Dissertations / Theses: 'School of Mathematics and Statistics'

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Hofbauer, Pamela S. Mooney Edward S. "Characterizing high school students' understanding of the purpose of graphical representations." Normal, Ill. : Illinois State University, 2007. http://proquest.umi.com/pqdweb?index=0&did=1414114601&SrchMode=1&sid=6&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1207664408&clientId=43838.

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Thesis (Ph. D.)--Illinois State University, 2007.
Title from title page screen, viewed on April 8, 2008. Dissertation Committee: Edward S. Mooney (chair), Cynthia W. Langrall, Sherry L. Meier, Norma C. Presmeg. Includes bibliographical references (leaves 112-121) and abstract. Also available in print.

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Leong, Jennifer. "High School Students' Attitudes and Beliefs Regarding Statistics in a Service-Learning-Based Statistics Course." Digital Archive @ GSU, 2007. http://digitalarchive.gsu.edu/msit_diss/12.

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Despite agreement among researchers about the powerful influence of attitudes and beliefs on the development of students’ mathematical knowledge base (Leder, Pehkonen, & Törner, 2002), relatively little is known about these constructs in statistics education. This study investigated the relationship between mathematics-and statistics-related attitudes and beliefs of 11 high school students in an introductory statistics course designed around a 13-week long service-learning project. Service-learning is a pedagogical approach that situates academic learning in the context of community service. The study utilized qualitative, teacher-researcher (Cochran-Smith & Lytle, 1993) methodology from an interpretivist perspective. The three primary modes of data collection were journals, narratives, and an open-ended survey (Survey of Mathematical and Statistical Affect). Observations and reflections were also recorded regularly in a researcher journal. Inquiry adhered to guidelines for trustworthiness and rigor as outlined by Lincoln and Guba (1985). Item, pattern, and structural levels of analysis were employed (LeCompte and Schensul, 1999b). Investigation into attitudes and beliefs was framed in accordance with Op t’ Eynde, De Corte, and Verschaffel’s (2002) conceptualization of the mathematics-related belief system and McLeod’s (1992) framework of the affective domain in mathematics education. Results indicate that participants’ attitudes toward mathematics and statistics tended to converge while participants’ beliefs regarding mathematics and statistics tended to diverge. Participants like mathematics and statistics that involve real-life scenarios. Participants also like mathematics and statistics that do not require complex mathematical tasks. Participants’ beliefs regarding statistics were generally more positive than beliefs regarding mathematics. Participants reported greater confidence doing statistics than mathematics and contribute this confidence, in part, to service-learning. Participants also experienced a heightened sense of social awareness and social responsibility through the service-learning project. These results provide evidence that service-learning can be utilized to solidify positive attitudes and beliefs regarding statistics among high school students, in spite of potentially less positive ones toward mathematics.

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Gardner, Kimberly D. "Investigating Secondary School Students' Experience of Learning Statistics." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/msit_diss/30.

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Although more students are taking courses in statistics before leaving high school, the research base on teaching and learning statistics at the high school level has not accumulated as rapidly (Garfield & Chance, 2000). Very little is known about how secondary school students learn statistics, how the misconceptions they bring to the subject impede their learning, and what should be taught or assessed (Watson & Callingham, 2003). Studies that have investigated these issues tend to focus on the K-5, undergraduate, and graduate levels of education (Groth, 2003). Therefore, more research is needed at the secondary level (Garfield & Chance, 2000). The purpose of this qualitative investigation is to examine how secondary school students' approaches to learning relate to how they assign meaning to statistics. Phenomenography (Marton & Booth, 1997) is the theoretical orientation that frames the study, and it examines the role human experience plays in learning, by reporting variations in the ways participants experience a phenomenon (Dall'Alba & Hasselgreen, 1996). The research questions for the study were: 1) What are the different ways high school students define statistics? 2) What are the different ways high school students learn statistics? 3) What are the different ways students experience learning statistics? The nine participants in the study were high school graduates who completed a course in Statistics or Advanced Placement Statistics while enrolled in high school in a suburban area in the southeast. Data sources were semi-structured interviews and journaling. Using phenomenographic methodology, students' descriptions of the experience of learning were analyzed and coded. An outcome space of the collective experiences was constructed. A hierarchical relationship between students' approach to learning and their learning strategies was found. Also, a hierarchical relationship between students' approaches to learning and the meaning they assigned to statistics was found.

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Groth, Randall E. Langrall Cynthia Willey Mooney Edward S. "Development of a high school statistical thinking framework." Normal, Ill. Illinois State University, 2003. http://wwwlib.umi.com/cr/ilstu/fullcit?p3087867.

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Thesis (Ph. D.)--Illinois State University, 2003.
Title from title page screen, viewed November 10, 2005. Dissertation Committee: Cynthia W. Langrall, Edward S. Mooney (co-chair), Beverly J. Hartter, Sharon S. McCrone. Includes bibliographical references (leaves 199-212) and abstract. Also available in print.

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Pickle, Maria Consuelo (suzie) Capiral. "Statistical Content in Middle Grades Mathematics Textbooks." Scholar Commons, 2012. http://scholarcommons.usf.edu/etd/4203.

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Statistical Content in Middle Grades Mathematics Textbooks Maria Consuelo (Suzie) Capiral Pickle Abstract This study analyzed the treatment and scope of statistical concepts in four, widely-used, contemporary, middle grades mathematics textbook series: Glencoe Math Connects, Prentice Hall Mathematics, Connected Mathematics Project, and University of Chicago School Mathematics Project. There were three phases for the data analysis. Phase 1 addressed the location and sequence of the statistical concepts. Phase 2 focused upon an examination of the lesson narrative, its components and scope. Phase 3 analyzed the level of cognitive demand required of the students to complete the exercises, and the total number of exercises per statistical concept. These three phases taken together provided insight into students' potential opportunity to learn statistical topics found in middle grades mathematics textbooks. Results showed that concepts, such as measures of central tendency, were repeated in several grades while other topics such as circle graphs were presented earlier than the recommendations in documents such as the National Council of Teachers of Mathematics Principles and Standards (2000) and the Common Core State Standards (2010). Further results showed that most of the statistical content was found in a chapter near the end of the book that would likely not be covered should time run short. Also, each textbook had a particular lesson narrative style. Moreover, most of the statistical exercises required low level cognitive demand of the students to complete the exercises, potentially hindering the development of deep understanding of the concepts.

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Webb, Derek, Glen Richgels, Marty J. Wolf, Todd Frauenholtz, and Ann Hougen. "Improving Student Interest, Mathematical Skills, and Future Success through Implementation of Novel Mathematics Bridge Course for High School Seniors and Post-secondary Students." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-81097.

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We present a new course titled “Introduction to the Mathematical Sciences.” The course content is 1/3 algebra, 1/3 statistics, and 1/3 computer science and is taught in a laboratory environment on computers. The course pedagogy departs radically from traditional mathematics courses taught in the U.S. and makes extensive use of spreadsheet software to teach algebraic and statistical concepts. The course is currently offered in area high schools and two-year postsecondary institutions with financial support from a Blandin Foundation grant (referenced under BFG). We will present empirical evidence that indicates students in this course learn more algebra than students in a traditional semester-long algebra course. Additionally, we present empirical evidence that students learn statistical and computer science topics in addition to algebra. We will also present the model of developing this course which depended on increasing future student success in a variety of disciplines at the post-secondary level of study.

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Webb, Derek, Glen Richgels, Marty J. Wolf, Todd Frauenholtz, and Ann Hougen. "Improving Student Interest, Mathematical Skills, and Future Successthrough Implementation of Novel Mathematics Bridge Course for High School Seniors and Post-secondary Students." Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 575 - 578, 2012. https://slub.qucosa.de/id/qucosa%3A1823.

