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Magal, Oran. "What is mathematical about mathematics?" Thesis, McGill University, 2013. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=119516.
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During a crucial period in the formation of modern-day pure mathematics, Georg Cantor wrote that "the essence of mathematics lies precisely in its freedom". Similarly, David Hilbert, in his landmark work on the axiomatization of geometry, took the view that we are free to interpret the axioms of a mathematical theory as being about whatever can be made to satisfy them, independently of pre-axiomatic ideas, seemingly intuitive truths, or typical empirical scientific applications of that theory. Cantor's and Hilbert's emphasis on the independence of pure mathematics from philosophical preconceptions, empirical applications, and so on raises the question: what is it about?In this dissertation, I argue that essential to mathematics is a certain kind of structural abstraction, which I characterise in detail; furthermore, I maintain that this abstraction has to do with combination and manipulation of symbols. At the same time, I argue that essential to mathematics is also a certain kind of conceptual reflection, and that there is a sense in which mathematics can be said to be a body of truths by virtue of the meaning of its concepts. I argue further that a certain ongoing interplay of intuitive content on the one hand and abstraction or idealization on the other hand plays a significant part in shaping pure mathematics into its modern, axiomatic form. These arguments are made in the course of analyzing and building on the work of both historical and contemporary figures.À une période cruciale de la formation des mathématiques pures modernes, Georg Cantor déclara que « l'essence des mathématiques, c'est la liberté ». De même, David Hilbert, dont l'oeuvre sur l'axiomatisation de la géométrie fut une étape charnière de l'élaboration des mathématiques modernes, soutenait que nous sommes libres d'interpréter les axiomes d'une théorie mathématique comme se rapportant à tout objet qui leur est conforme, indépendemment des idés préconçues, de ce qui semble intuitivement vrai et des applications scientifiques habituelles de la théorie en question. L'emphase que mettent Cantor et Hilbert sur l'indépendance des mathématiques pures des conceptions philosophiques préalables et des applications empiriques suscite la question: sur quoi, au fond, portent les mathématiques?Dans cette dissertation, je soutiens qu'une certaine forme d'abstraction structurelle, que je décris en détail, est essentielle aux mathématiques; de plus, je maintiens qu'à la base de cette abstraction sont la combinaison et la manipulation de symboles. En même temps, j'estime qu'au coeur des mathématiques est aussi un certain type de réflexion conceptuelle et qu'il existe un sens dans lequel les mathématiques sont un ensemble de vérités en vertu de la signification de leurs concepts. Je conclue qu'une intéraction continue entre le contenu intuitif d'un côté et l'abstraction ou l'idéalisation de l'autre joue un rôle important dans le développement des mathématiques axiomatiques modernes. J'avance ces arguments sur la base d'une analyse de travaux tant historiques que contemporains.
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Gates, Miriam Rebecca Galpin. "Mathematics Teacher Educators’ Visions for Mathematical Inquiry in Equitable Mathematics Spaces:." Thesis, Boston College, 2020. http://hdl.handle.net/2345/bc-ir:108775.
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Thesis advisor: Lillie R. AlbertIn mathematics education, there is an imperative for more just and equitable experiences in mathematics spaces, as well as ongoing efforts to move classroom instruction toward mathematical inquiry. While Mathematics Teacher Educators (MTEs) are expected to support multiple initiatives in mathematics education, they are particularly responsible for the professional learning of teachers and teacher candidates. MTEs must therefore prepare and support the professional learning of teachers to achieve twin goals. This study was designed to understand how MTEs envision their roles in supporting development of teachers across MTEs’ many professional functions in their work toward the twin goals of equity and inquiry. The findings suggest that identifying the forms mathematical knowledge takes is important for mathematical inquiry and that interrogating these forms can be used to counter pervasive social myths about who can do mathematics. Further, MTEs articulated three interrelated values for application of mathematics inquiry teaching for justice and equity: creating space, supporting sense-making, and naming how power and privilege have operated and continue to operate in mathematics spaces. Finally, MTEs described how mathematics inquiry practices are a mode for understanding the world and can be used to promote equity by uncovering biases and assumptions. These findings suggest a promising avenue for leveraging mathematical inquiry to increase equitable outcomes in mathematics spaces
Thesis (PhD) — Boston College, 2020
Submitted to: Boston College. Lynch School of Education
Discipline: Teacher Education, Special Education, Curriculum and Instruction
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Gordon, Calvert Lynn Melanie. "Mathematical conversations within the practice of mathematics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape7/PQDD_0027/NQ39532.pdf.
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Newing, A. "Mathematical recreations as a source of new mathematics." Thesis, University of Bristol, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.355096.
