Relevant bibliographies by topics / Tall's worlds of mathematics

Academic literature on the topic 'Tall's worlds of mathematics'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Tall's worlds of mathematics"

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Paz, Tamar, and Uri Leron. "The Slippery Road From Actions on Objects to Functions and Variables." Journal for Research in Mathematics Education 40, no. 1 (January 2009): 18–39. http://dx.doi.org/10.5951/jresematheduc.40.1.0018.

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Functions are all around us, disguised as actions on concrete objects. Composition of functions, too, is all around us, because these actions can be performed in succession, the output of one serving as the input for the next. In terms of Gray and Tall's (2001) “embodied objects” or Lakoff and Núñez's (2000) “mathematical idea analysis,” this “embodied scheme” of action on objects may serve as intuitive grounding for the function concept. However, as Gray, Tall, and their colleagues have shown, such embodied schemes can also lead to serious “epistemological obstacles” in later stages of concept development. In the same vein, our own data show that the intuitions about change and invariance entailed by the action-on-objects scheme, although helpful in earlier stages of learning functions, may later come to clash with the formal concepts of function and of composition of functions.
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Gouvea, F. Q. "MATHEMATICS: Parallel Worlds." Science 306, no. 5703 (December 10, 2004): 1893a—1894a. http://dx.doi.org/10.1126/science.1105298.

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Klaver, Elizabeth. "Possible Worlds, Mathematics, and John Mighton's Possible Worlds." Narrative 14, no. 1 (2006): 45–63. http://dx.doi.org/10.1353/nar.2005.0027.

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Rowe, David E. "Exotic worlds: Victorian mathematics." Metascience 22, no. 2 (October 9, 2012): 447–50. http://dx.doi.org/10.1007/s11016-012-9716-8.

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Apolloni, Bruno, Simone Bassis, and Dario Malchiodi. "Compatible worlds." Nonlinear Analysis: Theory, Methods & Applications 71, no. 12 (December 2009): e2883-e2901. http://dx.doi.org/10.1016/j.na.2009.06.104.

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Mancilla, Blanca, and John Plaice. "Possible Worlds Versioning." Mathematics in Computer Science 2, no. 1 (November 2008): 63–83. http://dx.doi.org/10.1007/s11786-008-0044-8.

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Maki, Daniel P., and John L. Casti. "Would-be Worlds." American Mathematical Monthly 105, no. 10 (December 1998): 972. http://dx.doi.org/10.2307/2589307.

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Barbour, A. D., and Gesine Reinert. "Small worlds." Random Structures and Algorithms 19, no. 1 (2001): 54–74. http://dx.doi.org/10.1002/rsa.1018.

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Pinheiro, M. R. "Medium worlds theories I." Applied Mathematics and Computation 188, no. 2 (May 2007): 1061–70. http://dx.doi.org/10.1016/j.amc.2006.05.213.

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AHMED, AFZAL. "Mathematics—A Tale of Three Worlds?" Teaching Mathematics and its Applications 14, no. 4 (1995): 141–48. http://dx.doi.org/10.1093/teamat/14.4.141.

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Dissertations / Theses on the topic "Tall's worlds of mathematics"

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Smart, Angela. "Undergraduate Students’ Connections Between the Embodied, Symbolic, and Formal Mathematical Worlds of Limits and Derivatives: A Qualitative Study Using Tall’s Three Worlds of Mathematics." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/24247.

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Calculus at the university level is taken by thousands of undergraduate students each year. However, a significant number of students struggle with the subject, resulting in poor problem solving, low achievement, and high failure rates in the calculus courses overall (e.g., Kaput, 1994; Szydlik, 2000; Tall, 1985; Tall & Ramos, 2004; White & Mitchelmore, 1996). This is cause for concern as the lack of success in university calculus creates further barriers for students who require the course for their programs of study. This study examines this issue from the perspective of Tall’s Three Worlds of Mathematics (Tall, 2004a, 2004b, 2008), a theory of mathematics and mathematical cognitive development. A fundamental argument of Tall’s theory suggests that connecting between the different mathematical worlds, named the Embodied-Conceptual, Symbolic-Proceptual, and Formal-Axiomatic worlds, is essential for full cognitive development and understanding of mathematical concepts. Working from this perspective, this research examined, through the use of calculus task questions and semi-structured interviews, how fifteen undergraduate calculus students made connections between the different mathematical worlds for the calculus topics of limits and derivatives. The analysis of the findings suggests that how the students make connections can be described by eight different Response Categories. The study also found that how the participants made connections between mathematical worlds might be influenced by the type of questions that are asked and their experience in calculus courses. I infer that these Response Categories have significance for this study and offer potential for further study and educational practice. I conclude by identifying areas of further research in regards to calculus achievement, the Response Categories, and other findings such as a more detailed study of the influence of experience.
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Hartmann, Jean-Gabriel Keiser. "Chaos and Scrambling in Quantum Small Worlds." Master's thesis, Faculty of Science, 2020. http://hdl.handle.net/11427/32266.