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We present a new course titled “Introduction to the Mathematical Sciences.” The course content is 1/3 algebra, 1/3 statistics, and 1/3 computer science and is taught in a laboratory environment on computers. The course pedagogy departs radically from traditional mathematics courses taught in the U.S. and makes extensive use of spreadsheet software to teach algebraic and statistical concepts. The course is currently offered in area high schools and two-year postsecondary institutions with financial support from a Blandin Foundation grant (referenced under BFG). We will present empirical evidence that indicates students in this course learn more algebra than students in a traditional semester-long algebra course. Additionally, we present empirical evidence that students learn statistical and computer science topics in addition to algebra. We will also present the model of developing this course which depended on increasing future student success in a variety of disciplines at the post-secondary level of study.

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Cheung, Pak-hong. "Statistical analysis of secondary school teachers' attitudes towards mathematics." [Hong Kong : University of Hong Kong], 1991. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13064873.

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Showalter, Daniel A. "Estimating the Causal Effect of High School Mathematics Coursetaking on Placement out of Postsecondary Remedial Mathematics." Ohio University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1395226381.

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Cheung, Pak-hong, and 張百康. "Statistical analysis of secondary school teachers' attitudes towards mathematics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1991. http://hub.hku.hk/bib/B31976517.

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Yum, Kim-hung, and 任劍熊. "Within the IEA Third international Mathematics and Science Study (TIMSS): the relationship between familybackground and mathematics achievement of Hong Kong students." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1996. http://hub.hku.hk/bib/B31959192.

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Helfgott, Michel. "A Sojourn Through Geometry and Algebra." Digital Commons @ East Tennessee State University, 2013. http://amzn.com/1492798894.

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This textbook is intended for college juniors or seniors majoring in mathematics, who plan to become high school teachers. It seeks to provide a deeper perspective on secondary mathematics, showing the interplay between plane geometry and algebra. A distinctive characteristic of the book is the frequent discussion of multiple paths to the solution of a problem or the proof of a theorem. Practically none of the topics covered in the book overlap with the content of courses taken by mathematics majors, say real analysis, abstract algebra, differential equations, combinatorics, probability and statistics, number theory, etc. These courses, and several others, provide indispensable mathematical maturity but are rather distant from the core of high school mathematics. Precisely, one of our main objectives is to bridge the gap between the latter and college-level mathematics.
https://dc.etsu.edu/etsu_books/1084/thumbnail.jpg

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Mullins, Sherry Lynn. "Statistics: Raising the Bar for the Seventh Grade Classroom." Digital Commons @ East Tennessee State University, 2006. https://dc.etsu.edu/etd/2221.

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After recognizing the need for a more thorough concentration of statistics at the seventh grade level, the author concluded that it would be a good idea to include statistics that cover both seventh and eighth grade Virginia Standards of Learning. Many years of administering the SOL mathematics test at the eighth grade level led the author to the understanding that some of the more advanced seventh graders would be missing some key concepts taught in eighth grade because those advanced students would be taking algebra in the eighth grade. In this thesis, the author has developed four units that she feels are appropriate for this level and will fill the gap.

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Sokhra, Mansur M. "A comparison of four mathematical models for projecting enrollment and teaching staff demand at the preparatory school level in Libya /." The Ohio State University, 1988. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487590702990914.

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Sabo, Melody. "Retaining Interests: The Relationship between Student Interests and Student Retention." Malone University Undergraduate Honors Program / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ma1463139891.

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Benak, David Rhys. "An analysis of mathematics instructional leadership behaviors among Indiana secondary school principals supportive of the implementation of the NCTM Standards." Virtual Press, 2002. http://liblink.bsu.edu/uhtbin/catkey/1233195.

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The purpose of this study was to investigate the degree to which Indiana secondary school principals engaged in mathematics instructional leadership behaviors that supported the implementation of the NCTM Standards.A self-reporting survey was sent to 300 randomly chosen secondary school principals, from a population of 672 public school secondary principals in the State of Indiana during the 2000-2001 school year. A total of 151 usable surveys were returned for a response rate of 50.3 percent. The 151 secondary school principals who returned the questionnaires were 22.5 percent of the population.The survey instrument was an adaptation of questionnaires developed by Horizon Research Incorporated, 1992; Cauley, Van de Walle, and Hoyt, 1993; and Horizon Research Incorporated; 1994. The survey instrument was designed to ascertain demographic information on the principal's school, personal background information on the principal, as well as information concerning the mathematics instructional leadership behaviors of the principal.The major findings from this study were:1. Principals who had more positive attitudes towards the NCTM Standards were more likely to have engaged in a higher degree of support for teachers who implemented the NCTM Standards. Also, principals who had more positive attitudes towards the NCTM Standards were more likely to provide a greater degree of direction to staff members with respect to the implementation of the NCTM Standards.2. Female principals engaged in mathematics instructional leadership behaviors to a greater degree than did male principals.3. Principals from urban schools engaged in mathematics instructional leadership behaviors to a greater degree than did principals from rural schools.
Department of Educational Leadership

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Kunene, Looksmart Lucky Zamokuhle. "Classroomlevel factors affecting mathematics achievement : a comparative study between South Africa and Australia using TIMSS 2003." Diss., University of Pretoria, 2011. http://hdl.handle.net/2263/25819.

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The purpose of the study was to explore and compare key classroom level factors affecting mathematics learner achievement for South Africa and Australia. The study focused in the classroom where teaching and learning takes place. This is a secondary analysis of classroom level factors influencing Grade 8 mathematics learner achievement using the Trends in International Mathematics and Science Study (TIMSS) 2003. TIMSS 2003 was chosen because it was the latest international study available to measure trends in mathematics learner achievement, where South Africa had participated. Quantitative research approach was employed and a survey research method was used which seeks, among others, to explore relationships and patterns. Survey research method was suitable to provide data that responded to the research questions. The data collection in South Africa and Australia was conducted in October-December 2002 as both countries are located in the Southern Hemisphere. The sample for South Africa consisted of 255 schools with 100% coverage and stratification done by a total of nine provinces, and language. This resulted in 8952 learners tested across the provinces (Joncas, 2004, p. 212). For Australia, the sample consisted of 207 schools with 100% coverage and stratification done by a total of 8 States and Territories and school type. This resulted in 4791 learners participating in the study. The sample included teachers of learners who were selected to participate in the TIMSS 2003 study for South Africa and Australia. The intended target was teachers of all learners at the end of their eight year of schooling. For each participating school, a single mathematics class was sampled and the mathematics teacher of the selected class was asked to complete a mathematics questionnaire. Mathematics teachers of sampled learners responded to questions about teaching emphasis on the topics in the curriculum frameworks, instructional practices, professional training and education and their views on mathematics. The mathematics teacher questionnaire was designed to take about 45 minutes to complete The main question for this study was “What are the key classroom factors that influence learner performance in mathematics?” The three sub questions for the study were: What key variables on classroom level are related to learner achievement in mathematics for South Africa? What key variables on classroom level are related to learner achievement in mathematics for Australia? How do the classroom level factors in mathematics performance of South Africa compare with classroom level factors in Australia? The conceptual framework for the study stressed classroom level factors including instructional quality, which includes teacher background factors, classroom climate, teaching requirements and mathematics curriculum. The framework describes the factors related to classroom interactions within the comprehensive education system, with regard to inputs – process – outputs – outcomes. The selection of variables for the inclusion in the models was guided by the conceptual framework and extensive preliminary analyses. Preliminary statistical analyses included exploring descriptive statistics, Varimax factor analysis, reliability, correlation analysis and stepwise multiple regression analysis. The results of the study indicate that several specific classroom level factors were associated with the higher levels of mathematics achievement of South Africa and Australia. The results for the final South African model were: age of teacher; years been teaching; outside school day grading tests; outside school day other; and computer shortage were identified to predict learner achievement. For Australia ten classroom factors, namely, teacher perception of school climate; teacher perception of school safety; teacher emphasis on mathematics homework; teacher repeat mathematics limiting factors; homework contribute towards learning; work conditions; unhappy learners; shortage of instructional equipment; geometric shapes; and algebraic functions were identified to predict learner achievement. South Africa has factors like teacher background and outside school activities by the teacher. Australia has factors like classroom climate, work conditions and curriculum quality. In the light of schools effectiveness research and school improvement research, a comparative study like this one would require more than one level (classroom level), two or three levels would have been ideal to draw other variables and enrich the analysis, especially the learner level and school level. School effectiveness places an emphasis on the ability and social background of the learners as factors that shape academic performance
Dissertation (MEd)--University of Pretoria, 2011.
Science, Mathematics and Technology Education
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Fay, Robert H. "Application of the Fusion Model for Cognitive Diagnostic Assessment with Non-diagnostic Algebra-Geometry Readiness Test Data." Scholar Commons, 2018. https://scholarcommons.usf.edu/etd/7285.