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Wilensky, Uriel Joseph. "Connected mathematics : builiding concrete relationships with mathematical knowledge." Thesis, Massachusetts Institute of Technology, 1993. http://hdl.handle.net/1721.1/29066.
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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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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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Holdaway, Emma Lynn. "Mathematical Identities of Students with Mathematics Learning Dis/abilities." BYU ScholarsArchive, 2020. https://scholarsarchive.byu.edu/etd/8536.
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The majority of research on the mathematics teaching and learning of students with mathematics learning dis/abilities is not performed in the field of mathematics education, but in the field of special education. Due to this theoretical divide, students with mathematics learning dis/abilities are far more likely to be in classes that emphasize memorization, direct instruction, and the explicit teaching of rules and procedures. Additionally, students with mathematics learning dis/abilities are often seen as "unable" to succeed in school mathematics and are characterized by their academic difficulties and deficits. The negative assumptions, beliefs, and expectations resulting from ableistic practices in the education system color the interactions educators, parents, and other students have with students with mathematics learning dis/abilities. These interactions in turn influence how students with mathematics learning dis/abilities view and position themselves as learners and doers of mathematics. My study builds on the theoretical framework of positioning theory (Harré, 2012) in order to better understand the mathematical identities of students with mathematics learning dis/abilities. The results of my study show how these students use their prepositions and enduring positions to inform the in-the-moment positions they take on in the mathematics classroom.
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Shabel, Lisa A. "Mathematics in Kant's critical philosophy : reflections on mathematical practice /." New York : Routledge, 2003. http://catalogue.bnf.fr/ark:/12148/cb38959242q.
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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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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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Segarra, Escandón Jaime Rodrigo. "Pre-service teachers' mathematics teaching beliefs and mathematical content knowledge." Doctoral thesis, Universitat Rovira i Virgili, 2021. http://hdl.handle.net/10803/671686.
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L’estudi del coneixement matemàtic i les creences de l’eficàcia de l’ensenyament de les matemàtiques en la formació inicial dels futurs mestres és fonamental, ja que influencia el rendiment acadèmic dels seus estudiants. L’objectiu d’aquesta tesi és estudiar tant el coneixement matemàtic inicial dels futurs mestres com també les seves creences sobre l’eficàcia matemàtica i la seva actitud envers les matemàtiques. Per a complir amb l’objectiu, es realitzen vàries investigacions. Primer, s’estudien els coneixements inicials de nombres i geometria dels estudiants del primer curs del Grau d’Educació Primària a la Universitat Rovira i Virgili (URV). En segon lloc, s’estudien les creences de l’eficàcia de l’ensenyament de les matemàtiques dels futurs mestres durant el grau. En tercer lloc, en aquesta Tesi es compara l’autoeficàcia i l’expectativa de resultats de l’ensenyament de les matemàtiques de futurs mestres, mestres novells i mestres experimentats. En quart lloc, s’estudia la relació entre les creences de l’ensenyament de les matemàtiques, l’actitud envers les matemàtiques i el rendiment acadèmic dels futurs mestres. En cinquè lloc, s’estudia la influència dels factors experiència docent, nivell d’educació i nivell d’ensenyament sobre les creences de l’eficàcia de l’ensenyament de les matemàtiques en mestres en actiu. Finalment, es compara l’autoeficàcia de l’ensenyament de les matemàtiques entre els estudiants del quart any del grau de mestres a la Universitat del Azuay i a la URV. Els resultats d’aquesta Tesi ofereixen informació potencialment important sobre el coneixement matemàtic, les creences, l’autoeficàcia de l’ensenyament de les matemàtiques i l’actitud envers les matemàtiques dels futurs mestres i dels mestres en actiu. Aquests resultats poden ajudar a desenvolupar polítiques adients a l’hora de dissenyar plans d’estudis i també assessorar als professors dels graus de mestre en les institucions d’educació superior.El estudio del conocimiento matemático y las creencias de la eficacia de la enseñanza de las matemáticas en la formación inicial de los futuros maestros es fundamental, ya que influye en el rendimiento académico de los estudiantes. El objetivo de esta tesis es estudiar tanto el conocimiento matemático inicial de los futuros maestros como sus creencias sobre la eficacia matemática y su actitud hacia las matemáticas. Para cumplir con el objetivo se realiza varias investigaciones. Primero, se estudia los conocimientos iniciales de números y geometría de los estudiantes de primer año del Grado de Educación Primaria en la Universidad Rovira y Virgili (URV). En segundo lugar, se estudia las creencias de la eficacia de la enseñanza de las matemáticas de los futuros maestros a lo largo del grado. Tercero, esta Tesis compara la autoeficacia y la expectativa de resultados de la enseñanza de las matemáticas de futuros maestros, maestros novatos y maestros experimentados. Cuarto, se estudia la relación entre las creencias de la enseñanza de las matemáticas, la actitud hacia las matemáticas y su rendimiento académico. Quinto, se estudia la influencia de los factores experiencia docente, nivel de educación y nivel de enseñanza, sobre las creencias de la eficacia de la enseñanza de las matemáticas en maestros en servicio. Finalmente, se compara la autoeficacia de la enseñanza de las matemáticas entre los estudiantes de cuarto año del grado de maestro en la Universidad del Azuay y en la URV. Los resultados de esta Tesis ofrecen información potencialmente importante sobre el conocimiento matemático, las creencias, la autoeficacia de la enseñanza de las matemáticas y la actitud hacia las matemáticas de los futuros maestros y maestros en servicio. Estos resultados pueden ayudar a desarrollar políticas adecuadas para diseñar planes de estudios y también asesorar a los profesores de los grados de maestro en las instituciones de educación superior.
