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Hong, Ye Yoon, Suzanne Kerr, Sergiy Klymchuk, et al. "Modelling the Transition from Secondary to Tertiary Mathematics Education: Teacher and Lecturer Perspectives." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-80200.
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The transition from school to tertiary study of mathematics is rightly coming under increasing scrutiny in research. This paper employs Tall’s model of the three worlds of mathematical thinking to examine key variables in teaching and learning as they relate to this transition. One key variable in the transition is clearly the teacher/lecturer and we consider the perspectives of both teachers and lecturers on teaching related matters relevant to upper secondary and first year tertiary calculus students. While this paper deals with a small part of the data from the project, which aims to model the transition, the results provide evidence of similarities and differences in the thinking of teachers and lecturers about the transition process. They also show that each group lacks a clear understanding of the issues involved in the transition from the other’s perspective, and there is a great
need for improved communication between the two sectors.
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Van, Heerden Thomas. "A cultural-historical activity theory based analysis of lecturer and student understanding of learning in the Department of Mathematics and Applied Mathematics at the University of Cape Town." Master's thesis, Faculty of Humanities, 2019. http://hdl.handle.net/11427/30135.
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Cultural-historical activity theory (CHAT) provides a framework for analysing activity systems. I use that framework to investigate teaching and learning in two first-year university mathematics courses at the University of Cape Town. The focus of this investigation is whether the different subjects of this activity system (i.e. the students and the lecturers) have different conceptions of learning, and what those possible differences mean for teaching and learning. The CHAT framework is well-suited to this type of work. CHAT’s theoretical roots are in Hegel’s dialectics and Vygotsky’s mediation. Teaching and learning are higher-order mental phenomena. Dialectics allow us to aggregate our data to draw conclusions about this type of higher-order phenomenon, and the notion of mediation (extended from Vygotsky’s initial work by Leont’ev and others) provides a means to understand how learning happens. Data are collected both through face-to-face interviews with a small group of subjects (n = 6) and more broadly through an online questionnaire (n = 55). The face-to-face interviews and the questionnaires make it clear that students and lecturers do have different conceptions of learning; in the language of CHAT, there are tensions in the system. These tensions can be categorised into two major themes: what students do and how they do it. These tensions will not be easily resolved; I suggest teaching some meta-cognitive skills rather than only mathematics as a first step.
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Mitchell, Karen E. "The effect of postorganizers on mathematics achievement following lectures." Morgantown, W. Va. : [West Virginia University Libraries], 1999. http://etd.wvu.edu/templates/showETD.cfm?recnum=682.
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Thesis (Ed. D.)--West Virginia University, 1999.<br>Title from document title page. Document formatted into pages; contains ix, 209 p. : ill. (some col.) Vita. Includes abstract. Includes bibliographical references (p. 172-195).
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Ng, Swee Fong. "Malaysian pre-service primary mathematics teachers and their lecturers : practice and beliefs about mathematics, teaching and learning." Thesis, University of Birmingham, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365276.
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Kailikole, Kathryn Leimomi. "Meaning making in a college mathematics lecture format the intersection of mathematics, language, and cultural meaning systems /." Diss., [La Jolla] : University of California, San Diego, 2009. http://wwwlib.umi.com/cr/ucsd/fullcit?p3359509.
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Thesis (Ed. D.)--University of California, San Diego, 2009.<br>Title from first page of PDF file (viewed July 7, 2009). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 185-190).
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Mali, Angeliki. "Lecturers' tools and strategies in university mathematics teaching : an ethnographic study." Thesis, Loughborough University, 2016. https://dspace.lboro.ac.uk/2134/25385.
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The thesis presents the analytical process and the findings of a study on: lecturers teaching practice with first year undergraduate mathematics modules; and lecturers knowledge for teaching with regard to students mathematical meaning making (understanding). Over three academic semesters, I observed and audio-recorded twenty-six lecturers teaching to a small group tutorial of two to eight first year students, and I discussed with the lecturers about their underlying considerations for teaching. The analysis of this thesis focuses on a characterisation of each of three (of the twenty-six) lecturers teaching, which I observed for more than one semester. I chose the teaching of three experienced lecturers, due to diversity in terms of ways of engaging the students with the mathematics, and due to my consideration of their commitment to teaching for students mathematical meaning making. The distinctive nature of the study is concerned with the conceptualisation of university mathematics teaching practice and knowledge within a Vygotskian perspective. In particular, I used for the characterisation of teaching practice and of teaching knowledge the notions tool-mediation and dialectic from Vygotskian theory. I also used a coding process grounded to the data and informed by existing research literature in mathematics education. I conceptualised teaching practice into tools for teaching and actions with tools for teaching (namely strategies). I then conceptualised teaching knowledge as the lecturers reflection on teaching practice. The thesis contributes to the research literature in mathematics education with an analytical framework of teaching knowledge which is revealed in practice, the Teaching Knowledge-in-Practice (TKiP). TKiP analyses specific kinds of lecturer s knowing for teaching: didactical knowing and pedagogical knowing. The framework includes emerging tools for teaching (e.g. graphical representation, rhetorical question, students faces) and emerging strategies for teaching (e.g. creating students positive feelings, explaining), which were common or different among the three lecturers teaching practice. Overall, TKiP is produced to offer a dynamic framework for researcher analysis of university mathematics teaching knowledge. Analysis of teaching knowledge is important for gaining insights into why teaching practice happens in certain ways. The findings of the thesis also suggest teaching strategies for the improvement of students mathematical meaning making in tutorials.
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Rejniak, Gabrielle. "Improving Student Learning in Undergraduate Mathematics." Master's thesis, University of Central Florida, 2012. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5455.