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In this thesis, we introduce a novel class of many-body quantum system, which we term ‘quantum small worlds'. These are strongly-interacting systems that interpolate between completely ordered (nearest-neighbour, next-to-nearest-neighbour etc.) and completely random interactions. They are systems of quantum spin particles in which the network topology is given by the Watts-Strogatz model of network theory. As such, they furnish a novel laboratory for studying quantum systems transitioning between integrable and non-integrable behaviour. Our motivation is to understand how the dynamics of the system are affected by this transition, particularly with regards to the ability of the system to scramble (quantum) information, and potential emergence of chaotic behaviour. Our work begins with a review of the relevant literature regarding algebraic graph theory and quantum chaos. Next, we introduce the model by starting from a well understood integrable system, a spin- 1 2 Heisenberg, or Ising, chain. We then inject a small number of long-range interactions and study its ability to scramble quantum information using two primary devices: the out-of-time-order correlator (OTOC) and the spectral form factor (SFF). We find that the system shows increasingly rapid scrambling as its interactions become progressively more random, with no evidence of quantum chaos as diagnosed by either of these devices.
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Kidd, Hugh Hollick Elsworth. "Secondary mathematics teachers' figured worlds and identities : stability and fluidity." Thesis, King's College London (University of London), 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.408551.

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Bamunoba, Alex Samuel. "Cyclotomic polynomials (in the parallel worlds of number theory)." Thesis, Stellenbosch : Stellenbosch University, 2011. http://hdl.handle.net/10019.1/17865.

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Thesis (MSc)--Stellenbosch University, 2011.
ENGLISH ABSTRACT: It is well known that the ring of integers Z and the ring of polynomials A = Fr[T] over a finite field Fr have many properties in common. It is due to these properties that almost all the famous (multiplicative) number theoretic results over Z have analogues over A. In this thesis, we are devoted to utilising this analogy together with the theory of Carlitz modules. We do this to survey and compare the analogues of cyclotomic polynomials, the size of their coefficients and cyclotomic extensions over the rational function field k = Fr(T).
AFRIKAANSE OPSOMMING: Dit is bekend dat Z, die ring van heelgetalle en A = Fr[T], die ring van polinome oor ’n eindige liggaam baie eienskappe in gemeen het. Dit is as gevolg van hierdie eienskappe dat feitlik al die bekende multiplikative resultate wat vir Z geld, analoë in A het. In hierdie tesis, fokus ons op die gebruik van hierdie analogie saam met die teorie van die Carlitz module. Ons doen dit om ’n oorsig oor die analoë van die siklotomiese polinome, hul koëffisiënte, en siklotomiese uitbreidings oor die rasionele funksie veld k = Fr(T).
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Brahier, Daniel J. "The Best of Both Worlds: Teaching Middle School and College Mathematics." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79502.

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As a full-time Professor of Mathematics Education, as well as a part-time eighth grade (13 and 14 year olds) mathematics teacher, I have the opportunity to experience the teaching profession from “both sides of the fence.” My university courses are enhanced by my work in the field, while my eighth graders’ learning is strengthened by educational principles studied at the university. In this paper (and presentation), I will explain this partnership and the benefits to both audiences.
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Welsh, Noel. "Learning and acting in unknown and uncertain worlds." Thesis, University of Birmingham, 2011. http://etheses.bham.ac.uk//id/eprint/1656/.