The study of mathematical content knowledge and teachers’ mathematics teaching beliefs of the pre-service teachers is fundamental, since it influences the academic performance of students. The objective of this Thesis is to study the initial mathematical knowledge of pre-service teachers and also their teachers’ mathematics teaching beliefs and their attitude towards mathematics. To meet the objective, various investigations are carried out. First, the initial knowledge of numbers and geometry of first-year students of the primary education degree at the Rovira and Virgili University (URV) is studied. Second, pre-service teachers’ mathematics teaching beliefs are studied throughout the grade. Third, this Thesis compares the self-efficacy and the expectation of results of the teaching of mathematics of pre-service teachers, novice in-service teachers and experienced in-service teachers. Fourth, the relationship between the teachers’ mathematics teaching beliefs, the attitude towards mathematics and their academic performance is studied. Fifth, the influence of the factors teaching level factor and level of training on the teachers’ mathematics teaching beliefs of in-service teachers is studied. Finally, the self-efficacy of mathematics teaching of fourth-year students at the Azuay University and at the URV is compared. The results of this Thesis offer potentially important information on the mathematical knowledge, beliefs, self-efficacy of mathematics teaching and the attitude towards mathematics of pre-service teachers and in-service teachers. These results can help develop policies for curriculum developers and teaching professors at institutes of higher education.
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Zell, Simon. "Using physical experiments in mathematics lessons to introduce mathematical concepts." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-81188.
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Physical experiments have a great potential in mathematics lessons. Students can actively discover how mathematical concepts are used. This paper shows results of research done how students got to know the different aspects of the concept of variable by doing simple physical experiments. Further it will be shown what other concepts could be touched by the same treatment.
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Verwey, Johanna Cornelia (Hanlie). "Investigating the interaction of mathematics teachers with learners' mathematical errors." Diss., University of Pretoria, 2010. http://hdl.handle.net/2263/24743.
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This study investigated the interaction of mathematics teachers with learners’ mathematical errors. The teachers’ verbal interaction with learners’ errors during learning periods and their written interaction in assessment tasks were explored. The study was contextualized in grade 9 secondary school classrooms in the Gauteng province of South Africa. The investigation was epistemologically underpinned by constructivism/socio-constructivism. The investigation was qualitatively approached through four case studies. Structured and semi-structured interviews, classroom observations and learners’ written assessment tasks were employed as sources of data. The participating teachers were described in terms of their beliefs about mathematics, their beliefs about learners’ mathematical errors, their observed prevalent teaching approach and their professed and enacted interaction with learners’ mathematical errors. Within-case and cross-case comparisons ensued. The findings proposed that when teachers believed that the value of learners’ errors was vested in the corrections thereof, rather than employing these opportunities for discussion, valuable opportunities for learners to develop and improve their meta-cognitive abilities might potentially be lost. The findings further indicated that a focus on the mere correction of learners’ errors probably denied learners opportunities to develop a mathematical discourse. The results of the investigation illuminated that an emphasis on achievement during assessment, together with a disapproving disposition towards errors among teachers and learners, were hindrances. They acted as barriers to engendering a socio-constructivist learning environment in which interactions with learners’ errors could enhance learning and establish a negotiating mathematical community. A concurrence between the teachers’ prevalent teaching approach and their mathematical beliefs was confirmed. However, in two of the four cases, a dissonance was revealed between their prevalent teaching approach and their interaction with learners’ errors. Interaction with learners’ mathematical errors was hence identified as a separate and discrete component of a teacher’s practice. The findings suggest the explicit inclusion of error-handling in reform-oriented teacher-training and professional development courses to utilize learners’ mathematical errors more constructively.Dissertation (MEd)--University of Pretoria, 2010.
