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Dissertations / Theses on the topic 'Mathematics education'

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1

Friesen, Sharon Linda. "Reforming mathematics in mathematics education." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0021/NQ54778.pdf.

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2

Copeland, Brian Dwight. "Perceptivist mathematics education." Thesis, University of British Columbia, 1989. http://hdl.handle.net/2429/28203.

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The aim of this paper is to outline and apply a perceptivist philosophy of education and a constructivitist theory of knowledge acquisition to a problem in secondary mathematics education. A working summary of perceptivism and constructivism is provided and a program and lesson materials are discussed within the context of perceptivist-constructivist ideas. The main thesis of this paper is that the way to translate perceptivist-constructivist ideas into practice in mathematics is to emphasize activities that lead to actual perceptions. The traditional problem with this is that often the computational abilities needed to deal with reality are too much for most students to deal with. The information age innovation that makes a utilitarian mathematics education more possible now, where it was not possible previously, is the development of the personal computer. The computer can act as an information processing "step up transformer" to boost students past computation to real, perceptual mathematics. The practical part of the paper consists of lessons aimed at a partial realization of perceptivism-constructivism in the classroom. The lessons concern concepts and skills from the traditional secondary mathematics curriculum areas; arithmetic, algebra, elementary function theory and calculus. The paper concludes with a report on field tests of the materials in the secondary classrooms of the author.
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3

Renert, Moses Eitan. "Living mathematics education." Thesis, University of British Columbia, 2011. http://hdl.handle.net/2429/36911.

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This dissertation searches for possible sources of life in mathematics pedagogy. It is motivated by my observation that much of mathematics education of today is obstructed by inertia. We teach mathematics today using methods and educational philosophies that have changed little in decades of practice, and we generally avoid the harder question of why do it at all? I use Wilber’s (1995) integral theory, a broad metatheory of psychosocial development, to conceptualize life in general, and aspects of life in mathematics education in particular. Wilber’s epistemological framework, called AQAL, describes reality as manifesting in four quadrants – subjective, objective, intersubjective, and interobjective – and in multiple developmental levels. I use AQAL to examine what is revealed about life in mathematics education through these perspectival lenses. The dissertation studies evolutionary dimensions of five related phenomena in mathematics education: purposes of teaching and learning mathematics, human relations in mathematics classes, the subject matter of mathematics, teachers’ mathematical knowledge, and ecological sustainability. I connect the diverse evolutions of these phenomena to reveal extant developmental pathologies in mathematics education, such as the Platonic barrier and excessive objectification. Moving beyond critique, the synthesis gestures toward a new emergent pedagogy – living mathematics education – that evolves mathematics education past these pathologies. The new pedagogy is elaborated through the examples of an instructional unit on circles and the participatory research methodology of concept study. I provide specific suggestions how living mathematics pedagogy may be practiced through dialogical classes, a new purpose of healing the world, a curriculum of sustainability, a skillful blending of Platonic and non-Platonic mathematics, and an improvisatory disposition towards teaching.
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4

Bergman, Ärlebäck Jonas. "Mathematical modelling in upper secondary mathematics education in Sweden." Doctoral thesis, Linköpings universitet, Tillämpad matematik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-54318.

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The aim of this thesis is to investigate and enhance our understanding of the notions of mathematical models and modelling at the Swedish upper secondary school level. Focus is on how mathematical models and modelling are viewed by the different actors in the school system, and what characterises the collaborative process of a didactician and a group of teachers engaged in designing and developing, implementing and evaluating teaching modules (so called modelling modules) exposing students to mathematical modelling in line with the present mathematics curriculum. The thesis consists of five papers and reports, along with a summary introduction, addressing both theoretical and empirical aspects of mathematical modelling. The thesis uses both qualitative and quantitative methods and draws partly on design-based research methodology and cultural-historical activity theory (CHAT). The results of the thesis are presented using the structure of the three curriculum levels of the intended, potentially implemented, and attained curriculum respectively. The results show that since 1965 and to the present day, gradually more and more explicit emphasis has been put on mathematical models and modelling in the syllabuses at this school level. However, no explicit definitions of these notions are provided but described only implicitly, opening up for a diversity of interpretations. From the collaborative work case study it is concluded that the participating teachers could not express a clear conception of the notions mathematical models or modelling, that the designing process often was restrained by constraints originating from the local school context, and that working with modelling highlights many systemic tensions in the established school practice. In addition, meta-results in form of suggestions of how to resolve different kinds of tensions in order to improve the study design are reported. In a questionnaire study with 381 participating students it is concluded that only one out of four students stated that they had heard about or used mathematical models or modelling in their education before, and the expressed overall attitudes towards working with mathematical modelling as represented in the test items were negative. Students’ modelling proficiency was positively affected by the students’ grade, last taken mathematics course, and if they thought the problems in the tests were easy or interesting. In addition empirical findings indicate that so-called realistic Fermi problems given to students working in groups inherently evoke modelling activities.
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Ferdinand, Victor Allen. "An elementary mathematics methods course and preservice teachers' beliefs about mathematics and mathematical pedagogy: A case study /." The Ohio State University, 1999. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488191124570001.

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6

Abdeljaber, Soha R. "High school mathematics teachers' perceptions of mathematics education in northwest Florida." Thesis, University of Phoenix, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3731744.

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In the United States, high school students have performed lower in mathematics than all the industrialized countries since the First International Study was administered in 1964. Studies revealed that a large number of high school graduates are not proficient in mathematics and are not ready for college mathematics or the workforce. This qualitative research intended to answer the question of why the U.S. high school students underperform in mathematics through teacher perceptions on the current curriculum and methods of instruction used in high school mathematics classes. The question was answered by exploring the perceptions of 12 high school mathematics teachers in northwest Florida through a survey of 16 open-ended questions and a focus group discussion that guided the research. Furthermore, the survey and focus group data were triangulated with teacher artifacts that included lesson plans. This resulted in an aggregate of 15 themes that included time, professional development, gap in the students’ knowledge, student encouragement, application to real world, resources, rigor, student encouragement, teacher collaboration, student ownership, standardized testing, traditional teaching, too many topics, two-tracks courses, practice and mental math, and student collaboration.