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The goal of this study was to investigate ways of improving student learning, par- ticularly conceptual understanding, in undergraduate mathematics courses. This study focused on two areas: course design and animation. The methods of study were the following: Assessing the improvement of student conceptual understanding as a result of team project-based learning, individual inquiry-based learning and the modi ed empo- rium model; and Assessing the impact of animated videos on student learning with the emphasis on concepts. For the first part of our study (impact of course design on student conceptual understanding) we began by comparing the following three groups in Fall 2010 and Fall 2011: 1. Fall 2010: MAC 1140 Traditional Lecture & Fall 2011: MAC 1140 Modi ed Empo- rium 2. Fall 2010: MAC 1140H with Project & Fall 2011: MAC 1140H no Project 3. Fall 2010: MAC 2147 with Projects & Fall 2011: MAC 2147 no Projects Analysis of pre-tests and post-tests show that all three courses showed statistically signifi cant increases, according to their respective sample sizes, during Fall 2010. However, in Fall 2011 only MAC 2147 continued to show a statistically signifi cant increase. Therefore in Fall 2010, project-based learning - both in-class individual projects and out-of-class team projects - conclusively impacted the students' conceptual understanding. Whereas, in Fall 2011, the data for the Modifi ed Emporium model had no statistical signifi cance and is therefore inconclusive as to its effectiveness. In addition the diff erence in percent of increase for MAC 1140 between Fall 2010 - traditional lecture model - and Fall 2011 - modi fied emporium model - is not statistically signi ficant and we cannot say that either model is a better delivery mode for conceptual learning. For the second part of our study, the students enrolled in MAC 1140H Fall 2011 and MAC 2147 Fall 2011 were given a pre-test on sequences and series before showing them an animated video related to the topic. After watching the video, students were then given the same 7 question post test to determine any improvement in the students' understanding of the topic. After two weeks of teacher-led instruction, the students took the same post-test again. The results of this preliminary study indicate that animated videos do impact the conceptual understanding of students when used as an introduction into a new concept. Both courses that were shown the video had statistically signifi cant increases in the conceptual understanding of the students between the pre-test and the post-animation test.<br>ID: 031001440; System requirements: World Wide Web browser and PDF reader.; Mode of access: World Wide Web.; Adviser: Cynthia Young.; Error in paging: p. xi followed by a page numbered xi.; Title from PDF title page (viewed June 26, 2013).; Thesis (M.S.)--University of Central Florida, 2012.; Includes bibliographical references (p. 105-107).<br>M.S.<br>Masters<br>Mathematics<br>Sciences<br>Mathematical Science; Industrial Mathematics
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Zessin, Hans. "Classical Symmetric Point Processes : Lectures held at ICIMAF, La Habana, Cuba, 2010." Universität Potsdam, 2010. http://opus.kobv.de/ubp/volltexte/2011/4961/.
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The aim of these lectures is a reformulation and generalization of the fundamental
investigations of Alexander Bach [2, 3] on the concept of probability in the work of Boltzmann [6] in the language of modern point process theory. The dominating point of view here is its subordination under the disintegration theory of Krickeberg [14]. This enables us to make Bach's consideration much more transparent. Moreover the point process formulation turns out to be the natural framework for the applications to quantum mechanical models.
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Hrubik-Vulanovic, Tatjana. "Effects of intelligent tutoring systems in basic algebra courses on subsequent mathematics lecture courses." Thesis, Kent State University, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3618883.
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<p> The purpose of this study was to investigate how intelligent tutoring system ALEKS, which was implemented in remedial Basic Algebra courses, affected students' success in subsequent lecture courses and how former ALEKS students and instructors in lecture courses perceived ALEKS learning environment. ALEKS courses were delivered in emporium style: instructors were available to answer students' questions, while ALEKS guided students through online exercises individually based on their skills and knowledge. </p><p> The participants were students from four mathematics lecture courses and their instructors. Some students took remedial courses in ALEKS prior to the lecture courses while some students did not. The quantitative part of the study compared ALEKS and non-ALEKS students on the final examination and students' self-reported-preparedness. The qualitative part of the study discussed students' and instructors' perceptions of ALEKS based on student surveys and instructor interviews. </p><p> No difference between ALEKS and non-ALEKS students was found in final examination scores and self-reported-preparedness. Students rated learning experience in ALEKS emporium on average at 2.74 on the scale of one to five, with five being the highest. One third of students liked studying at their own pace and ALEKS content (they rated ALEKS emporium at 3.29), while one fourth claimed that “nothing was good” in emporium courses (they rated ALEKS emporium at 1.55). Although ALEKS emporium was very different from lecture courses, only one fifth of students reported changes in their study habits. The instructors did not observe any difference between ALEKS and non-ALEKS students and mentioned benefits of ALEKS-like tool for drill-and-practice. One instructor observed positive shifts in student attitude towards mathematics but advised longer study to be conducted to confirm this observation. </p><p> Providing a choice to students between online and lecture courses, while increasing the role of instructors in online courses, may result in better student satisfaction. Students could also be gradually trained to effectively use online resources. The design changes in ALEKS could include the replacement of the “pie” with the bar chart, different types of feedback, explanation of how assessments are done, and ability to revisit problems on assessments. </p>
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Hrubik-Vulanovic, Tatjana. "EFFECTS OF INTELLIGENT TUTORING SYSTEMS IN BASIC ALGEBRA COURSES ON SUBSEQUENT MATHEMATICS LECTURE COURSES." Kent State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=kent1373337020.
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Benadé, Catharina Gertruida. "The transition from secondary to tertiary mathematics : exploring means to assist students and lecturers / C.G. Benadé." Thesis, North-West University, 2013. http://hdl.handle.net/10394/9109.
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Early in 2009 it became apparent from articles in the newspapers that first year
mathematics students were not performing as well as the students of previous
years. There was great concern regarding the insufficient transition from
secondary to tertiary mathematics, as well as the preparedness of first year
students for university studies. This research focuses on the different factors
that are potential causes of the underachievement of first year mathematics
students.
Students‟ and lecturers‟ beliefs are shaped by their experiences, the impact of
continuous perceptions from the world around them, the present dominant
paradigm, as well as the beliefs of their teachers. The different views of the
nature of school mathematics show how a worldview has an effect on these
views and the implications of this on the teaching of mathematics in secondary,
as well as tertiary institutions. The paradigm shift from the modern era to the
post-modern era caused an awareness of and interest in the construction of
meaningful mathematical understanding. The gap between first year students‟
and lecturers‟ beliefs regarding the nature of mathematics and how
mathematics is learned became apparent.
The changes in the thoughts about the structure of mathematics were
investigated and a better understanding of the processes through which
mathematical understanding develops emerged. This brought insight into the
gap between the reasoning abilities of incoming students from secondary
schools and the reasoning needed to succeed in university mathematics.
