The purpose of this study was to determine how the study of number theory might affect high school students' metacognitive functioning, mathematical curiosity, and/or attitudes towards mathematics. The study utilized questionnaire and/or interview responses of seven high school students from New York City and 33 high school students from Dalian, China. The questionnaire components served to measure and compare the students' metacognitive functioning, mathematical curiosity, and mathematics attitudes before and after they worked on a number theory problem set included with the questionnaire. Interviews with 13 of these students also helped to reveal any changes in their metacognitive tendencies and/or mathematics attitudes or curiosity levels after the students had worked on said number theory problems. The investigator sought to involve very motivated as well as less motivated mathematics students in the study. The participation of a large group of Chinese students enabled the investigator to obtain a diverse set of data elements, and also added an international flavor to the research. All but one of the 40 participating students described or presented some evidence of metacognitive enhancement, greater mathematical curiosity, and/or improved attitudes towards mathematics after the students had worked on the assigned number theory problems. The results of the study thus have important implications for the value of number theory coursework by high school students, with respect to the students' metacognitive processes as well as their feelings about mathematics as an academic discipline.

The new mathematical modeling standard found in the Common Core State Standards for Mathematics in 2010 immediately created a gap between teachers’ knowledge and the new curriculum. Mathematical modeling is a way of doing mathematics with which many teachers are not familiar. The trilogy of Teachers College Mathematical Modeling Handbooks (Handbooks) were created with this in mind and made to be used as a tool for teachers of mathematical modeling. This study utilized a professional development program to determine teachers’ perceptions of these Handbooks. This study used the qualitative case study approach with two active middle school teachers. Data were collected through researcher observations, journal entries of the two participants, and exit interviews. The data from this study show the two teachers found creating and working on their own models was the most useful activity in preparing to teach mathematical modeling. The teachers also reported positive perceptions toward reading background literature and being provided time to adapt the lesson modules from the Handbooks for their own classrooms. While the teachers did not utilize the theoretical structure provided in the third Handbook, they found the Handbooks, overall, to be an effective tool.

A key issue for the success of students entering a first year mathematics course at tertiary level is whether or not they have an integrated understanding and view of the mathematical concepts acquired at school. Various integrated applications from first year mathematics suggest that a compartmentalised view of mathematics would be detrimental to any student's chances of passing mathematics at this level. This study tried to assess whether learners do have an integrated understanding of mathematics at grade 12 level.

Thesis (MEd (Education))--Cape Peninsula University of Technology, 2016. / Education in South Africa is a concern to many stakeholders, including government, teachers, teacher unions and non-governmental organisations, owing to the poor academic performances of learners. Mathematics teachers, the focus of this study, are confronted with a constantly changing curriculum. Teachers are often targeted by the education authorities and general public as the primary cause of the poor outcomes of education in South Africa. This study considers the experiences of Grades 10–12 mathematics teachers in the Cape Winelands regarding curriculum change and its influence on their professional practice. The basic assumptions of social constructivism served as overarching theory. The researcher judged that a conceptual framework would make for a clearer and more systematic way of dealing with the constructs that underpin this study. The conceptual analysis framework, which was developed by combining the work of Rogan and Grayson, as well as that of Remillard, which is a perfect fit to this study, guided the interpretation and analysis of the data. A deductive approach in data analysis was applied in accordance with the conceptual framework used in this study. Being explorative in nature, this study is a qualitative design and therefore an interpretive methodological approach was followed. A purposive and convenience sampling method was used whereby teachers from six schools were pre-selected: two from ex-Model C schools, two from previously disadvantaged black schools and two from previously disadvantaged coloured schools. Semi-structured interviews were conducted. The findings of this study pointed to teachers’ acceptance of education reform and changes in the curriculum, provided they were not too radical. Teachers requested involvement on a broad spectrum throughout the planning and implementation process, and proper training and support prior to implementation. Factors that militated against implementation were, among others, poor facilities, resources and instructional aides; poorly trained change facilitators; poor leadership and management at schools; and the many constraints that the learners brought to the school and the classroom.

Over many years the practice or art of teaching Mathematics posed itself as, not only being different from the practice of teaching any other subject, but to have many challenges and opportunities that ask for exploration and understanding. Just after independence in 1990, Namibia has embarked upon a reform process for the entire education system. Many changes were brought about to create a uniform, equal system for all. However, many challenges still remain to be addressed. Mathematics education remains one of the key areas where Namibian teachers can contribute towards the improvement of the subject. Unsatisfactory results, under-qualified teachers, and a negative disposition towards Mathematics are some of the challenges. These challenges are not unique to Namibia. Across the globe psychologists, philosophers and educators continue to engage in debates and research projects in search of answers and solutions for the improvement of Mathematics education. Despite encountering numerous obstacles, many teachers are dedicated and achieve outstanding results with their learners. This thesis reports on a research project that focused on the Mathematics teaching practice of two teachers whose experiences can make a positive contribution to the improvement of Mathematics teaching in Namibia. Furthermore, this case study investigated and attempted to understand the Mathematics teaching practices of two proficient teachers who each claimed to have a specific and unique approach to teaching Mathematics. The one claimed to be mainly procedural in her Mathematics teaching, while the other one claimed to teach mainly in a conceptual manner. Both achieve very good results with their classes and attribute their own teaching orientations to a process of several experiences they went through as students and in their careers. The study revealed that both claims are substantiated and that each teacher was consistent in her claimed approach. Many challenges and constraints were encountered by both teachers, but in their unique and specific ways each teacher’s chosen teaching approach supported them to overcome these. It was evident from the findings that each teacher’s practice came about as an evolutionary process over an extended period of time. As many challenges and limitations are universal, it is believed that in sharing experiences, teachers can benefit from each other by improving their practice. It was clearly stated by both participants that the re-thinking of and reflecting on their own practices provided them with new insights and motivation. Peer support and sharing of practices contribute positively towards the improvement of the teachers’ classroom practices.