The findings of this research support the need to provide teachers with more time to teach, plan, and collaborate. Teachers also need more support from the educational leaders to provide professional development that will help teachers apply real-world, collaborative learning, and move away from the current traditional teaching that most of the participating teachers in this study prefer.

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7

Piatek-Jimenez, Katrina L. "Undergraduate mathematics students' understanding of mathematical statements and proofs." Diss., The University of Arizona, 2004. http://hdl.handle.net/10150/280643.

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This dissertation takes a qualitative look at the understanding of mathematical statements and proofs held by college students enrolled in a transitional course, a course designed to teach students how to write proofs in mathematics. I address the following three research questions: (1) What are students' understandings of the structure of mathematical statements? (2) What are students' understandings of the structure of mathematical proofs? (3) What concerns with the nature of proof do students express when writing proofs? Three individual interviews were held with each of the six participants of the study during the final month of the semester. The first interview was used to gain information about the students' mathematical backgrounds and their thoughts and beliefs about mathematics and proofs. The second and third interviews were task-based, in which the students were asked to write and evaluate proofs. In this dissertation, I document the students' attempts and verbal thoughts while proving mathematical statements and evaluating proofs. The results of this study show that the students often had difficulties interpreting conditional statements and quantified statements of the form, "There exists...for all..." These students also struggled with understanding the structure of proofs by contradiction and induction proofs. Symbolic logic, however, appeared to be a useful tool for interpreting statements and proof structures for those students who chose to use it. When writing proofs, the students tended to emphasize the need for symbolic manipulation. Furthermore, these students expressed concerns with what needs to be justified within a proof, what amount of justification is needed, and the role personal conviction plays within formal mathematical proof. I conclude with a discussion connecting these students' difficulties and concerns with the social nature of mathematical proof by extending the theoretical framework of the Emergent Perspective (Cobb & Yackel, 1996) to also include social norms, sociomathematical norms, and the mathematical practices of the mathematics community.
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Rodd, Mary Melissa. "Mathematical warrants, objects and actions in higher school mathematics." Thesis, Open University, 1998. http://oro.open.ac.uk/54372/.

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'Higher school mathematics' connotes typical upper secondary school and early college mathematics. The mathematics at this level is characterised by moves to (1) rigour in justification,(2) abstraction in content and (3) fluency in symbolic manipulation. This thesis investigates these three transitions - towards rigour, abstraction, and tluencyusing philosophical method: for each of the three transitions a proposition is presented and arguments are given in favour of that proposition. These arguments employ concepts and results from contemporary English language-medium philosophy and also rely crucially on classroom issues or accounts of mathematical experience both to elucidate meaning and for the domain of application. These three propositions, with their arguments, are the three sub-theses at the centre of the thesis as a whole. The first of these sub-theses (1) argues that logical deduction, quasi-empiricism and visualisation are mathematical warrants, while authoritatively based justification is essentially non-mathematical. The second sub-thesis (2) argues that the reality of mathematical entities of the sort encountered in the higher school mathematics curriculum is actual not metaphoric. The third sub-thesis (3) claims that certain 'mathematical action' can be construed as non-propositional mathematical knowledge. The application of these general propositions to mathematics in education yields the following: 'coming to know mathematics' involves:(1) using mathematical warrants for justification and self conviction; (2) ontological commitment to mathematical objects; and (3)developing a capability to execute some mathematical procedures automatically.
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Leung, King-shun, and 梁景信. "Pre-service teachers' attitudes towards mathematics and mathematics education." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1996. http://hub.hku.hk/bib/B30106515.

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Leung, King-shun. "Pre-service teachers' attitudes towards mathematics and mathematics education /." Hong Kong : University of Hong Kong, 1996. http://sunzi.lib.hku.hk/hkuto/record.jsp?B17595848.

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11

Patel, C. "Approaches to studying and the effects of mathematics support on mathematical performance." Thesis, Coventry University, 2011. http://curve.coventry.ac.uk/open/items/f079ef99-a237-4a3b-ae2d-344c89654741/1.

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The concern over undergraduate engineering students’ mathematical skills and the means of addressing this through the provision of mathematics support is the main driver of this research. With the emergence of mathematics support within mathematics education there has been an associated research community interested in measuring the effectiveness of mathematics support provision. Recent studies have measured improvements in mathematics performance for students who have used mathematics support against those who have not by comparing prior mathematical ability against examination results. This does not address the issue of individual differences between students and resulting changes in mathematical ability. However the provision of mathematics support for individual students is resource intensive hence evaluation of the effectiveness of the support is essential to ensure resources are efficiently used. This mathematics education research examines the effectiveness of mathematics support in addressing the mathematics problem. It does this by considering individual differences and the mismatch of mathematical skills for studying at University by analysing the effectiveness of mathematics support in improving mathematical skills. The dataset for the analysis comprises of over 1000 students from a Scottish Post-92 University, over 8% having made use of mathematics support, and nearly 2000 students from an English Russell Group University, with just over 10% having made use of the support. It was discovered that in both sets of data the students who came for mathematics support in comparison to their peers had a statistically significant lower mathematical skills base on entry to their course, and at the end of their first year had improved their mathematical skills base more than their counterparts. Although the analysis is based on data from UK Universities we believe the findings are relevant to the international community who are also engaged in the provision of mathematics support.
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12

Rundquist, Rebecka. "Mathematics education in Colombia : How education in mathematics is conducted in a development country." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-52736.

