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).

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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.

This dissertation will examine the Knowledge-as-Theory-and-Elements perspective on knowledge structure. The dissertation creates a set of theoretical criteria given within a template by which lesson plans can be designed to teach mathematics and the physical sciences. The dissertation also will test the Knowledge-as-Theory and-Elements theoretical perspective by designing lesson plans to teach a branch of mathematics, graph theory, by using the new template. The dissertation will include a comparative study investigating the effectiveness of the lesson plans conforming to the new template and the lesson plans designed by the traditional theoretical perspective Knowledge-as-Elements.

If one has three sticks (lengths), when can you make a triangle with the sticks? As long as any two of the lengths sum to a value strictly larger than the third length one can make a triangle. Perhaps surprisingly, if one is given 6 sticks (lengths) there is no simple way of telling if one can build a tetrahedron with the sticks. In fact, even though one can make a triangle with any triple of three lengths selected from the six, one still may not be able to build a tetrahedron. At the other extreme, if one can make a tetrahedron with the six lengths, there may be as many 30 different (incongruent) tetrahedra with the six lengths. Although tetrahedra have been studied in many cultures (Greece, India, China, etc.) Over thousands of years, there are surprisingly many simple questions about them that still have not been answered. This thesis answers some new questions about tetrahedra, as well raising many more new questions for researchers, teachers, and students. It also shows in an appendix how tetrahedra can be used to illustrate ideas about arithmetic, algebra, number theory, geometry, and combinatorics that appear in the Common Cores State Standards for Mathematics (CCSS -M). In particular it addresses representing three-dimensional polyhedra in the plane. Specific topics addressed are a new classification system for tetrahedra based on partitions of an integer n, existence of tetrahedra with different edge lengths, unfolding tetrahedra by cutting edges of tetrahedra, and other combinatorial aspects of tetrahedra.

The purpose of this study was to verify Bandura's theory on the relationship of self-efficacy and performance particularly in mathematics among high school students. A rural school in the Philippines was selected for its homogenous student population, effectively reducing the effects of confounding variables such as race, ethnic and cultural backgrounds, socioeconomic status, and language. It was shown that self-efficacy was a positive but minor predictor of future performance only for male students who previously had higher mathematics grades. The effects were different between genders. It was not a strong predictor for women regardless of previous grades, and men with weaker mathematics skills. On the other hand, mathematics self-efficacy was predicted by previous mathematics achievement for women; and also the number of siblings and parental education for the higher performing women. The use of a second language in the mathematics classroom negatively affected confidence and performance. It was also found that there were differences in terms of academic behavior, peers, and family life between students with high and low self-efficacy. Positive behaviors were found for all female students regardless of self-efficacy levels and fewer were found among men. Negative behaviors were only found among low self-efficacy students. No differences were found in terms of the lives and families of the participants, but the interviews revealed that family members and their experiences of poverty affected educational goals and ambitions. In terms of other dispositional factors, students expressed classroom and test anxieties, concerns of being embarrassed in front of their classmates, and beliefs that mathematics was naturally difficult and not enjoyable. The students who did not talk about any of these themes were better performing and had higher self-efficacy scores.

Mathematical Word Problem Solving of Students with Autistic Spectrum Disorders and Students with Typical Development - Young Seh Bae - This study investigated mathematical word problem solving and the factors associated with the solution paths adopted by two groups of participants (N=40), students with autism spectrum disorders (ASDs) and typically developing students in fourth and fifth grade, who were comparable on age and IQ (greater than 80). The factors examined in the study were: word problem solving accuracy; word reading/decoding; sentence comprehension; math vocabulary; arithmetic computation; everyday math knowledge; attitude toward math; identification of problem type schemas; and visual representation. Results indicated that the students with typical development significantly outperformed the students with ASDs on word problem solving and everyday math knowledge. Correlation analysis showed that word problem solving performance of the students with ASDs was significantly associated with sentence comprehension, math vocabulary, computation and everyday math knowledge, but that these relationships were strongest and most consistent in the students with ASDs. No significant associations were found between word problem solving and attitude toward math, identification of schema knowledge, or visual representation for either diagnostic group. Additional analyses suggested that everyday math knowledge may account for the differences in word problem solving performance between the two diagnostic groups. Furthermore, the students with ASDs had qualitatively and quantitatively weaker structure of everyday math knowledge compared to the typical students. The theoretical models of the linguistic approach and the schema approach offered some possible explanations for the word problem solving difficulties of the students with ASDs in light of the current findings. That is, if a student does not have an adequate level of everyday math knowledge about the situation described in the word problem, he or she may have difficulties in constructing a situation model as a basis for problem comprehension and solutions. It was suggested that the observed difficulties in math word problem solving may have been strongly associated with the quantity and quality of everyday math knowledge as well as difficulties with integrating specific math-related everyday knowledge with the global text of word problems. Implications for this study include a need to develop mathematics instructional approaches that can teach students to integrate and extend their everyday knowledge from real-life contexts into their math problem-solving process. Further research is needed to confirm the relationships found in this study, and to examine other areas that may affect the word problem solving processes of students with ASDs.