Science, Mathematics and Technology Education
unrestricted
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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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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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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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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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Rampersad, Roger. "Mathematics anxiety and achievement in mathematics 436." Thesis, McGill University, 2003. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=19394.
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Mathematics 436 is the advanced mathematics course offered to students in secondary IV in the province of Quebec. Although the course is designed to challenge students in the advanced stream, it has produced a high number of failures. This study examines the relationship between mathematics anxiety and achievement in Mathematics 436. Fifty-six students from an English high school on the island of Montreal took part in the study. The Mathematics Anxiety Rating Scale for Adolescents was used to measure the level of mathematics anxiety experienced by the students. In addition, grades from the previous year in mathematics were obtained, as well as grades from the present year, and the final examination. The results of the study suggest that students enrolled in Mathematics 436 experience a high level of mathematics anxiety. As well, higher levels of mathematics anxiety experienced by the students are associated with poor performance in mathematics.
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Lehmann, Jane Nedine. "Reading mathematics: Mathematics teachers' beliefs and practices." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186198.
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This study explores the relationship between university mathematics teachers' beliefs about the nature of reading mathematics and their practices regarding reading mathematics. It is a response to the calls for reform in mathematics education, particularly to the assertion made by the National Council of Teachers of Mathematics in 1989 that not all students can read mathematical exposition effectively and that all students need instruction in how to read mathematics textbooks. It presupposes a collaboration between reading and mathematics teachers to help students learn to read mathematics. The objectives were (1) to examine mathematics teachers' beliefs and practices regarding reading, mathematics, and thereby, reading mathematics; (2) to determine whether the theoretical perspectives implicit in those beliefs and practices could be characterized vis-a-vis the theoretical orientations that inform Siegel, Borasi, and Smith's (1989) synthesis of mathematics and reading; and (3) to determine the relationship, if any, that exists between mathematics teachers' beliefs about reading mathematics and their practices regarding reading mathematics. The synthesis presents dichotomous views of both mathematics and reading: Mathematics is characterized as either a body of facts and techniques or a way of knowing; reading, as either a set of skills for extracting information from text, or a mode of learning. The latter view, in each case, can be characterized as constructivist. The researcher was a participant observer in a university sumner program. The primary participants were fourteen mathematics instructors. Interviews were conducted using a heuristic elicitation technique (Black & Metzger, 1969). Field notes were taken during observations of classroom activities and other non-academic summer program activities. The data were coded using a constant comparative method (Glaser & Strauss, 1967) comparative method. Twelve instructors held conceptions of reading that were consistent with their conceptions of mathematics. Of those twelve, two held conceptions that could be characterized as constructivist; ten held conceptions that were not constructivist. Two instructors held conceptions of reading that were not consistent with their conceptions of mathematics. Of those two, one held a constructivist conception of reading but not of mathematics; one held a constructivist conception of mathematics but not of reading. Teachers' practices reflected their theoretical orientations. The study has implications for teacher education: If teachers' beliefs are related to their practices, then teacher education programs should (1) acknowledge the teachers' existing beliefs and (2) address the theoretical orientations implicit in various aspects of pedagogy.
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Novinger, Susan. "Talking mathematics : children's acquisition of mathematical discourse in a permeable curriculum /." free to MU campus, to others for purchase, 1999. http://wwwlib.umi.com/cr/mo/fullcit?p9953887.
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Khalo, Xolani. "Analysis of grade 10 mathematical literacy students’ errors in financial mathematics." Thesis, University of Fort Hare, 2014. http://hdl.handle.net/10353/1369.
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The main aim of the study was (1) to identify errors committed by learners in financial mathematics and (2) to understand why learners continue to make such errors so that mechanisms to avoid such errors could be devised. The following has been hypothesised; (1) errors committed by learners are not impact upon by language difficulties, (2) errors committed by learners in financial mathematics are not due to prerequisite skills, facts and concepts, (3) errors committed by learners in financial mathematics are not due to the application of irrelevant rules and strategies. Having used Polya’s problem-solving techniques, Threshold Concept and Newman’s Error Analysis as the theoretical frameworks for the study, a four-point Likert scale and three content-based structured-interview questionnaires were developed to address the research questions. The study was conducted by means of a case study guided by the positivists’ paradigm where the research sample comprised of 105 Grade-10 Mathematics Literacy learners as respondents. Four sets of structured-interview questionnaires were used for collecting data, aimed at addressing the main objective of the study. In order to test the reliability and consistency of the questionnaires for this study, Cronbach’s Alpha was calculated for standardised items (α = 0.705). Content analysis and correlation analysis were employed to analyse the data. The three hypotheses of this study were tested using the ANOVA test and hence revealed that, (1) errors committed by learners in financial mathematics are not due to language difficulties, as all the variables illustrated a statistical non-significance (2) errors committed by learners in financial mathematics are not due to prerequisite skills, facts and concepts, as the majority of the variables showed non-significance and (3) errors committed by learners in financial mathematics were due to the application of irrelevant rules and strategies, as 66.7% of the variables illustrated a statistical significance to the related research question.