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This study aims to examine the education in mathematics in Colombia and by examining a few cases aspires to describe how education in mathematics in Colombia can operate and which patterns that are common in those cases. This was actualized by using methodological triangulation at three schools in Colombia. The data collection methods that were combined were: observations, interviews with teachers, interviews with students and interpretation of national standards, as well as other essential documents used in mathematics education in Colombia. An analytic framework was created from prior studies that were conducted in Latin America and also from well known pedagogical research across the world. The results of the study were many and they indicated, inter alia, that the students, teachers and other employees had different views of the lessons and classes in mathematics. Furthermore, common concept within education – in mathematics and in general – appeared to be completely non-existent to every party.
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Simanjorang, Mangaratua. "Integrating ethics into mathematics education: A philosophical auto/ethnographic inquiry into Indonesian mathematics education." Thesis, Simanjorang, Mangaratua (2016) Integrating ethics into mathematics education: A philosophical auto/ethnographic inquiry into Indonesian mathematics education. PhD thesis, Murdoch University, 2016. https://researchrepository.murdoch.edu.au/id/eprint/35052/.

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Unity in diversity is the foundation principle of my country. For me this is the simplest yet clearest description of Indonesia. There is no Indonesia without diversity, and no Indonesia without unity. Differences that are implicit in diversity can be a reason for conflict or for the origin of harmony, depending on how we relate and respond to the other. My anxiety about potential conflict and my dream for a harmonious life in relation to the diversity of my country raises a question in my mind: what is my role as a mathematics educator to make that dream come true? This thought about my relation with the other and my ability to respond to the existence of the other brings forward a concern for ethics. Ethical responsibility may become the answer to both my anxiety and my dream, which then raises another question: how can I integrate ethics into mathematics education? This thesis is a story about my journey in pursuing an answer to these anxiety/dream questions. Trying to understand the meaning of the ancient term ‘ethics’ is like a journey in a deep dark jungle; filled with uncertainty, anything might happen. On this journey confusion, anxiety and loneliness frequently made me exhausted. However, when I reflected on these experiences I found that a light was illuminating my way. Adopting a multi-paradigmatic research approach, I shifted from one epistemology to another in appropriate ways. By means of critical self-reflection within a philosophical auto/ethnography I tried to construct a coherent understanding of the issues. I found the importance of listening when seeking understanding in differences, which allowed me to conceive of an integrative ethics perspective, with critical inclusivity as the quality standard. Drawing on a critical narrative inquiry method this thesis represents the story of my transformative learning experience.
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Schenkel, Benjamin D. "THE IMPACT OF AN ATTITUDE TOWARD MATHEMATICS ON MATHEMATICS PERFORMANCE." Marietta College / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=marietta1241710279.

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15

Owens, Beverly Karen. "The Language of Mathematics: Mathematical Terminology Simplified for Classroom Use." Digital Commons @ East Tennessee State University, 2006. https://dc.etsu.edu/etd/2242.

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After recognizing the need for a simpler approach to the teaching of mathematical terminology, I concluded it would be valuable to make a unit of simplified terms and describe methods of teaching these terms. In this thesis I have compared the terminology found in the Virginia Standards of Learning objectives to the materials found at each grade level. The units developed are as follows: The Primary Persistence Unit- for grades K-2; The Elementary Expansion Unit- for grades 3-5; and The Middle School Mastery Unit- for grades 6-8.
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Yoder, Gina Borgioli. "Understanding mathematics teachers' constructions of equitable mathematics pedagogy." [Bloomington, Ind.] : Indiana University, 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3330796.

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Thesis (Ph.D.)--Indiana University, School of Education, 2008.
Title from PDF t.p. (viewed on Jul 21, 2009). Source: Dissertation Abstracts International, Volume: 69-10, Section: A, page: 3849. Adviser: Signe Kastberg.
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Dickerson, David S. "High school mathematics teachers' understandings of the purposes of mathematical proof." Related electronic resource: Current Research at SU : database of SU dissertations, recent titles available full text, 2008. http://wwwlib.umi.com/cr/syr/main.

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18

Bergen, Sarah. "Mathematics and Foreign Language: Authentic Texts in Mathematics." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1492529675611436.

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19

Goodell, Joanne E. "Equity and reform in mathematics education." Thesis, Curtin University, 1998. http://hdl.handle.net/20.500.11937/397.

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This study focused on two themes which have recurred in education since the 1980's: equity of educational outcomes for all students and reform in mathematics education. The problem addressed in this study concerned the apparent inability of large- scale reforms to meet equity goals. The purpose of the study was to increase understanding of this problem from both theoretical and practical perspectives. The study was influenced by feminist perspectives in the choice of theoretical framework and methodology. Focusing specifically on gender equity, the study was set in the context of a large-scale reform in the USA, Ohio's Statewide Systemic Initiative, Project Discovery.There were three major objectives in this study. First was to synthesise the literature concerning gender equity in mathematics education to produce a definition of the ideal Connected Equitable Mathematics Classroom (CEMC). There were two parts to the literature review: one concerning explanations for observed gender differences in mathematics education, and another concerning initiatives implemented to try to bring about gender equity in mathematics education.The second objective was to use the definition of the ideal CEMC, derived from the literature, to determine the extent to which reform had occurred in mathematics classrooms in Ohio. This was accomplished through the analysis of quantitative data collected from a random sample of teachers and principals across the state, and qualitative data collected from seven case study sites. The third objective was to determine the barriers to and facilitators of the realisation of equity goals in middle-school mathematics classrooms involved in Project Discovery. This was accomplished through a cross-site analysis of data collected at the seven case- study sites, with the analysis framed around the characteristics of the CEMC.The outcomes of the study are set out in terms of these three objectives, culminating in a discussion of the implications and challenges which the findings of this study pose for researchers, reformers, equity advocates and practitioners.
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20

Wolfe, Kristen E. "The Core Plus Mathematics Project and high school students' mathematics achievement." Cleveland, Ohio : Cleveland State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=csu1216499106.