The theoretical study of the global theories of Piaget and Van Hiele gave insight
into conceptual development through different stages and that a person should
be on an appropriate conceptual level to make sense of what they learn. If not,
then rote learning is likely to occur. The local theory of Tall implies that to
facilitate understanding of a concept in mathematics, one should go through
three worlds of mathematics: the embodied world, symbolic world and the
formal world. The embodied view helps someone to give deep meaning to a concept, otherwise one can be trapped in the symbolic world and not be able to
move on to the formal world of mathematical thinking.
The theoretical investigations led to an empirical study in three phases. Phase 1
was an investigation into the views of mathematics held by the students and the
lecturers. In phase 2 an investigation was done to establish the students‟
preferences on how they learn mathematics and how mathematics should be
taught, using the Index of Learning Styles (ILS) questionnaire of Felder and
Silverman. The results were compared with the way lecturers want their
students to learn and how they themselves prefer to teach. Phase 3 included a
classification of the questions in the first mathematics test written at tertiary
level and subsequent analysis of the answers of students to obtain information
on the type of reasoning required from students at tertiary level, as well as the
reasoning abilities of the students.
The empirical study assisted in understanding the problematic transition from
secondary to tertiary mathematics with regard to the nature of mathematics, the
beliefs on teaching and learning of mathematics, as well as the reasoning skills
that the students possess when entering university.<br>Thesis (Ph.D. (Natural Sciences Education))--North-West University, Potchefstroom Campus, 2013
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Roelly, Sylvie. "Unas propiedades basicas de procesos de ramificación : Lectures held at ICIMAF La Habana, Cuba, 2009 and 2010." Universität Potsdam, 2010. http://opus.kobv.de/ubp/volltexte/2011/4962/.
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Aus dem Inhalt:
1. Unas propiedades de los procesos de Bienaymé-Galton-Watson de tiempo dis-
creto (BGW)
2. Unas propiedades del proceso BGW de tiempo continuo
3. Limites de procesos de BGW cuando la población es numerosa
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Loveland, Jennifer L. "Traditional Lecture Versus an Activity Approach for Teaching Statistics: A Comparison of Outcomes." DigitalCommons@USU, 2014. https://digitalcommons.usu.edu/etd/2086.
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Many educational researchers have proposed teaching statistics with less lecture and more active learning methods. However, there are only a few comparative studies that have taught one section of statistics with lectures and one section with activity-based methods; of those studies, the results are contradictory. To address the need for more research on the actual effectiveness of active learning methods in introductory statistics, this research study was undertaken.
An introductory, university level course was divided into two sections. One section was taught entirely with traditional lecture. The other section was taught using active learning methods and a minimal amount of lecture. Both sections were taught by the same instructor during the same semester. The experiment was repeated the next semester.
Students' exam scores were analyzed to determine if the activity-based teaching approach led to higher student comprehension and understanding of statistical concepts, and the ability to apply statistical procedures. Surveys were also administered to students to ascertain if the lecture or activity-based approach led to higher, more positive student attitudes toward statistics.
Analysis of the data did not show that the activity-based teaching method led to higher student comprehension or procedural ability. Neither teaching method led to signicantly higher student attitudes. Student comments indicated a positive response to the activity-based methods, but the responses also indicated a student desire for more teacher-centered time in the activity course.
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Ramollo, Jeanette Khabonina. "The construction of Foundation Phase Mathematics Pedagogy through Initial Teacher Education Programmes." Diss., University of Pretoria, 2014. http://hdl.handle.net/2263/45896.
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The focus of this study is on the Foundation Phase mathematical and pedagogical knowledge construction. This study is about how two lecturers and a number of final year B.Ed. Foundation Phase student teachers construct Foundation Phase mathematical and pedagogical knowledge during the initial teacher education programme.
The initial B.Ed. Foundation Phase teacher education provides student teachers with different mathematical knowledge for teaching. A Foundation Phase mathematics pedagogical knowledge construction framework was utilised to generate and analyse data. The Foundation Phase mathematics pedagogical knowledge construction framework is developed with the assumption that the integrated learning knowledge and the process of pedagogical reasoning action is a continuous process. Furthermore, it is assumed that student teachers’ active participation in their learning and paddling through the pedagogical reasoning action process, leads to the construction of Foundation Phase mathematical pedagogical knowledge.
The study utilised a qualitative case study design to investigate how two initial teacher education programmes construct Foundation Phase mathematical pedagogical knowledge in their programme to prepare student teachers to teach Foundation Phase mathematics. Data were collected from Foundation Phase mathematics lecturers through semi-structured interviews, focus group interviews with final year Foundation Phase student teachers as well as document analysis from the institutions to achieve triangulation. Data analysis and findings were based on themes and categories that emerged. The findings suggest that Foundation Phase mathematical and pedagogical knowledge construction is an interconnected and continuous process that includes different types of knowledge and pedagogical reasoning.<br>Dissertation (MEd)--University of Pretoria, 2014.<br>tm2015<br>Educational Psychology<br>MEd<br>Unrestricted
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Lewis, Hannah Mae. "Implementation and Effects of University College Algebra Growth Mindset Structured Assessments in Large Lectures." DigitalCommons@USU, 2019. https://digitalcommons.usu.edu/etd/7674.
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Recent scientific evidence shows the incredible potential of the brain to grow and change. Students with a growth mindset view errors and obstacles as opportunities for growth. These students welcome challenges and the opportunity to learn from their mistakes. Although some university instructors are incorporating growth mindset into their lectures, attitudes, and exams in small classes, the traditional exam method used in large lecture undergraduate mathematics classrooms follows a fixed mindset model. The growth mindset structured assessments developed for this study incorporate a testing center portion (matching, short answer, fill in the blank and free response) with structured rework opportunities, a written portion with peer reviews, and a group portion.
The purpose of this study was to understand the relationship between (1) large lecture college algebra undergraduate growth mindset structured assessments and (2) students’ achievement, drop/fail/withdraw rates, mindsets, and anxiety. This relationship is determined using the final exam scores, the withdraw and fail rates, and the responses from a Likert scale survey and a Qualtrics free response survey. No statistically significant difference in mean final exam scores was found, however, withdrawal and fail rates were lower for the class participating in the growth mindset structured assessments than the control classes. Lower levels of math test anxiety and higher levels of growth mindset were demonstrated in the class participating in the growth mindset structured assessments.
