bill that changed the placement methods for some incoming students to the Florida State College System in 2013. This analysis of state policy looks at Senate Bill 1720 as the treatment in an interrupted time-series trend study at one state college in Florida. This research attempts to answer three questions: (1) What is the enrollment trend over the last 10 years in first-level math courses, such as Intermediate Algebra (MAT1033), Liberal Arts Math (MGF1106), and Elementary Statistics (STA2023) for first time in college (FTIC) students? (2) What is the trend of course passing rates in the above listed gateway math courses before and after the developmental education requirements changed? (3) What are the trends in student success rates before and after the changes to developmental education requirements in these courses for various demographics, such as race, age, and gender, for FTIC students in these math courses? This study looked at one college’s gateway math sequence in terms of enrollment and student success. The observed benefits to this institution were the gains in FTIC student enrollment in the gateway math courses. There were observed decreases in FTIC passing rates in the three gateway math courses, yet the total share of FTIC students taking and passing gateway math courses increased. This study should be shared with the Mathematics Department with the hope that it will continue to track student success in its courses and investigate other research in the area of gateway math instruction for younger post-secondary students as their enrollment continues to follow a decrease in the average student’s age. / A Dissertation submitted to the Department of Educational Leadership and Policy Studies in partial fulfillment of the requirements for the degree of Doctor of Education. / Spring Semester 2019. / April 1, 2019. / Includes bibliographical references. / Toby Park, Professor Directing Dissertation; Elizabeth M. Jakubowski, University Representative; Shouping Hu, Committee Member; Stacey Rutledge, Committee Member.

Understanding mathematics and teaching mathematics involve numerous factors, one of which may be an individual's spatial ability. This paper examines research conducted on the relationship between spatial abilities and mathematics, gender differences in the area of spatial ability, the types of experiences that may affect one's spatial ability, and issues surrounding the teaching of spatial skills. Researchers have found that spatial ability does relate to mathematics and males tend to have greater spatial ability than females. Instruction has also been shown to be successful in helping individuals learn spatial skills. This paper also reports the results of a study that examined the differences in spatial ability among 98 participants (males, females, faculty, and students in the sciences and non-sciences) at a Pacific Northwest university. Although not all the results were statistically significant, they tend to agree with earlier studies that found gender advantages in spatial abilities favoring males over females. They also provide evidence of the existence of greater spatial abilities among participants who are engaged in scientific rather than non-scientific pursuits. The participants in this study also reported experiences that they believed influenced their success or failure in tasks requiring spatial ability. Such experiences were success in math and art classes, computer modeling, drafting, puzzles/games, Legos, construction, woodworking, and playing with blocks as a child. Participants also stated their belief that spatial ability related to success or lack of success in mathematics. Over half of the students felt that spatial ability would help in a math class. This study reveals that spatial ability does differ in individuals; that there exist experiences that individuals feel are important for developing spatial ability; and that spatial ability relates to mathematics. This information can be beneficial for both teachers and researchers. / Graduation date: 2002

By creating opportunities for participation and intellectual engagement, standardized classroom routines are large determinants of the conceptual meaning students make. It is through repeated engagement in patterns of talk and intellectual practices that students are socialized into ways of thinking and habits of mind. The focus of this study is on moment-to-moment interactions between teachers and students in order to describe, identify and operationalize meaningful regularities in their discourse. Using classroom-level measures, I investigate the robustness of relationships between students’ mathematics achievement and discursive patterns across multiple classrooms with the statistical methods of Hierarchical Linear Modeling. Specifically, I investigated two theoretically significant constructs reflected in teacher’s follow-up moves -- responsiveness and intellectual work. Responsiveness is an attempt to understand what another is thinking displayed in how she builds, questions, clarifies, takes up or probes that which another says. Intellectual work reflects the cognitive work requested from students with a given turn of talk. After developing coding schemes to measure and quantify these discursive constructs, statistical analyses revealed positive relationships between the responsiveness and intellectual work of teachers’ follow-up and student learning of rate and proportionality (p=.01 and .08, respectively). Additionally, classroom communities with higher levels of responsiveness and intellectual work moderate the effect of prior knowledge on student learning by decreasing the degree to which pretest scores predict students’ post-test achievement (though neither are statistically significant). Based on these results, I conclude that classroom discourse and normative interaction patterns guide and influence student learning in ways that improve achievement. Recommendations are primarily concerned with ways the educational community can support and encourage teachers to develop responsive, intellectually demanding discursive patterns in their classrooms. In particular, we need to increase the awareness of the power of discourse, provide appropriate and sustained support for teachers to change current patterns, re-examine the design of teacher preparation programs, and develop ways to thoughtfully integrate responsiveness and intellectual work with core mathematics content. There is tremendous and often unrealized power in the ways teachers talk with their students; it is our obligation to help teachers learn how to recognize and leverage this power. / text