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Thesis (M.Ed.)--Cleveland State University, 2008.
Abstracts. Title from PDF t.p. (viewed on Jan. 29, 2009). Includes bibliographical references (p. 22-23). Available online via the OhioLINK ETD Center. Also available in print.
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21

Laurenson, David James. "Patterns of interactions among mathematics educators: Perceptions of high school mathematics teachers and university mathematics faculty." Diss., The University of Arizona, 1992. http://hdl.handle.net/10150/185922.

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The aim of this study was to describe the interactions among mathematics educators, particularly high school mathematics teachers and university mathematics educators, with a view to determining the professional development that occurs in a university setting. Two university mathematics departments were selected for this study on the basis of their proactive stance in mathematics education. Data were collected through interviews, observations, and written materials pertaining to the mathematics education programs offered. Six university mathematics faculty members and six high school teachers were studied in depth to gain insight into the history, the current endeavors, the goals, the beliefs, and the outcomes of the various programs offered at the two sites. The data were analyzed using Glaser's (1967) constant comparison method to allow explicit coding procedures to accompany the generation of theory in a systematic manner. Having students as the focus of interactions is a characteristic at both sites as is an emphasis on problem solving. Both university educators and high school teachers believe in the work they are doing and think of themselves as being on the cutting edge of developments in mathematics education. The contexts in which the interactions operate display conditions of support, trust, respect, openness, commitment, and vision. The educators are involved in processes of mutual sharing in environments conducive to thinking about change. It can be concluded that interactions among mathematics educators in a university setting can be beneficial. The development of relations and interactive processes take time to establish and require the dedication of individuals who truly believe that mathematics education can be improved. Future studies could focus on the development of a framework for mathematics teachers' beliefs and on the ramifications of linkage structures that exist in collaborative ventures between schools and universities.
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Graumann, Günter. "Reflecting Problem Orientation in Mathematics Education within Teacher Education." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-82503.

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Braaten, Bailey M. "Mathematical Identities: Narratives and Discourses of Female Students in 8th and 9th Grade Mathematics." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1595000898006834.

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Hamburg, Maryanna P. "Financial Mathematical Tasks in a Middle School Mathematics Textbook Series: A Content Analysis." University of Akron / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=akron1258164585.

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25

Allie-Ebrahim, Ferial. "Students, texts and mathematics : an analysis of mathematics texts and the construction of mathematics knowledge." Master's thesis, University of Cape Town, 2001. http://hdl.handle.net/11427/10064.

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Bibliography: leaves 149-155.
This study deals with a systematic description of student production of mathematics texts and focused on written texts that appeared to be legitimate yet could not be upheld by a principled verbal description. A search of the literature on the analysis of students texts revealed that semiotic analysis, was not only scarce, but ideally suited to examining the social organisation of school mathematics practice. This study examines how student texts produced in response to typical school mathematics problems can, via a systematic analysis of texts, index the construction of mathematics knowledge. It outlines Dowlings' model of Social Activity Theory (1998) to produce a textual analysis which focuses on textual strategies to distribute message. These strategies and the message underpin the analysis. Practices that establish the message distributed indexes mathematics knowledge and curriculum practices. The notion of a mathematising gaze informing school practice was explored and was related to the construction of existing and pre-existing mathematics knowledge. To locate the effects of a mathematics gaze that could produce texts that lacked discursive elaboration in verbal discriptions, a comprehensive list of ideal types were developed to act as an interface between the empirical text produced that acted as a reading for constructive description of the theoretical terrain.
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Van, Dyken Kymn M. "Technology in mathematics education and TI-Navigator in the mathematics classroom." [Denver, Colo.] : Regis University, 2008. http://165.236.235.140/lib/KVanDyken2008.pdf.

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27

Goodell, Joanne E. "Equity and reform in mathematics education." Curtin University of Technology, Science and Mathematics Education Centre, 1998. http://espace.library.curtin.edu.au:80/R/?func=dbin-jump-full&object_id=12291.

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This study focused on two themes which have recurred in education since the 1980's: equity of educational outcomes for all students and reform in mathematics education. The problem addressed in this study concerned the apparent inability of large- scale reforms to meet equity goals. The purpose of the study was to increase understanding of this problem from both theoretical and practical perspectives. The study was influenced by feminist perspectives in the choice of theoretical framework and methodology. Focusing specifically on gender equity, the study was set in the context of a large-scale reform in the USA, Ohio's Statewide Systemic Initiative, Project Discovery.There were three major objectives in this study. First was to synthesise the literature concerning gender equity in mathematics education to produce a definition of the ideal Connected Equitable Mathematics Classroom (CEMC). There were two parts to the literature review: one concerning explanations for observed gender differences in mathematics education, and another concerning initiatives implemented to try to bring about gender equity in mathematics education.The second objective was to use the definition of the ideal CEMC, derived from the literature, to determine the extent to which reform had occurred in mathematics classrooms in Ohio. This was accomplished through the analysis of quantitative data collected from a random sample of teachers and principals across the state, and qualitative data collected from seven case study sites. The third objective was to determine the barriers to and facilitators of the realisation of equity goals in middle-school mathematics classrooms involved in Project Discovery. This was accomplished through a cross-site analysis of data collected at the seven case- study sites, with the analysis framed around the characteristics of the CEMC.The outcomes of the study are ++
set out in terms of these three objectives, culminating in a discussion of the implications and challenges which the findings of this study pose for researchers, reformers, equity advocates and practitioners.
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Hulet, Ashley Burgess. "Student Evaluation of Mathematical Explanations in anInquiry-Based Mathematics Classroom." BYU ScholarsArchive, 2015. https://scholarsarchive.byu.edu/etd/5715.