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Anderson, Dianne S. "The impact of writing and collaborative problem solving on student achievement and attitude in intermediate algebra /." ProQuest subscription required:, 1999. http://proquest.umi.com/pqdweb?did=990270451&sid=1&Fmt=2&clientId=8813&RQT=309&VName=PQD.
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Alotaibi, Bader Omran B. "How and why lecturers of mathematics at universities in the Kingdom of Saudi Arabia use or do not use ICT for teaching : a mixed methods study." Thesis, University of Warwick, 2014. http://wrap.warwick.ac.uk/66430/.
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This thesis has sought to examine how and why mathematics lecturers in Saudi Arabian universities use software for teaching. It is a large-scale, mixed methods study within a post positivist tradition, utilising data collected from interviews and a questionnaire. Eighteen lecturers from two mathematics departments at two major universities in the Kingdom of Saudi Arabia (KSA) were interviewed individually in their offices. Further, 151 lecturers responded to the questionnaire distributed to lecturers of Mathematics and Statistics at eight long-established state universities in KSA. This study explains why lecturers of mathematics at universities use or do not use ICT for teaching and, in so doing, contributes to an under-researched area of study. It raises questions as to how users and non-users of software regard the nature of teaching and learning of mathematics at universities and the contribution of ICT in university-level mathematics. Previous research on the use of software by mathematics teachers has identified a range of factors affecting take up and use of ICT, including access to ICT resources, knowledge of how to integrate technology into mathematics teaching, and beliefs about the role of technology in learning and teaching and assessing mathematics (e.g. an overreliance on technology, use of technology as a black box, use of calculators in examinations). However, there remains ongoing debate about the balance of internal and external factors in the take up of ICT and whether factors related to easy access to software are more (or less) influential than teachers’ beliefs. The findings of this study revealed that identification with the branch of mathematics was a key factor in determining the lecturers who are likely to be users of software in teaching. In particular, it was found that statisticians and computational mathematicians were more likely to be users of software because they were teaching courses which require the use of software. The findings suggested that despite all of the encouraging conditions, contextual and internal barriers — such as a curriculum with heavy and fixed content; software which was not assessed in many cases; lack of cooperation between lecturers to produce curricula which included the use of software; and doubts about the value of software — were at work here. This study has a special interest in Valsiner’s Zone Theory as a lens to study the take up of ICT. In particular, the Zone Theory demystifies why the take up of mathematical software by the mathematics lecturers was patchy despite the good access to ICT resources and the high potential of the use of software in mathematics teaching. From the Zone Theory’s perspective, lecturers worked within a particularly broad zone of free movement but a weak zone of promoted action so that lecturers’ activity was rarely ‘canalised’ into using mathematical software. The Zone Theory puts emphasis on agency-structure dualism, focusing on the actions carried out by individual lecturers as ‘agents’ in the context of constraining and enabling ‘structures’ when making a decision on whether software should be used in teaching. This thesis has reaffirmed the call for more theoretical and empirical research on the issue of the integration of mathematical software in the teaching and learning of mathematics in higher education.
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Ekwuocha, Anthonia O. "Standards-Based Instruction: A Case Study of a College Algebra Teacher." Digital Archive @ GSU, 2012. http://digitalarchive.gsu.edu/msit_diss/101.
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ABSTRACT
STANDARDS-BASED INSTRUCTION: A CASE STUDY OF
A COLLEGE ALGEBRA TEACHER
by
Anthonia Ekwuocha
The lecture method has dominated undergraduate mathematics education (Bergsten, 2007). The lecture method promotes passive learning instead of active learning among students, thus contributing to attrition in undergraduate mathematics. Standards-based instruction has been found to be effective in reducing students’ attrition in undergraduate mathematics (Ellington, 2005). College algebra is gatekeeper for higher undergraduate mathematics courses (Thiel, Peterman & Brown, 2008). Research indicates that if college algebra is taught with standards-based teaching strategies, it will help reduce students’ attrition and encourage more students to take higher level mathematics courses (Burmeister, Kenney, & Nice, 1996). Standards-based instructional strategies include but are not limited to real life applications, cooperative learning, proper use of technology, implementation of writing, multiple approaches, connection with other experiences, and experiential teaching (American Mathematical Association of Two-Year Colleges (AMATYC), 2006).
Despite all effort to improve undergraduate mathematics instruction, there are still limited empirical studies on standards-based instruction in college algebra. Research in undergraduate mathematics education is a new field of study (Brown & Murphy, 2000). Research reported that overall students’ attrition in college algebra could be as high as 41% in a community college (Owens, 2003). This high attrition rate in college algebra may impact students’ continuation in higher mathematics courses and their interest in the field of mathematics. As a result more research efforts must be focused on ways to improve college algebra instruction. Thus, the purpose of this study was to explore the teaching practices of a college algebra teacher who adopts standards-based techniques in his classroom. The research questions that guided the study were: What teaching practices are used in the mathematics classroom of a college algebra teacher? How are the teaching practices of the teacher aligned with the characteristics of standards-based instruction?
The participant of the study was a college algebra teacher who was identified as a standards-based teacher. The teaching practices of the teacher were analyzed and presented using a qualitative single case study method. Data were collected from interviews with the teacher, classroom observations, and artifacts. The research project was drawn from the frameworks of culturally relevant pedagogy theory, symbolic interaction theory, experiential teaching theory, and standards-based instruction.
Analysis of the data showed that the teaching practices of the participant were mathematical communication, proper use of technology in instruction and assessment, building mathematical connections, multiple representations, motivating students to learn mathematics, and repetition of key terms. The teaching practices aligned with the characteristics of standards-based instruction. Findings from the study suggest that standards-based instruction strategies should be used in undergraduate mathematics education, especially in teaching college algebra to alleviate some of the problems. Moreover, university administrators at college level should organize workshops and professional development about standards-based instruction strategies for their teachers.
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Olsen, McCabe J. "HILBERT BASES, DESCENT STATISTICS, AND COMBINATORIAL SEMIGROUP ALGEBRAS." UKnowledge, 2018. https://uknowledge.uky.edu/math_etds/52.
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The broad topic of this dissertation is the study of algebraic structure arising from polyhedral geometric objects. There are three distinct topics covered over three main chapters. However, each of these topics are further linked by a connection to the Eulerian polynomials.