What can be done to bring secondary mathematics courses in tempo with the present day needs and interests of the student? The purpose of this paper is to suggest a partial answer to this question. It is doubtless true that most boys and girls in the secondary school are far more interested in sports than in mathematics. Why not draw upon this common interest and bring sports into the mathematics classroom--or even take the mathematics classroom out to the field of sports? Such a question may seem unreasonable to those who have not given much thought to the possibility of approaching certain phases of mathematics through student interests in sports. Actually, such an approach is not at all unreasonable. The sports world offers practical examples of numerous mathematical relationships. / Typescript. / "May, 1949." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science under Plan II." / Includes bibliographical references (leaf 32).

Thesis (M.Sc.)--University of the Witwatersrand, Faculty of Science (Science Education), 1996. / This study explores ways in which first-year mathematics students use calculator as a tool of semiotic mediation. Twenty students out of a class of one hundred were loaned a graphic calculator for the academic year and were encouraged to use these during support tutorials. at year-end seven students (four with graphic calculator, three without) were audio-taped while solving a mathematical problem aloud in an interview situation. Also statistical data comparing graphic calculator and non-graphic calculator students' performance on a set of five questions was collected. The qualitative analysis of the interview data suggests that the calculator functioned primarily as a tool which amplified the zones of proximal development of the students, increasing efficiency and speed, rather than a semiotic which had been internalised. The quantitative analysis of the statistical data failed to support this notion of amplification. It is suggested that the add-on status of the graphic calculator undermined the possibility for statistical significance on this amplification effect.

This multiple probe across participants design evaluated the effectiveness of teaching early number sense skills (ENS) to young children (age 4) with autism spectrum disorder (ASD) using Number Talks with supports. Following participation in Number Talks with supports, young children with ASD learned the ENS skills of subitizing, one-to-one correspondence, number conservation, and magnitude discrimination. This study included a baseline condition, a Number Talks alone condition, and a Number Talks with supports condition in order to evaluate how much support young learners with ASD required to learn ENS skills during Number Talks. The Number Talks with support condition combined the socially constructivism learning techniques in Number Talks alone with the direct instruction practices of visual supports, a least to most prompting hierarchy, and explicit modeling. A functional relationship was found between Number Talks with supports and increased ENS skills of all three participants with ASD. The ENS skills were also maintained at near mastery criteria levels by all three participants with ASD. A peer comparison as well as peer pre and post-test data showed that peers also increased their ENS skills from baseline to the end of intervention. This study successfully combined the socially constructed learning technique of Number Talks with direct instruction support, and increased the ENS skills of young children with ASD and peers alike. Implications for practice and future research are discussed. / A Dissertation submitted to the School of Teacher Education in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester 2018. / July 3, 2018. / ASD, Autism Spectrum Disorder, Early Number Sense, Number Sense, Number Talks / Includes bibliographical references. / Kelly Whalon, Professor Directing Dissertation; Fengfeng Ke, University Representative; Mary Frances Hanline, Committee Member; Ian Whitacre, Committee Member.

"The purpose of this study was to investigate the conjecture that instruction in the strategies of Pattern Discovery, Trial and Error, Working Backward, Contradiction, Substitution, and Use of Diagrams would result in the development of problem-solving ability and that students under this instruction are likely to exhibit better achievement than students who do not receive explicit instruction in problem-solving strategies"--Introduction. / Typescript. / "August, 1985." / "Submitted to the Department of Curriculum and Instruction in partial fulfillment of the requirements for the degree of Doctor of Philosophy." / Advisor: Eugene D. Nichols, Professor Directing Dissertation. / Includes bibliographical references (leaves 78-85).

This multiple probe across participants design evaluated the effectiveness of teaching early number sense skills (ENS) to young children (age 4) with autism spectrum disorder (ASD) using Number Talks with supports. Following participation in Number Talks with supports, young children with ASD learned the ENS skills of subitizing, one-to-one correspondence, number conservation, and magnitude discrimination. This study included a baseline condition, a Number Talks alone condition, and a Number Talks with supports condition in order to evaluate how much support young learners with ASD required to learn ENS skills during Number Talks. The Number Talks with support condition combined the socially constructivism learning techniques in Number Talks alone with the direct instruction practices of visual supports, a least to most prompting hierarchy, and explicit modeling. A functional relationship was found between Number Talks with supports and increased ENS skills of all three participants with ASD. The ENS skills were also maintained at near mastery criteria levels by all three participants with ASD. A peer comparison as well as peer pre and post-test data showed that peers also increased their ENS skills from baseline to the end of intervention. This study successfully combined the socially constructed learning technique of Number Talks with direct instruction support, and increased the ENS skills of young children with ASD and peers alike. Implications for practice and future research are discussed. / A Dissertation submitted to the School of Teacher Education in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester 2018. / July 3, 2018. / ASD, Autism Spectrum Disorder, Early Number Sense, Number Sense, Number Talks / Includes bibliographical references. / Kelly Whalon, Professor Directing Dissertation; Fengfeng Ke, University Representative; Mary Frances Hanline, Committee Member; Ian Whitacre, Committee Member.