People use metaphors to describe or understand one thing in terms of another. The central idea of this thesis is that metaphors can be used to teach mathematics, particularly abstract topics such as directed numbers. Using directed numbers as a context, this study develops a framework and a coding scheme that can be used as a tool for analysing the use of metaphors in the teaching of mathematics. The part of the theoretical framework of the coding scheme is based on the work of Lakoff and Johnson (1980) and Lakoff and Nunez (2000). In those studies, the authors classify metaphors used for teaching mathematics into one of three categories: ontological, orientational and structural metaphors. By considering the source domain of metaphors, they can be classified into either grounding or linking metaphors. Similarly, the target domain of the metaphors can be categorized by the intended learning outcomes and by the functions of the metaphors. One of the primary contributions of this thesis is the development of a coding scheme that is specifically designed to analyze the use of metaphors in mathematics lessons. The scheme was then used and validated through the analysis of mathematics lessons taught by two teachers with contrasting academic backgrounds and teaching experiences. Three lessons taught by each teacher on the topic of directed numbers at Secondary One level were recorded and analysed. The metaphors used by each teacher were identified, coded and analyzed in order to determine how metaphors can be extended and transformed into other metaphors.. Finally, this thesis compared how the two teachers differed in their use of metaphors, particularly in terms of the selection, sequencing and organization of the metaphors used. This can be indicative the level of conceptual learning that is made available for students in their classes. The research questions: 1. What kinds of metaphors did the teachers use to introduce and explain the concepts and computational processes of directed numbers? 2. What functions did these metaphors serve? 3. What is the developmental path of these metaphors within and across the lessons? 4. What were the differences in the selecting, sequencing, and organization of the metaphor used by the two teachers? Findings This thesis designed and tested an original coding scheme. The findings revealed that the two teachers had used many kinds of metaphors in their lessons. They were used for classifying different kinds of numbers, constructing concepts, and explaining the properties and computational processes of directed numbers. Most of the metaphors found in this study were used to provide a cognitive function that facilitates the introduction of new mathematical concepts and helps the students make sense of the operational processes; only a few metaphors served a memorable function. When comparing the use of metaphors by the two teachers, we can analyze their teaching philosophies. Teacher 1’s use of metaphors demonstrated a linear development path from a simple to a more advance perspective, whereas Teacher 2’s use of metaphors revealed more comprehensive, sophisticated and multi-layered perspective. Significance of the study This study provides insights into the meaning and implication of using metaphors in teaching mathematical concepts. At research level, this study extends the existing work of Lakoff and develops an analytical tool specifically designed to understand the pedagogical values of using metaphors to teach abstract mathematical concepts such as directed numbers. At pedagogical level, the metaphor coding scheme can act as an initial foray into how metaphors can be used in and for teaching. Moreover, the Metaphor-Concept Development Chart developed in this study is a practical tool that can help teachers to analyze and improve their own use metaphors, thereby furthering their professional development and teaching effectivenss. / published_or_final_version / Education / Doctoral / Doctor of Education

This exploratory case study examines an alignment-focused coaching model of mathematics professional development during a school district's second-year implementation of the coaching model. Specifically, the study describes the content of coach-teacher talk as five coach-teacher pairs, grades K-8, engage in planning and analyzing mathematics lessons. Using an alignment framework designed around the components of curriculum, instruction, and assessment to analyze talk, four patterns unfold. Issues of curriculum, instruction, and assessment were more often discussed in isolation than interconnected, mathematics was most often the content focus when teacher and/or coach were using the state standards document to plan, student thinking and learning were most often a focus when students were struggling, and teachers often talked about instruction as actions isolated from student thinking and learning. In addition, teachers reported changes to instruction as an outcome of participating in coaching. Self-reported benefits to teachers' practice included planning lessons that focused on student learning, that is, considering the mathematics in the standards and ways students would learn the content. Teachers also reported asking "better questions" more often and in different ways, using models such as manipulatives and representations for connecting mathematics ideas, thinking more about student learning, and analyzing and scrutinizing textbooks to align with the state standards.

In this paper, students' bilingualism and multicultural experiences are examined as cognitive resources for mathematization. Capitalizing on the view of language as action, and on students' familiarity with certain experiences through direct participation, the study includes a conceptual framework, never used with bilingual mathematics learners, to investigate how bilingual students organize and coordinate actions to solve mathematical problems about familiar and unfamiliar experiences in English and Spanish. The study used a research methodology to investigate two questions: (a) How do bilingual students' mathematize familiar experience problems and unfamiliar experience problems in Spanish and English? (b) What do differences and similarities in bilingual students' mathematization across problems and languages reveal about experience and bilingualism as cognitive resources? Findings show important differences. In problems about familiar experiences, students generated more productive actions, more reflective actions, and less unproductive actions than in problems about unfamiliar experience. As for the bilingualism, students used Spanish and English differently. When solving problems in Spanish, they framed actions more socially by including partners or sharing the action with partners, whereas in English they framed actions more individually, more depersonalized, excluding partners and instead relying on words in problems to justify their individual actions. This suggests that reinventing mathematics and themselves as mathematical thinkers is part of using their bilingualism and experiences as cognitive tools, and attention to how they use each language for each type of problem can reveal substantial knowledge about how bilinguals learn mathematics. / text