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This study retrofitted a Diagnostic Classification Model (DCM) known as the Fusion model onto non-diagnostic test data from of the University of Chicago School Mathematics Project (UCSMP) Algebra and Geometry Readiness test post-test used with Transition Mathematics (Third Edition, Field-Trial Version). The test contained 24 multiple-choice middle school math items, and was originally given to 95 advanced 6th grade and 293 7th grade students. The use of these test answers for this study was an attempt to show that by using cognitive diagnostic analysis techniques on test items not constructed for that purpose, highly predictable multidimensional cognitive attribute profiles for each test taker could be obtained. These profiles delineated whether a given test taker was a master or non-master for each attribute measured by the test, thus allowing detailed diagnostic feedback to be disseminated to both the test takers and their teachers. The full version of the non-compensatory Fusion model, specifically, along with the Arpeggio software package, was used to estimate test taker profiles on each of the four cognitive attributes found to be intrinsic to the items on this test, because it handled both slips and guesses by test takers and accounted for residual skills not defined by the four attributes and twenty-four items in the Q-matrix. The attributes, one or more of which was needed to correctly answer an item, were defined as: Skills— those procedures that students should master with fluency; e.g., multiplying positive and negative numbers; Properties—which deal with the principles underlying the mathematics concepts being studied, such as being able to recognize and use the Repeated-Addition Property of Multiplication; Uses—which deal with applications of mathematics in real situations ranging from routine "word problems" to the development and use of mathematical models, like finding unknowns in real situations involving multiplication; and, Representations—which deal with pictures, graphs, or objects that illustrate concepts. Ultimately, a Q-matrix was developed from the rating of four content experts, with the attributes needed to answer each item clearly delineated. A validation of this Q-matrix was obtained from the Fusion model Arpeggio application to the data as test taker profiles showed which attributes were mastered by each test taker and which weren’t. Masters of the attributes needed to be acquired to successfully answer a test item had a proportion-correct difference from non-masters of .44, on average. Regression analysis produced an R-squared of .89 for the prediction of total scores on the test items by the attribute mastery probabilities obtained from the Fusion model with the final Q-matrix. Limitations of the study are discussed, along with reasons for the significance of the study.

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Nascimento, Sandro Grossi. "Situações didáticas e educação estatística: uma proposta de aprendizagem no estudo de centralidade para o ensino médio." Universidade Federal de Juiz de Fora (UFJF), 2015. https://repositorio.ufjf.br/jspui/handle/ufjf/3255.

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O presente trabalho é uma pesquisa, cujo objetivo é investigar atividades didáticas de estatística para alunos do Ensino Médio. Essas atividades propiciaram a construção e/ou a reconstrução das medidas de centralidade e, assim, obter um olhar mais detalhado para o estudo dessas medidas, com o intuito de preparar os alunos de forma mais eficiente no uso de situações problemas do cotidiano. Concomitantemente, analisar, a partir da Educação Estatística, com o viés da Literacia Estatística, a compreensão dos resultados obtidos na análise dessas medidas. A teoria da Engenharia Didática subsidiou a metodologia desta investigação enquanto as situações didáticas e as situações a-didáticas foram os aportes teóricos na análise das atividades propostas aos estudantes, culminando assim, em uma proposta de sequência didática para o Produto Educacional. Vale salientar que os sujeitos desta pesquisa são os estudantes de uma escola estadual, turma do terceiro ano do Ensino Médio da cidade de Paraíba do Sul, do Estado do Rio de Janeiro.
This work is a research whose aim is to investigate teaching of statistical activities for high school students. These activities led to the construction and / or reconstruction of the centrality measures and thus a more detailed look at the study of these measures, in order to prepare students more effectively in the use of everyday problems situations. Concomitantly, analyze, from the statistics, with the bias of Literacy Education Statistics, the understanding of the results obtained in the analysis of these measures. The theory of Didactic Engineering supported the methodology of this research while teaching situations and situations-teaching were the theoretical contributions in the analysis of the proposed activities to students, so culminating in a proposal of didactic sequence for the Educational Product. It is worth noting that the subjects of this research are students of a state school, class of third year of high school in the city of Paraiba do Sul, State of Rio de Janeiro.

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Basham, Jennifer Elizabeth. "The Effects of an Overnight Environmental Science Education Program on Students' Attendance Rate Change for Middle School Years." PDXScholar, 2015. http://pdxscholar.library.pdx.edu/open_access_etds/2730.

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Programs that engage middle students in participatory, real-world, and hands-on field based instruction can be a powerful asset to the educational experiences for students; motivating and inspiring some to appreciate and value school in a different way. Overnight environmental science programs have a unique opportunity to support students by creating experiences where students can participate in learning in vastly different ways from what they may engage with in the traditional 4-walled classroom, while concurrently developing a relationship with the natural world. Decreasing educational budgets and increased need to substantiate educational programs in terms of their impact on students has added pressure for overnight environmental science programs to validate their impact through quantitative means. Utilizing overnight environmental science education program attendance records and merging them with school district data relating to attendance, this study investigates the impact of one such overnight environmental science program on students' attendance rate change. Analyzing the secondary data using multiple linear regressions modeling, researchers explored how the overnight environmental program impacted student attendance rate change and how it varied by demographic characteristics to understand if and how the program addresses school district and educational policy reform targets.

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Zen, Priscila Dombrovski. "A importância da estatística no ensino médio." Universidade Estadual de Ponta Grossa, 2017. http://tede2.uepg.br/jspui/handle/prefix/2435.

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A presente pesquisa teve como objetivo principal a análise de documentos, livros didáticos e questões do ENEM a fim de verificar como os mesmos apontam os caminhos para trabalhar o conteúdo de Estatística dentro da disciplina de Matemática no Ensino Médio. A pesquisa será qualitativa, de cunho exploratório e se apoiará nos princípios da pesquisa-ação. Sustentando-se em tais princípios, optou-se pela revisão da literatura referente ao ensino de Estatística onde observou-se o potencial que a mesma apresenta perante o ensino da Matemática na Educação Básica. As legislações investigadas apontam que, cada uma no seu campo de interesse, tem a necessidade da formação completa, disponibilizando aos alunos artifícios capazes de torná-los cidadãos plenos nos aspectos físicos, cognitivos e socioemocionais. O próximo ponto analisado foi em relação a como, o conteúdo da disciplina em foco, é apresentado aos estudantes através dos livros didáticos. Para isso foi realizado um levantamento das coleções utilizadas pelos colégios e verificou-se o conjunto de obras mais utilizado na grande maioria das instituições. Também, segundo a análise realizada, o mesmo é o que contempla os pressupostos contidos na legislação direcionada, seguindo o sentido do proposto pelos autores contidos na literatura. Após as considerações levantadas, foram observadas as questões do ENEM, a fim de verificação referente à quantidade destas no uso da Estatística quando apresentada nas provas. Ainda, quais foram os devidos conteúdos abordados. Como produto final deste documento, foi elaborado um material didático de apoio ao professor, contendo duas propostas de ensino, que se ancoram com o suporte do Software Microsoft Office Excel. As mesmas foram contextualizadas sobre conteúdos básicos de Estatística voltados ao Ensino Médio.
The main objective of the present research was the analysis of documents, textbooks and ENEM questions in order to verify how they point out the ways to work the content of Statistics within Mathematics in High School. The research will be qualitative, exploratory and based on the principles of action research. Based on these principles, it was decided to review the literature regarding the teaching of Statistics, where it was observed the potential that it presents before the teaching of Mathematics in Basic Education. The legislations investigated point out that each one in their field of interest has the need for complete training, providing students with devices capable of making them full citizens in the physical, cognitive and social-emotional aspects. The next point analyzed was in relation to how the content of the subject in focus, is presented to the students through the textbooks. For this, a survey of the collections used by the colleges was carried out and the most used set of works was verified in the great majority of the institutions. Also, according to the analysis carried out, the same is what contemplates the assumptions contained in the targeted legislation, following the meaning proposed by the authors contained in the literature. After the considerations raised, the ENEM questions were observed, in order to verify the number of them in the use of Statistics when presented in the tests. Also, what were the appropriate content addressed. As a final product of this document, a didactic material to support the teacher was prepared, containing two teaching proposals that are anchored with the support of Microsoft Office Excel Software. These were contextualized on basic contents of Statistics directed to High School.