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Students do not always evaluate explanations based on the mathematics despite their teacher's effort to be the guide-on-the-side and delegate evaluation to the students. This case study examined how the use of three features of the Discourse—authority, sociomathematical norms, and classroom mathematical practices—impacted students' evaluation and contributed to students' failure to evaluate. By studying three pre-service elementary school students' evaluation methods, it was found that the students applied different types of each of the features of the Discourse and employed them at different times. The way that the features of the Discourse were used contributed to some of the difficulties that the participants experienced in their evaluation of explanations. The results suggest that researchers in the field must come to believe that resistance to teaching methods is not the only reason for student failure to evaluate mathematical explanations and that authority is operating in the classroom even when the teacher is acting as the guide on the side. The framework developed for the study will be valuable for researchers who continue to use for their investigation of individual student's participation in mathematical activity.
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Khateeb, Majeda Education Faculty of Arts &amp Social Sciences UNSW. "Cognitive load theory and mathematics education." Publisher:University of New South Wales. Education, 2008. http://handle.unsw.edu.au/1959.4/42635.

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Cognitive load theory uses the immense size of human long-term memory and the significantly limited capacity of working memory to design instructional methods. Five basic principles: information store principle, borrowing and reorganizing principle, randomness as genesis principle, narrow limits of change principle, and environmental linking and organizing principle explain the cognitive basics of this theory. The theory differentiates between three major types of cognitive load: extraneous load that is caused by instructional strategies, intrinsic cognitive load that results from a high element interactivity material and germane load that is concerned with activities leading to learning. Instructional methods designed in accordance with cognitive load theory rely heavily on the borrowing and reorganizing principle, rather than on the randomness as genesis principle to reduce the imposed cognitive load. As learning fractions incorporates high element interactivity, a high intrinsic cognitive load is imposed. Therefore, learning fractions was studied in the experiments of this thesis. Knowledge held in long-term memory can be used to reduce working memory load via the environmental linking and organizing principle. It can be suggested that if fractions are presented using familiar objects, many of the interacting elements that constitute a fraction might be embedded in stored knowledge and so can be treated as a single element by working memory. Thus, familiar context can be used to reduce cognitive load and so facilitate learning. In a series of randomized, controlled experiments, evidence was found to argue for a contextual effect. The first three experiments of this thesis were designed to test the main hypothesis that presenting students with worked examples concerning fractions would enhance learning if a real-life context was used rather than a geometric context. This hypothesis was tested using both a visual and a word-based format and was supported by the results. The last two experiments were intended to test the context effect using either worked examples or problem solving. The results supported the validity of the previous hypothesis using both instructional methods. Overall, the thesis sheds some light on the advantages of using familiar objects when mastering complex concepts in mathematics.
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Torr, Stuart. "Construal level theory and mathematics education." Master's thesis, University of Cape Town, 2013. http://hdl.handle.net/11427/9132.

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Includes bibliographical references.
A common complaint of mathematics students is that mathematics is highly abstract. Students often find it difficult to attach meaning to the mathematical concepts they are expected to master. In addition to coming to grips with the abstract nature of the subject, mathematical proficiency requires engagement at a more concrete level. Students must be able to perform step by step algorithmic procedures, detailed algebraic manipulations and master new symbol systems. Mathematical competence often requires thinking at high and low levels of abstraction almost simultaneously and this creates a tension which lies at the core of mathematics education. This tension has been addressed in the literature on procedural versus conceptual approaches to mathematics education and in the literature on cognitive and metacognitive mathematical demands. Construal level theory, and to a lesser extent dual process theory, are theories in cognitive and social psychology which provide a lens through which the difficulties of reasoning at multiple levels of abstraction can be viewed. Construal level theory posits that thinking about psychologically distant objects influences the extent to which we view possibly unrelated objects abstractly or concretely. Psychological distance and abstract thought are cognitively linked together and make up Far Mode thinking. Psychological proximity and concrete thinking are intrinsically linked together to form Near Mode thinking. It is argued that construal level theory forms a useful framework for interpreting much mathematics education research as well as helping to explain the difficulties students experience in implementing problem solving heuristic strategies. Evidence is presented suggesting that priming mathematics students to adopt either a Near or Far mental mode has an impact on their performance in solving conceptually challenging mathematical problems.
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31

Nivens, Ryan Andrew, and Samuel Otten. "Assessing Journal Quality in Mathematics Education." Digital Commons @ East Tennessee State University, 2017. https://dc.etsu.edu/etsu-works/246.

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Otten, Samuel, and Ryan Andrew Nivens. "Assessing Journal Quality in Mathematics Education." Digital Commons @ East Tennessee State University, 2017. https://dc.etsu.edu/etsu-works/215.

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33

Quinnell, Lorna M. "Literacy in mathematics in preservice education." Thesis, Queensland University of Technology, 2016. https://eprints.qut.edu.au/101162/1/Lorna_Quinnell_Thesis.pdf.

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Literacy in mathematics is an important topic in education, and one that is still poorly understood. This thesis is a comprehensive report on the teaching and learning of mathematics through the literacy lens, leading to the development of a model to guide the teaching and learning of literacy in mathematics. The research has practical implications, particularly for mathematics education courses in preservice primary teacher education programs. The study is particularly important due to the unique demands of literacy in mathematics, a key element of the content of mathematics.
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Galante, Dianna Rich Beverly Susan. "Web-based mathematics an examination of assessment strategies implemented in the online mathematics classroom /." Normal, Ill. Illinois State University, 2002. http://wwwlib.umi.com/cr/ilstu/fullcit?p3088022.

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Thesis (Ph. D.)--Illinois State University, 2002.
Title from title page screen, viewed January 5, 2006. Dissertation Committee: Beverly Rich (chair), Sherry Meier, Norma Presmeg. Includes bibliographical references (leaves 164-176) and abstract. Also available in print.
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Nakakoji, Yoshitaka. "The Mathematics and Science Nexus and the Transfer of Mathematical Learning at University." Thesis, The University of Sydney, 2017. http://hdl.handle.net/2123/16468.