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Foley, Catherine. "Girls' perceptions of mathematics : an interpretive study of girls' mathematical identities." Thesis, University of Reading, 2016. http://centaur.reading.ac.uk/65926/.
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This thesis explores girls’ perceptions of mathematics and how they make sense of their mathematical identity. It seeks to understand the characterisations girls make of mathematics and mathematicians, shedding light upon their positioning as mathematicians. This is important because there remains a tendency for able females to rate themselves lower than males of a similar attainment, and be less likely to continue into post-compulsory study of mathematics. This research followed an interpretive paradigm, taking a grounded, case-based approach and using a mosaic of qualitative methods. Fourteen girls from a school in the south-east of England aged 8-9 at the start of the study took part in the research over 15 months. The data collected comprised scrapbooks, concept maps, relationship wheels, drawings, digital photographs, metaphors, group and individual interviews. Data were analysed using open and focused coding, sensitising concepts and constant comparison to arrive at key categories and themes. The main conclusions of the study are that time taken to explore the diversity of girls’ perceptions of themselves as mathematicians provides a powerful insight into their identity formation. Many girls struggled to articulate the purpose of mathematics dominant in their vision of what it meant to be a mathematician. Whilst they recognised a rich variety of authentic mathematical activity at home, this was overwhelmed by number, calculation, speed and processes, with mathematics recognised as desk-bound and isolating. They made sense of their mathematical identity through their characterisations of mathematics alongside interactions and comparisons with others. The girls in the study took a high degree of responsibility for their own development, believing they could improve with ever-greater effort. However, this led to the need for a buffer zone, allowing teachers, family and friends to support the individual in continuing to grow and protecting them from mathematical harm. This research recommends the provision of safe spaces for mathematical exploration in terms of time, space and collaboration, connecting mathematical study with application and interest, reframing mathematics as a social endeavour and sharing responsibility with girls for their mathematical development. Finally, it suggests the value of practitioners paying close attention to girls’ evolving mathematical identities.
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Jakobsson-Åhl, Teresia. "Encouraging Participation in Mathematical Practices : Messages in the Boost for Mathematics." Thesis, Luleå tekniska universitet, Institutionen för konst, kommunikation och lärande, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-67660.
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In this thesis, focused attention is given to the idea of task solvers as active participants in mathematical practices. The theoretical assumptions of the study, reported in this thesis, are inspired by socio-political concerns. The aim of the study is to investigate the underlying view of participation in mathematical practices, as understood in a nationwide teacher professional development programme, the Boost for Mathematics, in Sweden. To be more precise, the study is arranged to problematise ways of encouraging students as active participants. This aim is approached by means of the following research questions: (1) What messages do mathematical tasks in the Boost for Mathematics send about people as participants in mathematical practices? and (2) What is the role of multiple representations in these messages? An empirical study is reported. The data of the study, i.e., three collections of problems, are drawn from the Boost for Mathematics. Data processing is conducted by using a modified version of a pre-existing data processing framework, focusing on mathematical practices as socio-political practices. The empirical study uncovers an implicit view of task solvers in mathematical practices and especially a detachment between students, as potential task solvers, and the social contexts where mathematical ideas and concepts are embedded. This implicit view is challenged from the assumption that it is motivating for a student to conceive him/herself as someone who is ‘qualified’ to take part in mathematical practices.
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Kilgore, Pelagia Alesafis. "Adult College Students' Perceptions about Learning Mathematics via Developmental Mathematical xMOOCs." Scholar Commons, 2018. http://scholarcommons.usf.edu/etd/7179.
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Debates over the promising change Massive Open Online Courses (MOOCs) might offer to traditional online learning now produce significant attention and discourse among the media and higher education. Ample articles discuss the potential benefits of MOOCs from the perspectives of faculty and administration. However, little is known about students’ perceptions of MOOCs. Given the lack of relevant literature and the reality that MOOCs are created to benefit students, it is important to elicit current college students’ perceptions of MOOCs since it is well documented learning mathematics online has its problems (Ashby, Sadera, & McNary, 2011; Frame, 2012; Ho et al., 2010; Hughes et al., 2005; Jameson & Fusco, 2014).