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Norwood, Rick. "How to Think." Digital Commons @ East Tennessee State University, 2015. https://amzn.com/0936414170.

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Thinking is what we do best. Our schools used to teach children to think. They don't any more. If you want to improve your critical thinking skills, read this short, fun, easy to read book. Hear yourself think -- Mind control -- New thoughts for old -- Garbage in, garbage out -- Good ideas -- Reading -- Ask the next question -- Sleep on it -- Lying, and other bad habits -- Angry thoughts -- Fallacies -- Advanced thinking -- Changing your mind.
https://dc.etsu.edu/etsu_books/1120/thumbnail.jpg

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Teng, Yunlong, and Yingrui Zhao. "Statistics in Ella Mathematics." Thesis, Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-21475.

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"Ella Mathematics" is a web-based e-learning system which aims to improve elementary school students’ mathematics learning in Sweden. Such an e-learning tool has been partially completed in May 2012, except descriptive statistics module summarizing students’ performance in the learning process. This project report presents and describes the design and implementation of such descriptive statistics module, which intends to allow students to check their own grades and learning progress; teachers to check and compare students’ grades and progress, as well as parents to compare their children’s grades and learning progress with the average grade and progress of other students. To better understand and design such functionalities, different mathematical e-learning systems were investigated. Another contribution of this project relates to the evaluation and redesign of the existing database model of the “Ella Mathematics” system. The redesign improved performance and reduced data redundancy.

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Gu, Nahai. "Styles cognitifs, langue chinoise et apprentissage des mathématiques et de la statistique : etude exploratoire dans le contexte de l'enseignement secondaire en Chine." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE2058/document.

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Dans cette étude de recherche, nous allons explorer les caractéristiques d’apprentissage des élèves de différents styles cognitifs de l’enseignement secondaire en Chine. Plusieurs études, y compris notre dernière recherche, ont mis en avant le fait que les étudiants universitaires des différents styles cognitifs ont manifesté différentes caractéristiques d’apprentissage. Dans notre travail précédent, nous avons constaté que les connaissances mathématiques sont essentielles pour l’apprentissage de la statistique. En même temps, les étudiants chinois des différents parcours d’étude ont manifesté différents styles cognitifs. De plus, certaines études ont montré les caractéristiques de la généralisation dans l’apprentissage des élèves chinois qui renvoie aux caractéristiques de l’apprentissage de la langue chinoise. Comme tous les étudiants chinois ne font pas leurs études dans le même contexte scolaire et le développement des styles cognitifs sont étroitement lié l’adaptation socioculturelle, nous nous somme intéressé aux relations entre les trois éléments qui sont respectivement le contexte culturel, les caractéristiques d’apprentissage et les styles cognitifs. Ainsi, en tant qu’une étude de continuation, cette thèse se concentre sur les caractéristiques d’apprentissage des mathématiques des lycéens chinois des différents établissements et des différents styles cognitifs. A travers cette thèse, nous visons dans un premier temps à valider des résultats qui sont mis au jour par différentes études recherches de différents contextes culturels. Ensuite, comme la sélection des élèves de chaque établissement est basée sur les concours nationaux qui joue un rôle essentiel à déterminer le contexte scolaire, nous nous intéressons spécifiquement aux styles cognitifs dépendant-indépendants à l’égard du champ et styles cognitifs réflexivité-impulsivité car les caractéristiques des deux types de style cognitif sont, à priori, étroitement lié au contexte de concours. Nous allons explorer les liens entre la sélection des élèves et différents styles cognitifs. Nous allons également voir la relation entre le style cognitif dépendant-indépendant à l’égard du champ et le style réflexivité-impulsivité. Éventuellement, nous allons présenter les différentes caractéristiques d’apprentissage des mathématiques des élèves des différents styles cognitifs et des différents établissements
In this research study, we will explore the learning characteristics of students of different cognitive styles of secondary education in China. Several studies, including our latest research, have highlighted the fact that students of different cognitive styles have manifested different learning characteristics. In our previous work, we noted that mathematical knowledge is essential for the learning of statistic. Meanwhile, Chinese students off different studies showed different cognitive styles. Moreover, some studies have shown the characteristics of generalization in Chinese student learning process which refers to the characteristics of Chinese language learning. Since all Chinese students do not study in the same context and the development of cognitive styles are closely linked to socio-cultural adaptation, we are interested in the relationships between the three elements that are respectively the cultural context, mathematics learning and cognitive styles. Thus, as a continuation study, this thesis focuses on the mathematics learning characteristics of the Chinese high school students of different campus and different cognitive styles.In this thesis, we aim firstly to validate the results that are revealed by different researches of different cultural contexts. Secondly, as the selection of students of each campus is based on the national competitions that play a key role in determining the school context, we are specifically interested in the field dependence-independence cognitive style as well as the reflexivity-impulsivity cognitive style as the characteristics of the two types of cognitive style are, theoretically, closely related to the competition context. We will explore the links between student selection and different cognitive styles. We will also see the relationship between the field dependent-independent cognitive style and the reflexivity-impulsivity cognitive style. Eventually, we will present the different mathematics learning characteristics of students of different cognitive styles and different school campus

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Fernandes, Rúbia Juliana Gomes. "Estatística e probabilidade: uma proposta para os anos iniciais do ensino fundamental." Universidade Tecnológica Federal do Paraná, 2014. http://repositorio.utfpr.edu.br/jspui/handle/1/2359.