Chapter 2 studies Euler-Mahonian identities arising from both the symmetric group and generalized permutation groups. Specifically, we study the algebraic structure of unit cube semigroup algebra using Gröbner basis methods to acquire these identities. Moreover, this serves as a bridge between previous methods involving polyhedral geometry and triangulations with descent bases methods arising in representation theory.
In Chapter 3, the aim is to characterize Hilbert basis elements of certain 𝒔-lecture hall cones. In particular, the main focus is the classification of the Hilbert bases for the 1 mod 𝑘 cones and the 𝓁-sequence cones, both of which generalize a previous known result. Additionally, there is much broader characterization of Hilbert bases in dimension ≤ 4 for 𝒖-generated Gorenstein lecture hall cones.
Finally, Chapter 4 focuses on certain algebraic and geometric properties of 𝒔-lecture hall polytopes. This consists of partial classification results for the Gorenstein property, the integer-decomposition property, and the existence of regular, unimodular triangulations.
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Axworthy, Angela. "Le statut des mathématiques en France au XVIe siècle : le cas d'Oronce Fine." Thesis, Tours, 2011. http://www.theses.fr/2011TOUR2009/document.
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Cette thèse se propose de déterminer les apports d’Oronce Fine (1494-1555) à la philosophie des mathématiques de la Renaissance. En tant que premier titulaire de la première chaire royale de mathématiques, ce mathématicien a joué un rôle important dans la revalorisation de l’enseignement des mathématiques dans la France du XVIe siècle. Dans cette mesure, sa conception des mathématiques permet de montrer l’évolution du statut épistémologique et institutionnel de ces disciplines dans le milieu académique parisien de cette période. Parmi les thèmes abordés par Fine dans sa définition du statut des mathématiques, nous avons choisi d’étudier, dans une première partie, la nature des objets du mathématicien, le statut épistémologique de l’astronomie, la nature des procédures démonstratives et des principes des mathématiques, ainsi que la fonction du quadrivium dans le processus éducatif. Dans une seconde partie, notre analyse de la pensée de Fine porte sur le statut des mathématiques pratiques et des disciplines subalternes des mathématiques, à savoir la perspective et la géométrie, ainsi que sur le profit qui peut être obtenu de l’apprentissage du quadrivium<br>The aim of this study is to determine the contributions of Oronce Fine (1494-1555) to Renaissance philosophy of mathematics. As first Royal lecturer in mathematics, Fine played a major part in the reassertion of the value of mathematical teaching in sixteenth-century France. Thus, his thought concerning mathematics allows to set forth the evolution of the epistemological and institutional status of these sciences within the parisian academic context of the period. Among the questions tackled by Fine in his definition of the status of mathematics, we consider, in a first part, the ontological status of mathematical things, the epistemological status of astronomy, the nature of mathematical demonstrations and principles, as well as the function of the quadrivium in the educative process. In a second part, our analysis of Fine’s conception on mathematics deals with the status of practical mathematics and of the sciences which are subalternated to mathematics, that is optics and geography, concluding with the definition of the profit which may be obtained from learning mathematics
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Silva, Rosana Rodrigues da. "A história da matemática no portal do professor : uma análise hermenêutica dos planos de aula." reponame:Repositório Institucional da UFABC, 2015.
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Orientadora: Profa. Dra. Virgínia Cardia Cardoso<br>Dissertação (mestrado) - Universidade Federal do ABC, Programa De Pós-Graduação em Ensino, História, Filosofia das Ciências e Matemática, 2015.<br>A presente pesquisa tem como objetivo analisar como a História da Matemática tem sido abordada nos planos de aulas para o Ensino Fundamental, elaborados e publicados no Portal do Professor no "Espaço da Aula". O portal é um espaço para a troca de experiências entre professores do ensino fundamental e médio de todo o país. Conta com sugestões de aulas de acordo com o currículo de cada disciplina e recursos metodológicos variados, dentre deles destacam-se vídeos, fotos, mapas, áudio e textos. Essas sugestões são preparadas pelos professores e publicadas com o objetivo de disseminar experiências educacionais nas e das diferentes regiões do Brasil. A pesquisa terá uma abordagem qualitativa, apresentando um enfoque analítico. Será realizada uma análise de dez planos de aula selecionados no Espaço da Aula do Portal do Professor (MEC) utilizando o Referencial Teórico da Hermenêutica de Profundidade (Thompson, 2011). Este referencial estrutura-se em três "dimensões" interligadas que são denominadas de análise sócio-histórica, análise formal ou discursiva e interpretação/reinterpretação. Realizamos uma análise discursiva das aulas selecionadas com a confrontação do nosso referencial teórico. Foram coletadas 741 aulas de Matemática dos anos finais do Ensino Fundamental, elaboradas e publicadas no Espaço da Aula. Destas, a História da Matemática esteve presente em 71 aulas publicadas, das quais escolhemos dez planos de aulas, um de cada bloco/tema de conteúdo matemático para a análise. Em nossas análises verificamos que os recursos à HM indicados nos planos convergem com as possibilidades pedagógicas apontadas em nosso referencial e são abordados em diferentes itens das aulas elaboradas. Vislumbramos o Portal do Professor como um espaço formativo e de autoria, para o acesso e criação de aulas, também com a HM, por professores de todo o país. Neste trabalho, consideramos a HM importante como um conhecimento para o professor, para o preparo de suas aulas e que tem potencialidades para ser abordada de diferentes formas, sendo uma possibilidade relevante, dentre outras, a ser considerada pelo professor, de acordo com os seus objetivos, apresentando a Matemática como criação humana de diferentes culturas.<br>This research aims to analyze how the history of mathematics has been addressed in the lesson plans for the elementary school, prepared and published in the Teacher Portal in "Space Lesson". The portal is a space for the exchange of experiences among middle and high school teachers across the country. Has suggestions classes according to the curriculum of each discipline and various methodological resources, among them stand out videos, photos, maps, audio and texts. These suggestions are prepared by teachers and published in order to disseminate the educational experiences and from different regions of Brazil. The research will have a qualitative approach, with an analytical approach. An analysis ten lesson plans selected in the Classroom Teacher Portal Space (MEC) using the Theoretical Reference Depth Hermeneutics (Thompson, 2011) will be held. This framework is structured in three "dimensions" intertwined that are called historic partner analysis, formal or discursive analysis and interpretation / reinterpretation. We conducted a discourse analysis of selected classes with the confrontation of our theoretical framework. They collected 741 classes of Mathematics of the final years of elementary school, prepared and published in the Lecture Room. Of these, the mathematics of history was present in 71 lessons published, which chose ten lesson plans, one at a block / mathematical content theme for analysis. In our analysis we find that the resources at HM indicated in the plans converge with the pedagogical possibilities outlined in our framework and are addressed in different items of elaborate lessons. We see the Teacher Portal as a formative and authoring space for access and creating classes, also with HM, teachers across the country. In this paper, we consider the important HM as a knowledge for the teacher to prepare their lessons and that has the potential to be approached in different ways, one relevant possibility, among others, to be considered by the teacher, according to their goals, presenting mathematics as a human creation of different cultures.