In this descriptive exploratory case study, I explored the perceptions of eight adult college students enrolled in a developmental mathematical xMOOC. I utilized constant comparative methods (open, axial, and selective coding) to analyze the data and identified overarching themes related to student perceptions of learning developmental mathematics via an xMOOC. XMOOCs are structured like large online lecture courses, usually with auto grading features for tests and quizzes and video-recorded lectures. I also employed post structural tenets to scrutinize the data through different lenses. My goals were to explore college students’ perceptions of learning via developmental mathematical xMOOCs, the reasons students chose to learn developmental mathematics via an xMOOC, students’ beliefs of personal characteristics needed to successfully complete a developmental mathematical xMOOC and their ideas about how to improve developmental mathematical xMOOCs. The study provides insights about college students’ learning and success via developmental mathematical xMOOCs and adds needed information to the literature on higher education distance learning.
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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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Hart, Hilary. "Mathematics Vocabulary and English Learners: A Study of Students' Mathematical Thinking." BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2573.
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This study examined the mathematical thinking of English learners as they were taught mathematics vocabulary through research-based methods. Four English learners served as focus students. After administering a pre-performance assessment, I taught a 10-lesson unit on fractions. I taught mathematics vocabulary through the use of a mathematics word wall, think-pair-shares, graphic organizers, journal entries, and picture dictionaries. The four focus students were audio recorded to capture their spoken discourse. Student work was collected to capture written discourse. Over the course of the unit, the four focus students used the mathematics vocabulary words that were taught explicitly. The focus students gained both procedural and conceptual knowledge of fractions during this unit. Students also expressed elevated confidence in their mathematics abilities.
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Prestwich, Paula Jeffery. "Mathematical Interactions between Teachers and Students in the Finnish Mathematics Classroom." BYU ScholarsArchive, 2015. https://scholarsarchive.byu.edu/etd/5785.
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The Finnish school system has figured prominently in the PISA international assessments for over 10 years. Many reasons are given for Finnish success yet few of them focus on what is happening in the mathematics classroom. This study addresses the question of “What does mathematics instruction in the Finnish mathematics classroom look like?” Eight Finnish mathematics classes, from 6th – 9th grade were recorded, translated, and analyzed using the Mathematical Quality of Instruction (MQI) 2013 video coding protocol. Other aspects and observations of these classes also are discussed. Although the study is small, this study gives a view into the nature of some Finnish mathematics classrooms.
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Hwang, Jihyun. "Bridge the gap between cognitive attributes and mathematics achievement: which cognitive attributes for mathematical modeling contribute to better learning in mathematics?" Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/6145.
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Mathematical modeling is a thinking process that applies various sets of cognitive attributes – one component of intellectual resources (i.e., cognitive resources). Students are able to develop cognitive attributes when they engage in mathematical modeling activities. Furthermore, using many of the cognitive attributes developed during the mathematical modeling process, students solve mathematics problems, for example, in assessments. Examining students’ mastery of these cognitive attributes, we can investigate relationships between students’ cognitive development through mathematical modeling practices in classrooms and their performance on mathematics assessments. The purpose of this research is to quantitatively and empirically investigate the relationships between students’ development of mathematics cognitive attributes and their achievement. For the current study, we selected the four cognitive attributes representing different stages of the mathematical modeling practices – select, analyze, compute, and represent. The generalized DINA (deterministic inputs, noisy “and” gate) is applied to generate students’ mastery profiles of the cognitive attributes from their responses to test items. Using students’ mastery profiles as datasets, three secondary analysis studies are conducted with linear regression analysis and multivariate approach to repeated measure ANOVA. The findings show that development of the four cognitive attributes in mathematical modeling is positively related to mathematics achievement. In addition, students, who developed select and compute throughout 4th to 8th grades, scored higher in mathematics assessment with large degrees of effects. The findings suggest important implications to teachers: Students need to have opportunities develop a wide range of cognitive attributes of mathematical modeling, which would result in higher achievement. Teachers need to have instructional emphases on different stages of mathematical modeling depending on grade levels: students’ representing a solution at elementary-school levels; and analyzing a problem situation and selecting strategies at middle-school levels. The study also suggests teachers shift an instructional emphasis from learning mathematics contents to high-order thinking like mathematical modeling to accomplish higher mathematics achievement.
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Bowers, David Matthew. "Impact of Mathematics Courses for Prospective Teachers on their Mathematical Knowledge for Teaching." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1460973988.
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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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Buie-Collard, Geoffrey. "HELPING STUDENTS AFFECTED WITH MATHEMATICS DISORDERS LEARN MATHEMATICS." Ohio University Art and Sciences Honors Theses / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ouashonors1586172168614395.
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Buie-Collard, Geoffrey Brock. "Helping Students Affected with Mathematics Disorders Learn Mathematics." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1592387017569857.