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Mathematics and science education are critical for further development of economies and the sustainability of modern societies. Mathematics is widely recognised as an important foundation of science. However, internationally academics in STEM disciplines face challenges, such as declining student participation rates, poor mathematical preparedness and low academic performance. Despite the importance of the mathematics and science nexus and challenges therein, there is a paucity of literature examining this relationship, especially in higher education. This research investigates the relationship between mathematics and science within the university context. In particular, the study explores the relationship between students’ learning in first year undergraduate mathematics services courses and later learning in the STEM disciplines of biology, biochemistry, engineering and physics. Several methods are used to explore this: 1) secondary data analysis examining association between attainment in mathematics and science; 2) the creation of an index for measurement of transfer of learning using university examinations; 3) the modeling of transfer’s relationship with other factors in learning; 4) think-aloud accounts of the processes in transfer tasks; and finally 5) interviews with both students and academics exploring the nexus between mathematics and science and issues relating to the transfer of learning between them. Initial analyses showed how high school preparation in mathematics, or a lack of it, was strongly related to university mathematics and science failure rates; and multiple regression analyses confirmed strong relationships between university mathematics and science attainment (R2 from .43 to .87; n from 57 to 308). For example, 84% of the variance in second semester biology scores can be explained by first semester biology and mathematics scores. This relationship may be explained, in part, by the shared general abilities assessed in these disciplines and also by transfer of learning. A Transfer Index (Roberts, Sharma, Britton & New, 2007) was calculated from content-matched questions in university mathematics and science exams. This identified transfer of mathematics learning to physics and engineering (n from 27 to 382), but the biology and biochemistry exams provided no opportunity to demonstrate transfer. Path analyses demonstrated the complex relationships between various factors and the Transfer Index, including its strong association with overall mathematics performance and also general educational ability – as reflected in university entrance scores. Students’ thinking processes in transfer were then examined using think-aloud accounts (n=10) of how they solved physics questions requiring mathematical knowledge and skills covered in their mathematics service course curriculum. The degree of transfer observed varied considerably and obstacles to transfer were identified. Students used thinking processes (interpretation, integration, planning, and execution) recursively, in tandem with a range of metacognitive strategies. Follow up interviews with students and academics showed disparities in their respective views of transfer and also their perceptions of the mathematics and science nexus. While constrained by the focus on a single institution in Australia, this study makes a contribution to our understanding of transfer of mathematical learning and demonstrates an innovative, naturalistic mixed methodology approach. Future research is needed to further develop more naturalistic accounts of transfer, examine long-term effects and explore the diverse contexts in which transfer of learning may occur. Important implications for teaching, learning and assessment are discussed.
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Saintine, Thierry. "Mathematics Confidence in an Urban High-School: Black students' perception of mathematics education." Diss., Temple University Libraries, 2017. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/444144.

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Urban Education
Ph.D.
This was an investigation of students’ mathematics confidence and how it is shaped by their accumulated experiences in mathematics education, and informs their view of the purpose of mathematics in their current and envisioned lives. There is no shortage of studies on black students’ poor performance in mathematics education and its seeming persistence in spite of reform initiatives and policy changes. Conversely, there is a dearth of studies in the field on high achieving black students and the construction of their mathematics identities. Some scholars have argued that the plenitude of data on the failure of black students in mathematics education has contributed to mainstream beliefs of a racial hierarchy of mathematics ability in America. This perception has not only shaped attitudes and behaviors of educational scholars, policymakers, practitioners, but it has contributed to the alienation of many students from the community of “doers of mathematics.” In an effort to combat the pervasiveness of race-based beliefs of math ability, some researchers in the field of mathematics have advocated for the need to refocus research on better understanding students’ mathematics identity and its relationship to their performance. In light of this, this study, using ethnographic methods, examined the mathematics confidence—a subset of mathematics identity—of a group of seniors enrolled in honor’s pre-calculus at an under resourced urban comprehensive high school. Data collected and analyzed for this study showed that participants, in spite of a history of mostly success in math and despite being socialized to view the classroom as opportunity to challenge disparaging views of African Americans, refused to seek or claim membership to the community of math people. This study provides new insights into black students’ perception of and sense of belongingness to mathematics, and its potential impact on their academic and economic prospects.
Temple University--Theses
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Quinlan, James E. "Profiles of software utilization by university mathematics faculty." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1180441531.

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Wong, Yue-tak. "The nature of mathematical knowledge : a phenomenological review and it's implications on mathematics education /." Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20545514.

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Feldhaus, C. Adam. "How Mathematical Disposition and Intellectual Development Influence Teacher Candidates' Mathematical Knowledge for Teaching in a Mathematics Course for Elementary School Teachers." Ohio University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1343753975.

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Lewis, Matthew. "Laboratory Experiences in Mathematical Biology for Post-Secondary Mathematics Students." DigitalCommons@USU, 2016. https://digitalcommons.usu.edu/etd/5219.

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In addition to the memorization, algorithmic skills and vocabulary which is the default focus in many mathematics classrooms, professional mathematicians are expected to creatively apply known techniques, construct new mathematical approaches and communicate with and about mathematics. We propose that students can learn these professional, higher level skills through Laboratory Experiences in Mathematical Biology (LEMBs) which put students in the role of mathematics researcher creating mathematics to describe and understand biological data. LEMBs are constructed so they require no specialized equipment and can easily be run in the context of a college math class. Students collect data and develop mathematical models to explain the data. In this work examine how LEMBs are designed with the student as the primary focus. We explain how well-designed LEMBs lead students to interact with mathematics at higher levels of cognition while building mathematical skills sought after in both academia and industry. Additionally, we describe the online repository created to assist in the teaching and further development of LEMBs. Since student-centered teaching is foreign to many post-secondary instructors, we provide research-based, pedagogical strategies to ensure student success while maintaining high levels of cognition.
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Sulaiman, N. A. J. "Exploring Kuwaiti mathematics : student-teachers' beliefs toward using Logo and mathematics education." Thesis, Nottingham Trent University, 2011. http://irep.ntu.ac.uk/id/eprint/117/.