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Capelo, Cobo Susana. "Interpretació i elaboració del llenguatge escrit a matemàtiques amb alumnat de Primer Cicle de Primària." Doctoral thesis, Universitat de Barcelona, 2016. http://hdl.handle.net/10803/392654.
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Malgrat tots els moviments de renovació pedagògica sorgits en els últims anys i de la preocupació de la comunitat educativa i concretament de mestres i professors de matemàtiques, el procés d'ensenyament i aprenentatge d'aquesta disciplina continua sent, avui en dia, difícil i associat a problemàtiques molt diverses.
Aquesta realitat serveix de punt de partida d'aquest treball, que mitjançant un estudi longitudinal i de l'elaboració de materials propis per a la investigació, intenta abordar els diferents factors que contribueixen a aquesta realitat, sabent que són molts i de índole molt diversa.
El nostre treball està centrat en donar resposta a quina és la implicació de la comprensió lectora i el domini de les estructures bàsiques del llenguatge, en la resolució de problemes aritmètics en el primer cicle de la Educació Primària.
Sovint sentim a dir, que les matemàtiques són un llenguatge que el nen aprèn de manera simultània als primers aprenentatges lògic-matemàtics, i manté una relació amb el llenguatge general tant oral com a escrit. Moltes de les dificultats que es troben habitualment en el camp de la resolució de problemes aritmètics a les primeres edats, no tenen tant a veure amb la comprensió de l'algoritme sinó que pertanyen a la lectura i comprensió de l'enunciat, a la selecció i organització de les informacions que ofereix l'enunciat, i a la traducció a termes matemàtics.
Aquesta recerca dóna algunes respostes a preguntes com ara: Quina implicació tenen la comprensió lectora i el domini de les estructures bàsiques del llenguatge, en la resolució de problemes aritmètics en alumnes de primer cicle de Educació Primària? Aquesta pregunta a la que diversos autors s'han acostat a la problemàtica de la comprensió lectora associada a la resolució de problemes, però la nostra recerca aprofundeix fent un seguiment d'un grup d'alumnes de 6 a 8 anys durant dos cursos escolars, en l'etapa final de consolidació del procés de lecto-escriptura, aquest fet diferencial marca aquesta recerca.
Els resultats segons els test de comprensió lectora ACL-1 ens mostren que el grup d'estudi està força equilibrat en el nivell de comprensió lectora, si agrupem als alumnes amb un resultat alt o moderadament alt, i els de nivell baix i inferior, ens dona un nombre bastant similar, també succeeix si ho comparem amb el grup de puntuació normal. Però aquesta prova ens permet un altre tipus d'anàlisi que creiem interessant aportar a la recerca. Sabem que cada una de les preguntes que conformen el test, correspon a una tipologia textual concreta i a una dimensió de la comprensió lectora. I hem vist que el major nombre d’errades ha estat en el text narratiu i respecte a la dimensió de la comprensió lectora més compromesa, em comprovat que és la comprensió inferencial.
Respecte dels resultats de les diferents proves de resolució de problemes ens hem trobat amb un grup que tenen un bon nivell i que es relaciona amb els resultats obtinguts amb les proves de llenguatge.<br>Despite the latest educational advances taking place in the last few years, as well as the concern of the educational community, especially involving maths teachers in both primary school, the teaching and learning process in this field is still an arduous task associated with a wide variety of causes.
This fact has been used as the starting point of this research project, which aims to deal with the different factors that contribute to this reality by means of a long-term study, as well as the creation of specific resources, taking into consideration that there are a great many and of diverse nature.
Our research project is based on analysing to what extent reading comprehension as well as good command of basic structures in the language have an influence on mathematical problem solving in the first grades of Primary School students.
We have often been told, that mathematics is a language a child learns simultaneously with the first mathematical logical learning processes, as well as that it is closely related to both oral and written language. Many of the difficulties we usually might come up against when it comes to arithmetic problem solving at early ages, do not stem from the understanding of the algorithm involved, but from the reading comprehension of the written information provided, the selection an organization of the insight given in the question and the translation of this information into mathematical terms.
This research project gives answer to questions such as: How do reading comprehension and a lack of command of basic structures of the language affect arithmetic problem solving in the first stages of Primary school?
Several experts have attempted to give answer to the issue of how reading comprehension affects maths problem solving, however, this research deepens its roots in the last stage of the consolidation of the literacy process, by carrying out a follow-up study among pupils aged 6-8 for two school years.
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Paterno-Mahler, Rachel. "Determining the AGN fraction of galaxy groups." Pomona College, 2007. http://ccdl.libraries.claremont.edu/u?/stc,17.
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Using the Chandra X-ray Observatory, Martini et al. (2006) found that the AGN fraction of galaxy clusters was five times higher than previous optical studies suggested. Using visual observations only, Dressler et al. (1985) estimated the AGN fraction of field galaxies to be 5%, while that of clusters was thought to be 1%. To understand the role that the environment plays in AGN fueling, the author studied a variety of environments, ranging from the field to groups to clusters. Will the AGN fraction of groups also be higher than that of the field? The author demonstrates how the AGN fraction of groups compares to that of clusters. In the following sections, the author describes the mechanics of X-ray astronomy, the group environment, and the characteristics of active galactic nuclei. The author briefly describes the possible mechanisms for AGN fueling.
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Wainwright, C. L. "The effects of spin-orbit coupling on gravitational wave uncertainties." Pomona College, 2007. http://ccdl.libraries.claremont.edu/u?/stc,20.