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Acompanha: Sequência de ensino: estatística e probabilidade nos anos iniciais do ensino fundamental
O presente trabalho teve como objetivo analisar quais os impactos que uma Sequência de Estudo - SE, pautada no ensino e aprendizagem da Estatística e Probabilidade, poderá causar para os anos iniciais do Ensino Fundamental. Com a intenção de alcançar tal objetivo, desenvolveu-se uma pesquisa aplicada, com enfoque qualitativo de cunho interpretativo numa turma de alunos do 4° ano do Ensino Fundamental da Rede Municipal de Educação da cidade de Curitiba. A fundamentação teórica pauta-se em autores que abordam o ensino de Estatística e Probabilidade, bem como as competências de letramento, pensamento e raciocínio estatístico, como: Cazorla (2002, 2006, 2008), Lopes (2003, 2008, 2010a, 2010b), Silva (2007), Cazorla, Kataoka e Silva (2010), Campos, Wodewotzki e Jacobini (2011), dentre outros. Inicialmente realizou-se uma análise prévia com relação aos conteúdos básicos de Estatística e Probabilidade que os alunos possuíam, por meio de um instrumento diagnóstico (pré-teste). Na sequência trabalhou-se uma sequência de ensino voltada aos conteúdos básicos de Estatística e Probabilidade, utilizando dados coletados na turma, ou seja, contextualizados. Assim, constatou-se, durante o trabalho com a SE, grande interesse, disposição e entusiasmo dos alunos para realização das atividades, além do envolvimento mais acentuado com relação aos conteúdos em questão. Os resultados das análises referentes ao desempenho e aproveitamento dos alunos após o trabalho (pós-teste) com a SE evidenciaram que a proposta favoreceu para que houvesse avanços relevantes quanto à apropriação dos conteúdos básicos de Estatística e Probabilidade dos alunos, em relação à representação tabular e gráfica, probabilidade, combinatória e média aritmética. Apesar disso, é importante destacar que, mesmo com os progressos obtidos, os alunos não compreenderam plenamente todos os conhecimentos sistematizados, ficando latente a necessidade do desenvolvimento de outros encaminhamentos pedagógicos de tais conteúdos. Para esta pesquisa foi elaborado um material didático de apoio, para os professores que atuam no nos anos iniciais do Ensino Fundamental, apresentando uma SE envolvendo os conteúdos básicos de Estatística e Probabilidade, a qual está anexada nesta dissertação.
This research aimed to analyze which contributions of a Sequência de Ensino (SE), based on the teaching and learning Statistics and Probability, can provoke in the irst years of Elementary School. With the intention to reach this aim, an applied esearch was developed, focusing the quality, with interpretative analysis, in a group of 4th year of Elementary School in a public institution in Curitiba, PR. The theory applied is based on theorists engaged in the Statistics and Probabilities teaching, as well as the competences of literacy and statistical thinking and reasoning, such as Cazorla (2002), Lopes (2003, 2008, 2010, 2010b), Silva (2007), Cazorla, Kataoka and Silva (2010), Jacobini et al. (2010), Campos, Wodewotzki and Jacobini (2011), and others. Initially an analysis about the student's Statistics and Probabilities knowledge was made concerning to the basis contents of Statistics and Probability. Using data collected in a group, it means, contextualized data. Then we could figure out, during the work with the SE, a big interest, disposition and enthusiasm from the students to do the activities, beyond the more pronounced engagement with the content in question. The results of the analysis from the (post-test) referring to the student's performance and achievement after working with the SE showed that the proposal favored the relevant advances regarding the appropriation of the students’ basic contents Statistics and Probability concerning the tabular and graphic representation, probability, combinatorial and half arithmetic. Therefore, it is important to remark that, even with the obtained progress, the students did not understand completely all the systematized knowledge, staying salient the necessity of development of other pedagogical ways of these contents. For this research we designed a didactic support material for teachers working in Elementary school in the early years, with a SE involving the basic Statistics and Probability contents, which is attached in this dissertation.

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Flodin, Mikael, and Shadi Khatibi. "Betyg och kön : likvärdighet eller diskriminering?" Thesis, KTH, Lärande, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-227802.

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Nationella och internationella kunskapsmätningar i matematik visar likartade resultat för flickor och pojkar. Trots det visar statistiken att flickor erhåller systematiskt högre slutbetyg. Denna studie undersöker huruvida betyg tjänar som likvärdigt mått på kunskap hos flickor och pojkar i gymnasiets matematikämne. Detta görs dels utifrån en kvantitativ ansats och dels utifrån en enkätstudie. Med utgångspunkt i nationell registerdata (SCB) för slutbetyg och resultat på nationella provet undersöks, medelst fyra olika analysmetoder, könsskillnader med avseende på kurs, skolform och län. Studien visar att flickor generellt erhåller högre slutbetyg än pojkar i relation till resultatet på nationella provet, vilket bekräftar tidigare forskning. Vidare påvisar analysen särskilt stora diskrepanser på betygsnivå C och högre; i matematikkurser på yrkesförberedande program; i senare kurser inom samtliga program; i Västernorrlands, Västmanlands, Gotlands och Kalmar län; liksom i fristående skolor. Korrelationsanalys tydliggör hur nationella provet utgör en mindre del av betygsunderlaget för flickor jämfört med pojkar. Dessutom avslöjar analysen ett omvänt samband mellan könsbetingad relativ prestation på nationella provet och avvikelse i slutbetyget. Enkätstudien undersöker bedömningspraktiken hos matematiklärare. Filtrering på lärarens kön, ålder, program och skolform, har tillämpats. Resultatet tyder på systematiska skillnader i bedömningspraktik mellan olika lärarkategorier, vilket innebär att betygssättningen kan brista i likvärdighet. Skillnader har påvisats mellan, i första hand, lärare på yrkesprogram och naturvetenskapliga program, såväl som mellan lärare i kommunala och fristående skolor. Också lärarens kön och ålder tycks ha viss betydelse. Studien avslutas med en diskussion kring möjliga lösningar.
National and international assessments in mathematics show similar results for girls and boys. Despite this, statistics show that girls receive systematically higher final grades. This study examines whether grades serve as an equivalent measure of knowledge of girls and boys in high school mathematics. This is done partly on the basis of a quantitative approach and partly on the basis of a survey. Based on national register data (Statistics Sweden) for final grades and results of national tests, using four different methods of analysis, gender differences with respect to course, school form and county, are examined. The study shows that girls generally get a higher final grade than boys in relation to their results on the national test, confirming previous research. Furthermore, the analysis shows particularly large discrepancies at grade C and higher; in mathematics courses on vocational programs; in later courses within all programs; in V¨asternorrland, V¨astmanland, Gotland and Kalmar County; as well as in independent schools. Correlation analysis clarifies how the national test constitutes a smaller part of the assessment basis for girls compared to boys. The analysis also reveals an inverse relationship between gender dependent relative performance on the national test and the final grade deviation. The survey examines the assessment practice among mathematics teachers. Filtering on the teacher’s gender, age, program and school form has been applied. The result suggests systematic differences in assessment practice between different teacher categories, implying that grades can break in equality. Differences have been shown between, primarily, teachers in vocational programs and science programs, as well as between teachers in municipal and independent schools. Also the teacher’s gender and age seems to be of some importance. The study concludes with a discussion about possible solutions.

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Bigattão, Junior Pedro Alceu. "Concepção do professor de matemática sobre o ensino da estocástica." Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11507.

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Made available in DSpace on 2016-04-27T17:13:01Z (GMT). No. of bitstreams: 1 Pedro Alceu Bigattao Junior.pdf: 657763 bytes, checksum: 231de498bcd3a6349bfadd0a70a6756c (MD5) Previous issue date: 2007-05-07
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Secretaria da Educação do Estado de São Paulo
The propositions for the teaching of probability and statistics to the Junior High School suffered successive transformations without, many times, discussions by the teachers that are going to put them into practice. So, the purpose of this study was to verify how the teachers of Junior High School see the stochastic concepts when confronted to the problem situations that involve variability in the exploratory analysis of the data. The bibliographic research for the presenting of the theoretical foundation of the studies was performed. The research methodology was based on the Mathematics teachers conceptions about scholastic teaching. So, a descriptive research was performed, whose data were given by the collaborating teachers. Thus, an inquiry with 23 questions was applied. The analysis of the answers was made with the support of the Classification. Hierarchical Implicative and Cohesive Software (C.H.I.C) that enabled to evidence the inter-relations found on the answers. The study concluded that the teachers researched although teaching the scholastic contents, in the majority of times, without the didactic book or no pedagogical material do not dominate this concept, since no one teaches what they do not know
As propostas para o ensino da probabilidade e estatística para o Ensino Fundamental II sofrem transformações sucessivas sem que, muitas vezes, sejam discutidas pelos professores que as colocarão em pratica. Desse modo, o presente estudo tem como objetivo verificar como os docentes de Ensino Fundamental II vêem os conceitos estocásticos quando confrontados com situações problema que envolva variabilidade na análise exploratória dos dados. Foi realizada uma pesquisa bibliográfica a fim de apresentar a fundamentação teórica dos estudos. A metodologia da pesquisa baseou-se nas concepções dos professores de Matemática sobre o ensino estocástico; desse modo foi realizada uma pesquisa descritiva cujos dados foram fornecidos pelos professores colaboradores. Assim, foi aplicado um questionário com 23 questões. A analise das respostas foi feita com o apoio do software Classificação Hierárquica Implicativa e Coesiva (C.H.I.C) que possibilitou evidenciar as inter-relações encontradas nas respostas. O estudo conclui que os professores pesquisados mesmos ensinando os conteúdos estocásticos na maioria das vezes sem o livro didático ou nenhum material pedagógico não domina este conteúdo, visto que ninguém ensina o que não sabe