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The main objective of this study is to explore the effect of one taught course, a Logo module, on Kuwaiti elementary mathematics student-teachers’ beliefs about Information and Communication Technology (ICT) and Logo. The Logo module incorporated ICT, in particular the Logo programming language, as a cognitive tool, that supports the constructivist perspective for mathematics instruction. The Logo module comprised of 24-sessions (deducted from the hours of the Methods of Teaching Mathematics course) and was non-compulsory and non-credit bearing. It was developed and taught by the researcher during the Fall semester 2007 at the College of Basic Education in the State of Kuwait. The researcher was not employed by the College of Basic Education: his only relationship with the College was to conduct his research there. The intention of the module was to give student-teachers the opportunity to experiment with a powerful innovation in a practical mathematics instruction context, both as students and as teachers, thus, enable them to reflect on and reevaluate their beliefs about the nature of mathematics, the teaching and learning of mathematics, and using Logo as an ICT tool. The study explores how participation in the Logo module course may have influenced these beliefs and promoted more positive beliefs toward using ICT and in particular Logo programming language in their future mathematics classroom, and its potential to reform education and enhance students’ learning. The fact that Logo is not used yet in Kuwaiti schools for mathematics education is one of the drivers of this study. A mixed methodology was used, to explore mathematics student-teachers’ beliefs. Two instruments for collecting quantitative and qualitative data were used to explore student-teachers’ beliefs prior to and following their participation in the Logo module: 1. A beliefs questionnaire, administered to thirty-two (32) mathematics student-teachers as a pre- and post-test; 2. A Semi-structured interview, administered to six (6) student-teachers as a pre- and post-test. Specifically, data collected by these instruments, in this study, attempted to investigate and answer the following two key questions: 1. What are Kuwaiti mathematics student-teachers’ beliefs about mathematics teaching and learning and the impact of ICT? 2. What is the effect of using Logo in a mathematics education course on Kuwaiti mathematics student-teachers’ beliefs about Logo and the teaching of mathematics? Analysis of the results showed a strong change in beliefs in support of the use ICT in general and in particular the use of Logo in their future mathematics instruction, as well as toward using constructivist teaching pedagogies.
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黃裕德 and Yue-tak Wong. "The nature of mathematical knowledge: a phenomenological review and it's implications on mathematics education." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B3196056X.

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43

Stratton, Piper I. "Highly Effective Instructional Practices in High School Mathematics Classes." Thesis, National-Louis University, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3683746.

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Abstract Over 40 years of research, three categories of instructional practices are consistently shown to enhance student achievement, including (a) Evidence-based (EB) Strategy Instruction, (b) Feedback, and (c) Formative Assessment. It was the hypothesis of this study that Grade 9 Algebra 1 classrooms do not routinely use these EB practices to enhance their instruction. Data was collected from 12 Algebra 1 classrooms utilizing a researcher developed systematic observation tool featuring highly effective instructional practices from the 2001 Marzano, Pickering, and Pollack and 2009 Hattie meta-analyses. Study results suggested that the frequency of EB instructional practices varied remarkably among teachers. However, the preponderance of teaching time was spent in two forms of practice with little time devoted to other EB strategies and informal formative assessment practices often lacked variety and depth. Last, the frequency or type of EB instructional practices used did not differ between classes designed for students with average math skills compared to classes designed for lower skilled students. Recommended methods for increasing the widespread use of highly effective EB instructional practices included: (a) system-wide improvements in pre-service teacher training in highly effective instructional practices, (b) more effective on-the-job professional development and implementation practices, and (c) the use of structured professional learning communities focused on improving pedagogy.

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Vaughn, Christy H. "Middle School Mathematics Students' Perspectives on the Study of Mathematics." ScholarWorks, 2011. https://scholarworks.waldenu.edu/dissertations/980.

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This qualitative study addressed the perceptions toward the study of mathematics by middle school students who had formerly been in a remedial mathematics program. The purpose of the study was to explore the past experiences of nine students in order to determine what is needed for them to feel successful in mathematics. The conceptual framework of the study was grounded in philosophies of motivation, including achievement goal theory, self-worth theory, self-efficacy theory, expectancy-value theory, and attribution theory. The study used a phenomenological research design to answer the key research question, which focused upon the experiences of students and the meaning that was given to these experiences. Data were collected and analyzed from individual interviews with 9 students and a focus group session. The findings of the study revealed that participants' past experiences influenced their current attitudes about the study of mathematics. Perceptions of mathematical ability, history of success or failure with grades, and the influence of the teacher and peers in the learning environment most influenced students' attitudes about mathematics. Moreover, current feelings impact the degree to which a student puts forth effort in the study of mathematics, and the relationship with the mathematics teacher had the greatest impact on student attitudes. To improve the perceptions that students have about the study of mathematics, expanded professional development opportunities may bring increased awareness of students' perceptions of the study of mathematics, and develop remedial mathematics programs that remove the negative stigma associated with them. The research study could lead to social change as its purpose is to improve student achievement in mathematics through changes in the remedial mathematics program.
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Marshall, Anne Marie 1974. "Understanding opportunities to practice what we preach mathematical experiences of mathematics education doctoral students /." College Park, Md.: University of Maryland, 2008. http://hdl.handle.net/1903/8750.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2008.
Thesis research directed by: Dept. of Curriculum and Instruction. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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46

Szabo, Attila. "Mathematical abilities and mathematical memory during problem solving and some aspects of mathematics education for gifted pupils." Doctoral thesis, Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-146542.