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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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Cronk, Carol Elizabeth. "Effects of mathematics professional development on growth in teacher mathematical content knowledge." CSUSB ScholarWorks, 2012. https://scholarworks.lib.csusb.edu/etd-project/139.
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The purpose of this project was to determine if there was a correlation between teachers' scores on fractions items on project assessments and the percentage of participation time in professional development activities.
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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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Kim, In Hong. "Preschool Teachers’ Knowledge of Children’s Mathematical Development and Beliefs About Teaching Mathematics." Thesis, University of North Texas, 2013. https://digital.library.unt.edu/ark:/67531/metadc407808/.
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Early childhood education emphasizes the need of providing high quality early childhood mathematics programs for preschool children. However, there is little research that examines the importance of preschool children’s mathematical knowledge development and teachers’ beliefs about how to teach mathematics to young children. The purposes of this study were to investigate pre-service and in-service preschool teachers’ knowledge of children’s mathematical development and their beliefs about teaching mathematics in the preschool classroom and also to determine how experience differentiates the two groups. This research employed a non-experimental research design with convenient sampling. Ninety-eight pre-service teachers and seventy-seven in-service preschool teachers participated in the research. The Knowledge of Mathematical Development survey (KMD) and the Beliefs survey were used to investigate possible differences between pre-service and in-service preschool teachers’ knowledge of children’s mathematical development and between their beliefs about teaching mathematics. The findings of this study indicate a statistically significant difference between pre-service teachers and in-service preschool teachers in relation to their knowledge of mathematical development. This finding shows that pre-service teachers’ knowledge of children’s mathematical development is somewhat limited; most pre-service teachers have difficulty identifying the process of preschool children’s development of mathematics skills. A second finding reveals a statistically significant difference between pre-service teachers and in-service preschool teachers in relation to their beliefs about (a) age-appropriateness of mathematics instruction in the early childhood classroom, (b) social and emotional versus mathematical development as a primary goal of the preschool curriculum, and (c) teacher comfort with mathematics instruction. No statistically significant difference was found between pre-service teachers’ and in-service preschool teachers’ beliefs regarding the locus of generation of mathematical knowledge. Both groups believe it is the teacher’s responsibility to intentionally teach mathematics to young children. This result suggests that both pre-service and in-service preschool teachers believe that teachers should play a central role in the teaching of mathematics to preschool children. However, both groups would need appropriate education and training to learn how to teach mathematics to young children. Pre-service and in-service preschool teachers’ varying levels of experiences and different levels of education may help explain why there is a significant difference between their knowledge of mathematical development and beliefs about teaching mathematics.
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Durfee, Lucille J. "BIO-MATHEMATICS: INTRODUCTION TO THE MATHEMATICAL MODEL OF THE HEPATITIS C VIRUS." CSUSB ScholarWorks, 2016. https://scholarworks.lib.csusb.edu/etd/428.
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In this thesis, we will study bio-mathematics. We will introduce differential equations, biological applications, and simulations with emphasis in molecular events. One of the first courses of action is to introduce and construct a mathematical model of our biological element. The biological element of study is the Hepatitis C virus. The idea in creating a mathematical model is to approach the biological element in small steps. We will first introduce a block (schematic) diagram of the element, create differential equations that define the diagram, convert the dimensional equations to non-dimensional equations, reduce the number of parameters, identify the important parameters, and analyze the results. These results will tell us which variables must be adjusted to prevent the Hepatitis C virus from becoming chronic.
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Cox, Raymond Taylor. "Mathematical Modeling of Minecraft – Using Mathematics to Model the Gameplay of Video Games." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1431009469.
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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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Brown, Gary I. Dossey John A. "Jean D'Alembert, mixed mathematics and the teaching of mathematics." Normal, Ill. Illinois State University, 1987. http://wwwlib.umi.com/cr/ilstu/fullcit?p8726500.
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Thesis (D.A.)--Illinois State University, 1987.Title from title page screen, viewed August 11, 2005. Dissertation Committee: John A. Dossey (chair), Robert K. Ritt, Lawrence C. Eggan, Ira Cohen, Marcia D. Young. Includes bibliographical references (leaves 270-277) and abstract. Also available in print.
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GieSinger, Patricia. "Teaching practices and secondary mathematics students' perceptions about mathematics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape7/PQDD_0023/MQ51346.pdf.
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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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Aljundi, Liam. "Moving Mathematics : Exploring constructivist tools to enhance mathematics learning." Thesis, Malmö universitet, Institutionen för konst, kultur och kommunikation (K3), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-42981.