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Paper discusses the expected uncertainty of orbital parameters of binary stars as measured by the space-based gravitational wave observatory LISA (Laser Interferometer Space Antenna) and how the inclusion of spin in the model of the binary stars affects the uncertainty. The uncertainties are found by calculating the received gravitational wave from a binary pair and then performing a linear least-squares parameter estimation. The case of a 1500 solar mass black hole that is 20 years from coalescing with a 1000 solar mass black hole--both of which are 50 x 10^6 light years away--is analyzed, and the results show that the inclusion of spin has a negligible effect upon the angular resolution of LISA but can increase the accuracy in mass and distance measurements by factors of 15 and 65, respectively.
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Whyburn, Gordon Patrick. "A simple organic solar cell." Pomona College, 2007. http://ccdl.libraries.claremont.edu/u?/stc,21.
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Finding renewable sources of energy is becoming an increasingly important component of scientific research. Greater competition for existing sources of energy has strained the world’s supply and demand balance and has increased the prices of traditional sources of energy such as oil, coal, and natural gas. The experiment discussed in this paper is designed to identify and build an inexpensive and simple method for creating an effective organic solar cell.
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Alemu, Birhanu Moges. "Active learning approaches in mathematics education at universities in Oromia, Ethiopia." Thesis, 2010. http://hdl.handle.net/10500/4133.
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Meaningful learning requires active teaching and learning approaches. Thus, with a specific focus on Mathematics teaching at university in Oramia, the study aimed to:
• examine the extent to which active learning/student-centered approaches were implemented;
• assess the attitudes of university lecturers towards active-learning;
• investigate whether appropriate training and support have been provided for the implementation of an active learning approaches
• assess the major challenges that hinder the implementation of active learning approaches and
• recommend ways that could advance the use of active learning approaches in Mathematics teaching at university.
A mixed-methods design was used. Among the six universities in the Oromia Regional State of Ethiopia, two of the newly established universities (younger than 5 years) and two of the old universities (15 years and older) were involved in the study. A total of 84 lecturers participated in the study and completed questionnaires. This was complemented by a qualitative approach that used observation checklists and interviews for data gathering: 16 lessons were observed while the lecturers taught their mathematics classes (two lecturers from each of the four sample universities were twice observed). In addition, semi-structured interviews were conducted with four mathematics department heads and eight of the observed lecturers. The study adhered to ethical principles and to applied several techniques to enhance the validity/trustworthiness of the findings.<br>Psychology of Education<br>D. Ed. (Psychology of Education)
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Ban, Sun Young. "The Influence of Teaching Instruction and Learning Styles on Mathematics Anxiety in the Developmental Mathematics Classroom." Thesis, 2019. https://doi.org/10.7916/d8-gwy2-b609.
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In the US, an estimated 25% of four-year college students and up to 80% of community college students suffer from a moderate to high degree of mathematics anxiety (MA) (Chang & Beilock, 2016). Many scholars have noted that mathematics anxiety can be regarded as a significant factor in determining a student's achievement and mathematics related jobs.
In the existing literature body, many researchers noted that MA may stem from teaching methods that are more conventional and rule-bounded such as lecture-style classroom models. On the other hand, MA can be mitigated by inquiry-based learning classroom models where students construct knowledge through inquiry, communication, critical thinking, and group work. However, the current literature has not built the connection between different teaching styles and students' individual differences with respect to MA. The individual differences are associated with the personality of the learner, learning styles, learning speed, and needs and interests of the learner. Depending on a student's learning style and a compatible teaching style, the student may actively participate in their own learning with less mathematics anxiety. Thus, the purpose of this study is to determine the influence of different teaching styles on MA, when interacted with Kolb’s and Gregorc’s (1984) four different learning and thinking styles. The research questions investigated in this study are: 1) What is the difference between a lecture classroom model (LCM) and an inquiry-based learning classroom model (IBL) on students’ mathematics anxiety levels over a fifteen-week semester of a college-level remedial mathematics course?; 2) What is the difference between a lecture classroom model (LCM) and an inquiry-based learning classroom model (IBL) on mathematics anxiety levels for students with different learning and thinking styles (as defined by Kolb’s and Gregorc’s learning styles) over a fifteen-week semester?; and 3) What aspects of instructional approaches (LCM and IBL) do students with different learning and thinking styles report as being related to mathematics anxiety? The abbreviated version of the mathematics anxiety rating scale (A-MARS), Kolb’s learning styles inventory, Gregorc’s thinking styles, and Written questionnaire were used to measure students’ MA levels and identify their learning and thinking styles.
The results provided evidence that IBL instruction is beneficial for the students with MA, especially with mathematics test anxiety and mathematics course anxiety. Only numerical task anxiety was not significant. Thus, student-centered learning pedagogies turned out to be an effective and engaging method for lowering MA. However, there was no evidence to support the overall relationship between the constructs of learning and thinking styles and MA levels, above and beyond the instructional approaches. Classifying students according to learning and thinking styles did not influence students’ MA levels in this study over the 15 academic weeks. Moreover, after a 15 academic weeks, students in both LCM and IBL classes responded positively to key components of LCM and IBL classroom models. This implies that both LCM and IBL approaches still are important models regardless of students’ MA levels.
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Cannon, Tina Renee. "Student success a study of computer-based instruction versus lecture-based instruction in developmental mathematics at a Tennessee community college /." 2005. http://etd.utk.edu/2005/CannonTina.pdf.
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Su, Ying-Te, and 蘇英德. "The Research and Editing Lecture of Mathematical Course for the First Year of Senior High School." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/48855686540363578086.
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碩士<br>中原大學<br>應用數學研究所<br>98<br>Abstract
Since the right of compiling the senior high school teaching materials was open to the publishers, choosing the appropriate one has caused teachers trouble. To settle the problem, the first three popular versions at the market as well as considerable literature are reseached and then compiled into a new one.
As Piaget says, students’ learning process is constructed from the simple to the complex. Based on the principle, the recompiled Math teaching material involves not only the traditional teacher’s explanation but also the on-line interactive e-learning, which is presented in the form of animation and designed as a reminder to help learners gain a distinct conception of Math. By the priciple of sharing with others, the On-line Interactive E-learning for the First Grade Senior High Math Learners is put on the net. Those who are interested in the teaching material could download and use it freely.