The primary purpose of this study was to determine the manner in which assessment in mathematics is carried out in the Middle Schools. The study further identified problems educators encountered in assessing learners in mathematics and suggested possible solutions to problems encountered by educators in assessing learners in mathematics. Data was collected through questionnaires responded to by Middle Schools' mathematics educators and through the structured interview. Senior Phase mathematics educators responded to the questionnaire, which contained a blend of both dosed and open-ended questions. Educators took part in the structured interview in which a tape recorder was used. The study established that educators find it challenging to assess learners' mathematics work within the context of Outcomes Based Education and Curriculum 2005, even though the research was able to establish that in-service workshops on assessment in mathematics were conducted. Perhaps this calls for a new approach in conduction in-service workshops. Central to the recommendations of this research is a suggestion that there is a need for in-service workshops, which should focus on areas such as skills to be assessed in homework, class work, tests, examinations, projects, investigative activities and assignments. It was further recommended that educators should be trained on how to prepare rubrics for assessment of learners' mathematics work. / (M.Ed.) North-West University, Mafikeng Campus, 2005

The purpose of this study was to gain insight into observed discrepancies between continuous assessment and final examination average marks in Grade 10 Mathematics in the Oshikoto region of Namibia. The study is framed as a case study and is grounded within the interpretive paradigm. A mixed methods approach was applied, eliciting both quantitative as well as qualitative data. The study took place in two phases. In Phase 1, continuous assessment and Grade 10 final examination average marks for 62 Junior Secondary Schools for the period 2008-2010 were gathered and analyzed. Schools were characterized in terms of the relationship between their continuous assessment and final examination average marks for each of the three years. Phase 2, which was informed by Phase 1, took the form of structured interviews with a sample of three Mathematics teachers and three principals along with a focus-group interview of twelve teachers in order to investigate more deeply the perceptions of teachers and principals toward assessment policy and practice. The study shows that Grade 10 assessment practice in Namibian schools is far from ideal. Many teachers are not fully conversant with the various continuous assessment components as outlined by policy, and teachers are not confident about setting appropriate continuous assessment tasks. There is a strong perception that continuous assessment marks can easily be inflated and those teachers who gave high continuous assessment marks to their learners were generally perceived as being either incompetent or dishonest. While continuous assessment was seen as an important component of teaching and learning, it is evident that teachers and principals would welcome greater clarity, along with standardization and moderation, with respect to continuous assessment practice.

Thesis (MTech (Education))--Cape Peninsula University of Technology, 2009 / Huidiglik is die uitslae van wiskunde in Suid-Afrika baie swak in vergelyking met ander lande. Selfs die meeste Afrika-Iande presteer beter, Die doel van hierdie studie is om die redes en gevolge vir hierdie swak prestasies vas te stel. Dit is ook die navorser se poging om 'n bydrae te lewer tot beter wiskundige ontwikkeling ten opsigte van getalbegrip in die Grondslagfase deur aanbevelings vir opvoeders daar te stel wat benut kan word om hierdie doel te verwesenlik. In die literatuurstudie is Konstruktivisme, soos gesien deur Piaget en Vygotsky, breedvoerig bespreek. Die Realistiese benadering tot wiskundige ontwikkeling in getalbegrip is ook bestudeer. Verder is gefokus op.verskeie aspekte wat wiskundige ontwikkeling beinvloed, Die rede vir graad een en twee leerders se swak getalbegrip van 1 tot 99 en 'n moontlike oplossing vir hierdie probleem gee aanleiding tot die volgende navorsingsvrae: Dien die Plannemakerprogram as 'n doeltreffende hulpmiddel vir grade een en twee opvoeders om leerders se getalbegrip 1 tot 99 te verbeter? en Verbeter die Realistiese benadering, 5005 gevolg in die Plannemakerprogram, leerders se getalbegrip 1 tot 99? 'n Kwalitatiewe navorsingsontwerp is gebruik om die empiriese studie te voltooi. Vier skole in die Overberg-distrik, twee relatief groot en twee multi-graadskole, is gebruik. Gestruktureerde onderhoude is gevoer met ses graad een- en twee opvoeders en getalbegriptoetse is met hul leerders afgele, Die navorsingsresultate het getoon dat opvoeders wei riglyne benodig vir suksesvol!e ontwikkeling van getalbegrip in die Grondslagfase. Dit bevestig ook dat die grondlegging van goeie getalbegrip in graad een gele word en indien leemtes in hierdie belangrike aanvangsjaar ontstaan, leerders vorentoe probleme ondervind. Leerders by skole een en drie, waar die Plannemakerprogram gevolg is, se uitslae is heelwat hoer as skole twee en vier waar opvoeders ander benaderings gevolg het. Die uitslae van skool een se graad twee leerders, waar die Plannemakerprogram reeds vanaf graad een gevolg is, is ook beduidend hoer as skool drie waar die Plannemakerprogram slegs vanaf graad twee gevolg is. Hierdie navorsingstudie ondersoek, analiseer en bespreek die resultate met aanbevelings.