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Dumitriu, Ioana 1976. "Eigenvalue statistics for beta-ensembles." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/29347.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.
Includes bibliographical references (p. 155-163) and index.
Random matrix theory is a maturing discipline with decades of research in multiple fields now beginning to converge. Experience has shown that many exact formulas are available for certain matrices with real, complex, or quaternion entries. In random matrix jargon, these are the cases β = 1, 2 and 4 respectively. This thesis explores the general P > 0 case mathematically and with symbolic software. We focus on generalizations of the Hermite distributions originating in physics (the "Gaussian" ensembles) and the Laguerre distributions of statistics (the "Wishart" matrices). One of our main contributions is the construction of tridiagonal matrix models for the general (β > 0) 0 β-Hermite and (β > 0, a > β(m - 1)/2) β-Laguerre ensembles of parameter a and size m, and investigate applications of these new ensembles, particularly in the areas of eigenvalue statistics. The new models are symmetric tridiagonal, and with entries from real distributions, regardless of the value of β. The entry distributions are either normal or X, so "classical", and the independence pattern is maximal, in the sense that the only constraints arise from the symmetric/semi-definite condition. The β-ensemble distributions have been studied for the particular 1, 2, 4 values of p as joint eigenvalue densities for full random matrix ensembles (Gaussian, or Hermite, and Wishart, or Laguerre) with real, complex, and quaternion entries (for references, see [66] and [70]). In addition, general -ensembles were considered and studied as theoretical distributions ([8, 51, 50, 55, 56]), with applications in lattice gas theory and statistical mechanics (the parameter being interpreted as an arbitrary inverse temperature of a Coulomb gas with logarithmic potential).
(cont.) Certain eigenvalue statistics over these general β-ensembles, namely those expressible in terms of integrals of symmetric polynomials with corresponding Hermite or Laguerre weights, can be computed in terms of multivariate orthogonal polynomials (Hermite or Laguerre). We have written a Maple Library (MOPs: Multivariate Orthogonal Polynomials symbolically) which implements some new and some known algorithms for computing the Jack, Hermite, Laguerre, and Jacobi multivariate polynomials for arbitrary. This library can be used as a tool for conjecture-formulation and testing, for statistical computations, or simply for getting acquainted with the mathematical concepts. Some of the figures in this thesis have been obtained using MOPs. Using the new β-ensemble models, we have been able to provide a unified perspective of the previously isolated 1, 2, and 4 cases, and prove generalizations for some of the known eigenvalue statistics to arbitrary β. We have rediscovered (in the Hermite case) a strong version of the Wigner Law (semi-circle), and proved (in the Laguerre case) a strong version of the similar law (generalized quarter-circle). We have obtained first-order perturbation theory for the P large case, and we have reason to believe that the tridiagonal models in the large n (ensemble size) limit will also provide a link between the largest eigenvalue distributions for both Hermite and Laguerre for arbitrary P (for β = 1, 2, this link was proved to exist by Johannson [52] and Johnstone [53]) ...
by Ioana Dumitriu.
Ph.D.

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Elizalde, Sergi 1979. "Statistics on pattern-avoiding permutations." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/16629.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.
Includes bibliographical references (p. 111-116).
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
This thesis concerns the enumeration of pattern-avoiding permutations with respect to certain statistics. Our first result is that the joint distribution of the pair of statistics 'number of fixed points' and 'number of excedances' is the same in 321-avoiding as in 132-avoiding permutations. This generalizes a recent result of Robertson, Saracino and Zeilberger, for which we also give another, more direct proof. The key ideas are to introduce a new class of statistics on Dyck paths, based on what we call a tunnel, and to use a new technique involving diagonals of non-rational generating functions. Next we present a new statistic-preserving family of bijections from the set of Dyck paths to itself. They map statistics that appear in the study of pattern-avoiding permutations into classical statistics on Dyck paths, whose distribution is easy to obtain. In particular, this gives a simple bijective proof of the equidistribution of fixed points in the above two sets of restricted permutations.
(cont.) Then we introduce a bijection between 321- and 132-avoiding permutations that preserves the number of fixed points and the number of excedances. A part of our bijection is based on the Robinson-Schensted-Knuth correspondence. We also show that our bijection preserves additional parameters. Next, motivated by these results, we study the distribution of fixed points and excedances in permutations avoiding subsets of patterns of length 3. We solve all the cases of simultaneous avoidance of more than one pattern, giving generating functions which enumerate them. Some cases are generalized to patterns of arbitrary length. For avoidance of one single pattern we give partial results. We also describe the distribution of these statistics in involutions avoiding any subset of patterns of length 3. The main technique consists in using bijections between pattern-avoiding permutations and certain kinds of Dyck paths, in such a way that the statistics in permutations that we consider correspond to statistics on Dyck paths which are easier to enumerate. Finally, we study another kind of restricted permutations, counted by the Motzkin numbers. By constructing a bijection into Motzkin paths, we enumerate them with respect to some parameters, including the length of the longest increasing and decreasing subsequences and the number of ascents.
by Sergi Elizalde.
Ph.D.

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Silva, Wanessa Cristine Costa e. "Contribuições para o desenvolvimento de competências estatísticas no ensino médio por meio dos registros de representação semiótica." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/97/97138/tde-04122018-144950/.

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A escola hoje tem o desafio de atuar na formação de cidadãos capazes de consumir e pensar criticamente as informações que permeiam suas vidas diariamente, que saibam tomar decisões e participem positivamente na construção da sociedade em que vivem. Com o objetivo de colaborar nessa formação, apresenta-se uma proposta de ensino de Matemática, com foco nos conteúdos estatísticos, que possa contribuir no desenvolvimento das competências de letramento, raciocínio e pensamento estatísticos dos alunos. Para isso, utilizaram-se sequências de ensino, contextualizadas com temas do cotidiano selecionados pelo grupo de estudantes, elaboradas a partir de questionários que traçaram o perfil e conhecimentos prévios do grupo. A base para a formalização e análise das sequências foram os pressupostos dos registros de representação semiótica de Duval (2003). Ao final, investigaram-se as habilidades desenvolvidas e as impressões dos alunos por meio de questionários finais. O método utilizado foi pesquisa-ação e o trabalho realizado foi com alunos de duas turmas de 3º ano do Ensino Médio, de uma escola pública do interior do estado de São Paulo. A pesquisa desenvolvida mostrou a importância do ensino e aprendizagem de conceitos estatísticos durante toda a trajetória escolar. O desenvolvimento da proposta foi considerado positivo, pois os alunos participaram ativamente e responderam a ela de forma satisfatória.
The current school has the challenge of acting the formation of citizens who are able to consume and think critically the information that permeates their daily lives, who know how to make choices and participate positively in the construction of the society in which they live. With the objective of collaborating in this training, a proposal of Mathematics teaching is presented, with a focus on statistical content, which can contribute to the development of students` literacy, reasoning and statistical thinking skills. Therefore, teaching sequences were used, contextualized with themes of daily life selected by the group of students, elaborated from questionnaires that traced the profile and previous knowledge of the group. The basis for the formalization and analysis of the sequences were the Duval`s (2003) assumptions of the semiotic representation records. At the end, student`s skills and impressons were investigated through final questionnaires. The used method was action research and the work was carried out with students from two classes of 3rd year of High School, from a public school in a state of São Paulo small town. The developed research showed the importance of teaching and learning statistical concepts throughout the school trajectory. The development of the proposal was considered positive, since the students participated actively and responded to it in a satisfactory way.