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This thesis reports on two different investigations. The first is a systematic review of pedagogical and organizational practices associated with gifted pupils’ education in mathematics, and on the empirical basis for those practices. The review shows that certain practices – for example, enrichment programs and differentiated instructions in heterogeneous classrooms or acceleration programs and ability groupings outside those classrooms – may be beneficial for the development of gifted pupils. Also, motivational characteristics of and gender differences between mathematically gifted pupils are discussed. Around 60% of analysed papers report on empirical studies, while remaining articles are based on literature reviews, theoretical discourses and the authors’ personal experiences – acceleration programs and ability groupings are supported by more empirical data than practices aimed for the heterogeneous classroom. Further, the analyses indicate that successful acceleration programs and ability groupings should fulfil some important criteria; pupils’ participation should be voluntary, the teaching should be adapted to the capacity of participants, introduced tasks should be challenging, by offering more depth and less breadth within a certain topic, and teachers engaged in these practices should be prepared for the characteristics of gifted pupils. The second investigation reports on the interaction of mathematical abilities and the role of mathematical memory in the context of non-routine problems. In this respect, six Swedish high-achieving students from upper secondary school were observed individually on two occasions approximately one year apart. For these studies, an analytical framework, based on the mathematical ability defined by Krutetskii (1976), was developed. Concerning the interaction of mathematical abilities, it was found that every problem-solving activity started with an orientation phase, which was followed by a phase of processing mathematical information and every activity ended with a checking phase, when the correctness of obtained results was controlled. Further, mathematical memory was observed in close interaction with the ability to obtain and formalize mathematical information, for relatively small amounts of the total time dedicated to problem solving. Participants selected problem-solving methods at the orientation phase and found it difficult to abandon or modify those methods. In addition, when solving problems one year apart, even when not recalling the previously solved problem, participants approached both problems with methods that were identical at the individual level. The analyses show that participants who applied algebraic methods were more successful than participants who applied particular methods. Thus, by demonstrating that the success of participants’ problem-solving activities is dependent on applied methods, it is suggested that mathematical memory, despite its relatively modest presence, has a pivotal role in participants’ problem-solving activities. Finally, it is indicated that participants who applied particular methods were not able to generalize mathematical relations and operations – a mathematical ability considered an important prerequisite for the development of mathematical memory – at appropriate levels.

At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: In press.

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Tynes, Curry Tiffany D. "A Comparative Study of Elementary Mathematics Specialists and Mathematics Coaches on Fourth Grade Students' Mathematics Achievement." ScholarWorks, 2017. https://scholarworks.waldenu.edu/dissertations/3731.

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Federal dollars are utilized to develop instructional programs for students not demonstrating mathematical proficiency on state standardized mathematics assessments, but there is a lack of empirical data on the effectiveness of two different approaches that were used in the local context. The purpose of this quantitative, nonexperimental, casual-comparative study was to determine if state achievement test scores of students in fourth grade who received instruction from a Mathematics Specialist (MS) during the 2007-2009 academic years demonstrated a statistically significant difference from the mathematics state achievement test scores of fourth grade students who received instruction from Grades 1-8 credentialed teachers supported by a Math Coach (MC) during the 2012-2014 academic years. The theoretical base includes two components: National Council of Teachers of Mathematics Standards and Federal No Child Left Behind educational policy, which focus on standards-based education, curriculum, assessment, and instruction to meet students' mathematical needs. Data was collected from a census sample of 13,671 students' state scores from school years 2007-2008, 2008-2009 (MS) and 2012-2013, 2013-2014 (MC). The research question was whether there is a difference in MS and MC scores. An independent samples t test was used to compare the means of all the scores. The results show that the MS program produced statistically higher math scores than the MC. This supports the limited literature in favor of MS. Positive social change includes supporting increasing the use of the MS program in the local context to increase mathematics test scores and the potential for redistribution of federal funds to develop MS programs nationwide.
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Sugarman, Carling. "Using Topology to Explore Mathematics Education Reform." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/54.

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Mathematics education is a constant topic of conversation in the United States. Many attempts have been made historically to reform teaching methods and improve student results. Particularly, past ideas have emphasized problem-solving to make math feel more applicable and enjoyable. Many have additionally tackled the widespread problem of “math anxiety” by creating lessons that are more discussion-based than drill-based to shift focus from speed and accuracy. In my project, I explored past reform goals and some added goals concerning students' perceptions of mathematics. To do so, I created and tested a pilot workshop in topology, a creative and intuitive field, for use in 4th-6th grade classrooms. Preliminary results suggest some success in altering student views on mathematics.
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Skouroupathis, Nicolas. "Outdoor Education in the Greek Mathematics Textbooks." Thesis, Linköpings universitet, Institutionen för kultur och kommunikation, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-94681.

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Outdoor education is a promising educational field that can support indoor education and provide benefits beyond the evidentknowledge. Outdoor and indoor education together can formulate the ground for an integrated learning. In Greece, like manycountries, outdoor education and its potential contribution to the learning process have not been clearly and intentionally testedyet, even though the country tends to follow a progressive educational philosophy. This research focuses on the subject ofmathematics and explores the connections between the existing philosophy and practices of mathematics education in Greece andoutdoor education theory and practice. Following the method of content analysis, the connections were identified through theexistence of basic outdoor education concepts in the mathematics textbooks of the last three grades of primary school. Althoughthe expectations, because of the lack of personal experiences, could not be high, the application of outdoor education seems to befar from impossible in Greece. It could rather flourish even without any changes in the books, when its potentialities are realizedby the teachers.
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McNamara, Olwen. "The construction of knowledge in mathematics education." Thesis, Manchester Metropolitan University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.294592.

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