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The challenges faced by mathematics education reflect the more immense difficulties of the schooling system as a whole. This thesis investigates such challenges in the light of an ethical learning foundation and aims for a transformation through the use of technologies as learning tools. Interaction design methods are used to craft constructivist learning kits that aim to move mathematics students from passive receivers of knowledge to active learners. The proposed tools modify new technologies by adapting them to teachers’ and learners’ needs to be best suited for mathematics classroom adoption. Additionally, social, political, and economic issues that may hinder the adoption of constructivist learning are presented and critically discussed. Finally, this thesis paves the way for future designers who aim to design mathematics educational kits by providing a design framework based on the learning theory and the design process presented in this thesis.
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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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De, Lange Laura. "Generating shared interpretive resources in the mathematics classroom: using philosophy of mathematics to teach mathematics better." Thesis, Rhodes University, 2017. http://hdl.handle.net/10962/4293.
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Every student has a unique mathematical lived experience: a unique amalgamation of ideas about mathematics, exposure to mathematical concepts and feelings about mathematics. A student's unique set of circumstances means that not every explanatory account of mathematics will cohere with her previous experiences. For an explanation to have explanatory potential, it must provide an account which coheres with the other beliefs a student has about mathematics. If an explanation has no such coherence, it will not be recognisable as an explanation of the phenomenon of mathematics for the student. Our explanatory accounts of mathematics and mathematical knowledge are our philosophies of mathematics. Different philosophies of mathematics will better explain different sets of mathematical lived experiences. In this thesis I will argue that students should be exposed to a multiplicity of philosophies of mathematics so that they can endorse the philosophy of mathematics which has the most explanatory potential for their particular set of mathematical lived experiences. I argue that this will improve student understanding of mathematics. The claims inherent in any given philosophy of mathematics, when combined with other stereotypes or prejudices, can work to unjustly exclude members of subordinated groups, such as poor, black or female students, from mathematical participation. If we want to avoid reinforcing and reinscribing prejudicial claims about people in the mathematics classroom, we need to be aware of how a certain philosophy of mathematics can exclude certain students. In this thesis I will be defending the idea that, as mathematics educators, we should diversify the way we see mathematics so that we decrease this exclusion from mathematics. In order to diversify the way in which we see mathematics so as to decrease unjust exclusion, members of subordinated groups should be encouraged to share their mathematical experiences in a space sensitive to the power dynamics present in the mathematics classroom. These accounts can then be combined with existing philosophies of mathematics to create new ways of making sense of mathematics which do not unjustly exclude members of subordinated groups.
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Quillen, Mary Addington. "Relationships Among Prospective Elementary Teachers' Beliefs About Mathematics, Mathematics Content Knowledge, and Previous Mathematics Course Experiences." Diss., Virginia Tech, 1998. http://hdl.handle.net/10919/11120.
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The problem this study addresses is the relationship among the constructs content knowledge, beliefs, and previous experiences of prospective elementary teachers. The 36 participants in the study, 35 females and one male, were recent graduates from a five-year Elementary Education licensure program at a major university located in the Mid-Atlantic region. A correlational research design was used to investigate the relationships that might exist among the three constructs using Praxis I Pre-professional Math test scores, Beliefs Survey scores, and Previous Mathematics Experience Questionnaire [PMEQ] scores. Scores from the Praxis I Pre-professional Math test were self-reported and verified by the Licensure Coordinator in the Center for Teacher Education [CTE]. Scores for the Beliefs Survey and Previous Mathematics Experience Questionnaire [PMEQ] were collected from the survey and questionnaire completed by each participant and the data were analyzed using SPSS software. A frequency distribution was constructed for the Praxis I Math Test scores, the Beliefs Survey scores, and the PMEQ scores. A Pearson correlation was constructed to analyze the relationship among the following variables: Praxis I Math Test, beliefs, and previous mathematics experiences (feelings, teaching tools, and quantity of math courses taken). An alpha level of .05 was used for all statistical tests. A significant positive correlation was found to exist between Praxis I Math Test scores and feelings about mathematics using a two-tailed test indicating that prospective elementary math teachers who have higher Praxis I math test scores tend to report having more positive feelings about mathematics. A significant negative correlation was found to exist between beliefs and teaching tools using a two-tailed test. This indicates a tendency by prospective teachers to favor more relational beliefs when their previous experiences included the use of a wide variety of teaching tools. The prospective teachers' responses to the essay question and interview questions support their stated beliefs about the importance of teachers emphasizing relational understanding. On their essay responses, all 36 participants indicated a desire to provide a relational oriented learning-environment in their future classrooms. The findings in the study support the notion that the prospective teachers in this group with stronger content knowledge tended to report more positive feelings about mathematics. They also tended to favor a relational teaching/learning environment if they had experiences using a wide variety of teaching tools. No significant correlation was found to exist between any of the other variables that were tested.Ph. D.
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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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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.