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Nordheimer, Swetlana. "Beziehungshaltigkeit und Vernetzungen im Mathematikunterricht der Sekundarstufe I." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2014. http://dx.doi.org/10.18452/16922.

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Die Notwendigkeit einer Untersuchung über Beziehungshaltigkeit und Vernetzungen im Mathematikunterricht ergibt sich einerseits aus den aktuellen bildungspolitischen Forderungen, andererseits aus den reichhaltigen bildungsphilosophischen Traditionen im deutschsprachigem Raum(KMK 2012, 11). Das Ziel der vorliegenden Arbeit besteht vor allem in der Reflexion von Beziehungshaltigkeit und Vernetzungen im Mathematikunterricht. Diese Reflexion ist durch drei Fragen bestimmt: Was kann man als Lehrer über Beziehungshaltigkeit wissen? Wie kann man als Lehrer handeln, so dass die Schüler Beziehungen zwischen mathematischen Inhalten erkennen bzw. selbständig herstellen? Um handeln zu können, muss man die Wirklichkeit oder die Praxis (bzw. Empirie) kennen, in der man handelt. In diesem Sinne ist die vorliegende Arbeit aufgebaut. Dabei wird ein Versuch unternommen, die klassische Aufteilung zwischen Theorie und Empirie bzw. Praxis des Mathematikunterrichts aufzubrechen, um eine Verzahnung zwischen diesen zu verstärken. Das Herzstück der Arbeit bilden zwei ausgearbeitete und in der schulischen Arbeit erprobte Aufgabennetze (Pythagorasbaum und Rund ums Sechseck), die den Rahmen zur Reflexion bieten.
The need for a study on relations sustainability and networks in mathematics stems, on the one hand, from current education policy requirements, and, on the other, from the rich philosophical traditions of education in the German-speaking countries (KMK 2012, 11). The goal of the present work consists, above all, in reflecting on relations sustainability and networks in mathematics lessons. This reflection is guided by three questions: What can one know, as a teacher, about relations sustainability? How can one act a teacher to ensure that students recognise relationships between mathematical content, or independently produce such relations? In order to act, one must know the reality or practice (e.g. empiricism) in which one acts. The project is focused on the development and testing of worked examples of concrete task networks ("Pythagoras’ tree" and "Around the hexagon").

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Bourget, Alain. "Nodal statistics for the Lame ensemble." Thesis, McGill University, 2001. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=37872.

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The Lame polynomials naturally arise when separating variables in Laplace's equation in elliptic-spherical coordinates. The products of these polynomials form a class of spherical harmonics, which are the joint eigenfunctions of a quantum completely integrable system of commuting, second-order differential operators P0 = DSN , P2,..., PN -1 acting on Cinfinity( SN ). These operators depend on parameters and thus constitute an ensemble.
In the main result presented in this thesis, we compute the limiting mean level spacings distribution for the zeroes of Lame polynomials in various thermodynamic, asymptotic regimes. We give results both in the mean and pointwise, for an asymptotically full set of values of the parameters. As an application, we compute the limiting level spacings distribution of the zeroes of Van Vleck polynomials.

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He, Siqian. "Statistics and dynamics of stiff chains." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/38400.

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Marte, Michael. "Models and Algorithms for School Timetabling." Diss., lmu, 2002. http://nbn-resolving.de/urn:nbn:de:bvb:19-9369.

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Steingrímsson, Einar. "Permutations statistics of indexed and poset permutations." Thesis, Massachusetts Institute of Technology, 1992. http://hdl.handle.net/1721.1/35952.

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Ma, Yanyuan 1970. "Studies in matrix perturbation and robust statistics." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/85305.

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Degenhardt, Sheldon. "Weighted-inversion statistics and their symmetry groups /." The Ohio State University, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487941504293867.

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Thayne, Jeffrey L. "Making statistics matter| Self-data as a possible means to improve statistics learning." Thesis, Utah State University, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10250713.

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Research has demonstrated that well into their undergraduate and even graduate education, learners often struggle to understand basic statistical concepts, fail to see their relevance in their personal and professional lives, and often treat them as little more than mere mathematics exercises. Undergraduate learners often see statistical concepts as means to passing exams, completing required courses, and moving on with their degree, and not as instruments of inquiry that can illuminate their world in new and useful ways.

This study explored ways help learners in an undergraduate learning context to treat statistical inquiry as mattering in a practical research context, by inviting them to ask questions about and analyze large, real, messy datasets that they have collected about their own personal lives (i.e., self -data). This study examined the conditions under which such an intervention might (and might not) successfully lead to a greater sense of the relevance of statistics to undergraduate learners. The goal is to place learners in a context where their relationship with data analysis can more closely mimic that of disciplinary professionals than that of students with homework; that is, where they are illuminating something about their world that concerns them for reasons beyond the limited concerns of the classroom.

The study revealed five themes in the experiences of learners working with self-data that highlight contexts in which data-analysis can be made to matter to learners (and how self-data can make that more likely): learners must be able to form expectations of the data, whether based on their own experiences or external benchmarks; the data should have variation to account for; the learners should treat the ups and downs of the data as more or less preferable in some way; the data should address or related to ongoing projects or concerns of the learner; and finally, learners should be able to investigate quantitative or qualitative covariates of their data. In addition, narrative analysis revealed that learners using self-data treated data analysis as more than a mere classroom exercise, but as exercises in inquiry and with an invested engagement that mimicked (in some ways) that of a disciplinary professional.

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39

Liu, Fangda, and 刘芳达. "Two results in financial mathematics and bio-statistics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B46976437.

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Marriott, Paul. "Applications of differential geometry to statistics." Thesis, University of Warwick, 1990. http://wrap.warwick.ac.uk/55719/.

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Chapters 1 and 2 are both surveys of the current work in applying geometry to statistics. Chapter 1 is a broad outline of all the work done so far, while Chapter 2 studies, in particular, the work of Amari and that of Lauritzen. In Chapters 3 and 4 we study some open problems which have been raised by Lauritzen's work. In particular we look in detail at some of the differential geometric theory behind Lauritzen's defmition of a Statistical manifold. The following chapters follow a different line of research. We look at a new non symmetric differential geometric structure which we call a preferred point manifold. We show how this structure encompasses the work of Amari and Lauritzen, and how it points the way to many generalizations of their results. In Chapter 5 we define this new structure, and compare it to the Statistical manifold theory. Chapter 6 develops some examples of the new geometry in a statistical context. Chapter 7 starts the development of the pure theory of these preferred point manifolds. In Chapter 8 we outline possible paths of research in which the new geometry may be applied to statistical theory. We include, in an appendix, a copy of a joint paper which looks at some direct applications of differential geometry to a statistical problem, in this case it is the problem of the behaviour of the Wald test with nonlinear restriction functions.

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Lodhia, Asad. "Topics in linear spectral statistics of random matrices." Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/112898.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 78-83).
The behavior of the spectrum of a large random matrix is a topic of great interest in probability theory and statistics. At a global level, the limiting spectra of certain random matrix models have been known for some time. For example, the limiting spectral measure of a Wigner matrix is a semicircle law and the limiting spectral measure of a sample covariance matrix under certain conditions is a Marc̆enko-Pastur law. The local behavior of eigenvalues for specific random matrix ensembles (GUE and GOE) have been known for some time as well and until recently, were conjectured to be universal. There have been many recents breakthroughs in the universality of this local behavior of eigenvalues for Wigner Matrices. Furthermore, these universality results laws have been proven for other probabilistic models of particle systems, such as Beta Ensembles. In this thesis we investigate the fluctuations of linear statistics of eigenvalues of Wigner Matrices and Beta Ensembles in regimes intermediate to the global regime and the microscopic regime (called the mesoscopic regime). We verify that these fluctuations are Gaussian and derive the covariance for a range of test functions and scales. On a separate line of investigation, we study the global spectral behavior of a random matrix arising in statistics, called Kendall's Tau and verify that it satisfies an analogue of the Marc̆enko-Pastur Law.
by Asad Lodhia.
Ph. D.