This thesis involves five chapters. Chapter one is introduction. Chapter two is literature review. Chapter three is the analysis of the first three popular versions of Math teaching materials. Chapter four is the presentation of the recompiled teaching material. Chapter five goes to suggestion and recommendation.
It’s a pity that only the first grade senior high Math is recompiled as a model in this thesis. The others are expected to be done by those who are interested in the subject.
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Rakhudu, Nnane Franscina. "Exploring challenges faced by level 3 National Certificate vocational students in understanding hyperbolic functions in mathematics." Diss., 2017. http://hdl.handle.net/10500/23523.
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The results of mathematics level 3 have always been a problem at TVET colleges as this hampers the certification rate and the progress of the students to level 4. Students who did not do well in the current subject are not allowed to register that subject in the following level. Even though the students are allowed to progress to level 4 they won’t be certificated for both levels until they pass the remaining subject. The above challenges made the researcher to check during the marking and moderation of November / December examination the course of poor results for mathematics level 3. In the process of checking the researcher discovered that rectangular hyperbola is one of the topics that the students of mathematics level 3 are struggling with. This study therefore focuses on exploring the challenges faced by TVET Level 3 NCV students in understanding the hyperbolic function in mathematics.
In addition to the literature review, an empirical investigation based on a qualitative approach and involving semi-structured interviews with the students of a TVET college in North West was conducted to collect data. The analysis of documents relevant to the study was also used as the other method.
The study used participatory action research, where the researcher, collaborators and students work alongside each other to collect data and to improve practice and follow the spiral pattern of reflection, analysing the results and adapting the action. The research design and methodology was qualitative. This helped the researcher to understand the challenges students faced in the learning of rectangular hyperbola and also came up with ways to minimise those challenges. The data collection methods used was interviewing using semi-structured questions, pre-test and post-tests. During data collection different interventions (IN1 –IN3) was used depending on the understanding of the students. For ethical consideration, ethical clearance was obtained from UNISA. DHET, the principal of the college, collaborators, parents and students will also give written consent on forms which will be sent out explaining what we envisage. Since research was voluntary, an explanation was given that this was not compulsory and that participation was completely voluntary and that they could withdraw at any time.
In this study, various methods to empower students were recommended. Recommendations are also made on what was found in this study, as are recommendations for further study.<br>Mathematics Education<br>M. Ed. (Mathematics Education)
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Bekele, Asnake Muluye. "Investigating the influence of pre-calculus mathematics refreshment module to first year engineering students in an Ethiopian university." Thesis, 2019. http://hdl.handle.net/10500/25761.
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The quality of mathematics knowledge attained by students entering university in Science, Technology, Engineering and Mathematics (STEM) fields has been decreasing. There is a need to enhance students’ mathematical knowledge in order to maintain the standards of STEM curriculum at university. The rationale of this study was to investigate the influence of Pre-Calculus Mathematics Refreshment module taught using Meta-cognitive skills and Co-operative Learning (MCL), or Co-operative Learning (CL) only, or Traditional lecture (T) intervention method to First Year pre-engineering Students on their Applied Calculus 1 in an Ethiopian university. The study further investigated the influence of Pre-Calculus Mathematics Refreshment module for MCL, or CL, or T intervention method on male and female students’ achievement. The refreshment module and Applied Calculus 1 scores were measured through posttest and normal class room score of Applied Calculus 1 result. The dependent variables were student achievement in pre-calculus refreshment Module and Applied Calculus 1. Out of 29 universities in Ethiopia only four were selected to participate in this study. Population of this study was all pre-engineering first year students in those universities in 2016/2017. The sample consisted of 200 pre-engineering university students who studied in four of Ethiopian universities and one class was randomly selected by lottery method from existing pre-engineering classes in each university. Two experimental groups which were taught MCL and the other CL intervention method and two of them were control groups upon whom the control novice with traditional lecture method and control without intervention was applied. In each group 50 students of 25 males and 25 females were purposely selected from sampled class. A pre-calculus mathematics Pre-test was administered first, where the average scores of all students Pre-test result was below 33%. Then, first MCL and CL intervention methods were discussed and exercised for one week before implementing the study. For the study, selected pre-calculus mathematics topics was taught in all classrooms for 32 periods i.e. 50min x32= 26.7hrs at the beginning of the first semester parallel with Applied Calculus 1 for the academic year 2016 / 2017.
The statistical tools used under this procedure include descriptive statistics percentage, mean and standard deviation and inferential statistics, T-test, and one-way analysis of variance (one-way ANOVA). The results show statistically significant differences (Sig 0.00) at the significance level (0.05) between students that learnt pre-calculus refreshment module and control group which did not. Among the students those learned pre-calculus refreshment module through MCL, CL and T method students in the MCL and CL groups’ posttest scores significantly different from T group in pre-calculus results both with Sig of 0.00. But there was no significant difference between MCL & CL groups were Sig is 0.97. Additionally, the female students in the MCL group was not significant different from CL and T group, on an impact of refreshment module, in Applied Calculus 1 mathematics where Sig is 0.994 and 0.237 respectively, and CL female group scores significantly different from T group in Applied Calculus 1 results with Sig 0.042. The male students in the MCL and CL groups were significantly different from T group in Applied Calculus 1with Sig of 0.07 and 0.012 respectively. Also, there was a positive correlation between Pre-Calculus refreshment module and Applied Calculus 1 with correlation coefficient of 0.835. Lastly, the result of pre-calculus mathematics posttest scores with the female students in MCL relatively increased than male students, than in CL and T groups, which indicated that MCL benefit more female students than male students. The differences were more in favor of pre-calculus mathematics refreshment with MCL intervention method. To improve success in engineering participation of all students, recommended that a pre-calculus module should be offered by all universities for first year engineering students, structured co-operative learning with purpose has significant gains for effective instruction, and to increase the success rate of female students this study has proven that they are trainable and therefore, meta-cognition skills have to be nurtured for female students.<br>Mathematics Education<br>D. Phil (Mathematics Education in Science and Technology)
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Luquette, Marie. "Nature et rôle des inférences impliquées dans la résolution de problèmes mathématiques." Thèse, 2017. http://hdl.handle.net/1866/20053.
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Carvill, Robert Lee, and Til Karen Van. "Perspective vol. 5 no. 4 (Aug 1971)." 2013. http://hdl.handle.net/10756/251228.
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