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Stadler, Jonathan. "Schur functions, juggling, and statistics on shuffled permutations /." The Ohio State University, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487947501135397.

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Connell, Matthew Aaron. "Generalized Laguerre Series for Empirical Bayes Estimation: Calculations and Proofs." Ohio University Honors Tutorial College / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ouhonors1619179966891297.

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Gustafsson, Anna-Lena, and Sofia Larsson. "Vägen till ett lyckat resultat : hur kan vi minimera antalet elever som lämnar grundskolan utan betyg i matematik." Thesis, University of Skövde, University of Skövde, University of Skövde, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:his:diva-2766.

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Vi har under året fått larmrapporter om att Sveriges matematikundervisning är undermålig. Enligt Skolverkets statistik får vi också detta bekräftat. Undersökningen avser att ta reda på hur lärare uttrycker sig kring undervisning, elevens självbild och kunskapsbedömning när det gäller att minimera antalet elever som lämnar grundskolan utan betyg i matematik. I denna kvalitativa studie har vi valt att intervjua sex matematiklärare i grundskolans senare år. Med dessa intervjuer vill vi synliggöra tänkbara orsaker till att svenska elever tappar mark när det gäller matematikkunskaper. Vi har valt att fokusera på hur undervisning och kunskapsbedömning ser ut på skolor med högt respektive lågt antal elever som ej uppnått målen för matematik i grundskolan. Vi har dessutom valt att lägga fokus på hur elevens självbild påverkar förmågan att tillägna sig matematikkunskaper. I vårt resultat visar det sig att våra sex respondenter inte skiljer sig anmärkningsvärt i hur de undervisar och kunskapsbedömer sina elever utifrån högt eller lågt antal elever som ej uppnått målen för grundskolan i matematik. Vad vi däremot kan se är att matematiklärarna är kritiska till hur undervisningen fungerar i de tidigare åldrarna. Respondenterna ger också en tydlig bild av att vår samhällsstruktur har förändrats vilket ger dem elever med skiftande social och kulturell bakgrund. Vi har behandlat dessa iakttagelser i vår diskussionsdel där vi med stöd från olika litteratur och styrdokument ger tänkbara orsaker om hur vi kan åtgärda resultatet utifrån frågor som var ansvaret ligger men också påvisa olika faktorers samspel i den komplexa verklighet vår skola befinner sig.

We have during the year received alarming reports concerning the inferior state of the Swedish mathematics teaching. According to the statistics from the Department of Education we also get this confirmed. The survey intends to find out how teachers express themselves about teaching, the pupil's self-image, and judging of knowledge when it comes to minimizing the number of pupil's who leave elementary school without any grades in mathematics. In this qualitative study we have chosen to interview six teachers of mathematics from the later years of the elementary school. With these interviews we would like to make visible possible causes why Swedish pupils are falling behind when it comes to knowledge in mathematics. We have chosen to focus on how teaching and judging of knowledge look like at schools with a high respectively low number of pupils who haven't reached the goals set up for mathematics in elementary school. We have also chosen to focus on how the self-image of the pupil affects the ability to acquire knowledge in mathematics. Our results show that our six respondents do not in a considerable way differ in the way they teach and judge the knowledge from a point of view where a high or low number of pupils that have not reached the goals set for the elementary school is concerned. What we can see on the other hand is that the teachers of mathematics are critical about the way the teaching works in the earlier years. The respondents also provide a clear picture that the structure of our society has changed which gives them pupils of shifting social and cultural background. We have treated these observations in our discussion section where we with support from different literature and steering documents present thinkable causes about how we can take measures from questions concerning where the responsibility lies but also show the interplay between different factors in the complex reality where our school is.

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Seier, Edith, and Karl H. Joplin. "Introduction to STATISTICS in a Biological Context." Digital Commons @ East Tennessee State University, 2011. http://amzn.com/1463613377.

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Kritchevski, Evgenij. "Nodal statistics of Heine-Stieltjes and Van Vleck polynomials." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=81348.

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We study the polynomial solutions of the Lame differential equation Azy'' z+2Bz y'z+C zyz=0 where A(z), B( z), C(z) ∈ C [z] are polynomials of degree N + 1, N and N - 1 respectively. We review classical results concerning the location of the zeros of y(z) and C(z) and their electrostatic interpretation. Asymptotic distribution of the zeros as the degree K of y(z) approaches infinity is then discussed. We also derive numerical methods that allow us to compute solutions of high degree K and present a variety of new fine experimental results such as the asymptotic nearest neighbor spacing distribution and the description of complex configurations.

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Bunge, John Arnold. "Distribution theory for record statistics from random record models /." The Ohio State University, 1989. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487671108306781.

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48

Murphy, Sean. "Some topics in spatial probability and statistics." Thesis, University of Bath, 1989. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280810.

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Lochner, Michelle Aileen Anne. "New applications of statistics in astronomy and cosmology." Doctoral thesis, University of Cape Town, 2014. http://hdl.handle.net/11427/12864.

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Over the last few decades, astronomy and cosmology have become data-driven fields. The parallel increase in computational power has naturally lead to the adoption of more sophisticated statistical techniques for data analysis in these fields, and in particular, Bayesian methods. As the next generation of instruments comes online, this trend should be continued since previously ignored effects must be considered rigorously in order to avoid biases and incorrect scientific conclusions being drawn from the ever-improving data. In the context of supernova cosmology, an example of this is the challenge from contamination as supernova datasets will become too large to spectroscopically confirm the types of all objects. The technique known as BEAMS (Bayesian Estimation Applied to Multiple Species) handles this contamination with a fully Bayesian mixture model approach, which allows unbiased estimates of the cosmological parameters. Here, we extend the original BEAMS formalism to deal with correlated systematics in supernovae data, which we test extensively on thousands of simulated datasets using numerical marginalization and Markov Chain Monte Carlo (MCMC) sampling over the unknown type of the supernova, showing that it recovers unbiased cosmological parameters with good coverage. We then apply Bayesian statistics to the field of radio interferometry. This is particularly relevant in light of the SKA telescope, where the data will be of such high quantity and quality that current techniques will not be adequate to fully exploit it. We show that the current approach to deconvolution of radio interferometric data is susceptible to biases induced by ignored and unknown instrumental effects such as pointing errors, which in general are correlated with the science parameters. We develop an alternative approach - Bayesian Inference for Radio Observations (BIRO) - which is able to determine the joint posterior for all scientific and instrumental parameters. We test BIRO on several simulated datasets and show that it is superior to the standard CLEAN and source extraction algorithms. BIRO fits all parameters simultaneously while providing unbiased estimates - and errors - for the noise, beam width, pointing errors and the fluxes and shapes of the sources.

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Pedrick, Micah G. "Complexity of Linear Summary Statistics." Scholarship @ Claremont, 2017. https://scholarship.claremont.edu/hmc_theses/99.

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Families of linear functionals on a vector space that are mapped to each other by a group of symmetries of the space have a significant amount of structure. This results in computational redundancies which can be used to make computing the entire family of functionals at once more efficient than applying each in turn. This thesis explores asymptotic complexity results for a few such families: contingency tables and unranked choice data. These are used to explore the framework of Radon transform diagrams, which promise to allow general theorems about linear summary statistics to be stated and proved.

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Dissertations / Theses on the topic 'School of Mathematics and Statistics'

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