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This dissertation addresses the problem of learning to act in an unknown and uncertain world. This is a difficult problem. Even if a world model is available, an assumption not made here, it is known to be intractable to learn an optimal policy for controlling behaviour (Littman 1996). Assuming no world model is known leads to two approaches: model-free learning, which attempts to learn to act without a model of the environment, and model learning, which attempts to learn a model of the environment from interactions with the world. Most earlier approaches make a priori assumptions about the complexity of the model or policy required, the upshot of which is that a fixed amount of memory is available to the agent. It is well known that in a noisy environment, the type assumed within, an environment specific amount of memory is required to act optimally. Fixing the capacity of memory before any interactions have occurred is thus a limiting assumption. The theme of this dissertation is that representing multiple policies or environment models of varying size enables us to address this problem. Both model-free learning and model learning are investigated. For the former, I present a policy search method (usable with a wide range of algorithms) that maintains a population of policies of varying size. By sharing information between policies I show that it can learn near optimal policies for a variety of challenging problems, and that performance is significantly improved over using the same amount of computation without information sharing. I investigate two approaches to model learning. The first is a variational Bayesian method for learning POMDPs. I show that it achieves superior results to the Bayes-adaptive algorithm (Ross, Chaib-draa and Pineau 2007) using their experimental setup. However, this experimental setup makes strong assumptions about prior information, and I show that weakening these assumptions leads to poor performance. I then address model learning for a simpler model, a topological map. I develop a novel non-parametric Bayesian map that sets no limit of the model size, and show experimentally that maps can be learned from robot data with weak prior knowledge.
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Lane, Lorenzo David. "Bridge between worlds : relating position and disposition in the mathematical field." Thesis, University of Edinburgh, 2017. http://hdl.handle.net/1842/23545.

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Using ethnographic observations and interview based research I document the production of research mathematics in four European research institutes, interviewing 45 mathematicians from three areas of pure mathematics: topology, algebraic geometry and differential geometry. I use Bourdieu's notions of habitus, field and practice to explore how mathematicians come to perceive and interact with abstract mathematical spaces and constructions. Perception of mathematical reality, I explain, depends upon enculturation within a mathematical discipline. This process of socialisation involves positioning an individual within a field of production. Within a field mathematicians acquire certain structured sets of dispositions which constitute habitus, and these habitus then provide both perspectives and perceptual lenses through which to construe mathematical objects and spaces. I describe how mathematical perception is built up through interactions within three domains of experience: physical spaces, conceptual spaces and discourse spaces. These domains share analogous structuring schemas, which are related through Lakoff and Johnson's notions of metaphorical mappings and image schemas. Such schemas are mobilised during problem solving and proof construction, in order to guide mathematicians' intuitions; and are utilised during communicative acts, in order to create common ground and common reference frames. However, different structuring principles are utilised according to the contexts in which the act of knowledge production or communication take place. The degree of formality, privacy or competitiveness of environments affects the presentation of mathematicians' selves and ideas. Goffman's concept of interaction frame, front-stage and backstage are therefore used to explain how certain positions in the field shape dispositions, and lead to the realisation of different structuring schemas or scripts. I use Sewell's qualifications of Bourdieu's theories to explore the multiplicity of schemas present within mathematicians' habitus, and detail how they are given expression through craftwork and bricolage. I argue that mathematicians' perception of mathematical phenomena are dependent upon their positions and relations. I develop the notion of social space, providing definitions of such spaces and how they are generated, how positions are determined, and how individuals reposition within space through acquisition of capital.
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Fontaine, Caitlyn. "Exploring the Narratives of Female Undergraduate Students in Math-Intensive Programs." Thesis, Université d'Ottawa / University of Ottawa, 2020. http://hdl.handle.net/10393/41502.

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In recent years, researchers have continued to examine factors that contribute to the ongoing loss of women in mathematics programs and careers at a higher rate than their male counterparts. An important element in women choosing to persist in mathematics may be the ability to identify as mathematically able, however popular culture often constructs ideas of ‘mathematicians’ and ‘femininity’ in ways which render them difficult to reconcile. This research explores the narratives of Canadian female undergraduate students in mathematics-intensive programs in order to develop further understanding of how they negotiate identities as ‘feminine’ and mathematically able. Four students from a Canadian university were recruited to participate in narrative research interviews. Using Holland et al.’s (2003) concept of figured worlds, this study employs a thematic analysis of the data to examine how participants use, adapt or reject available discourses to perform identities as feminine and mathematically able. Depuis quelques années, les chercheurs continuent d'examiner les facteurs contribuant à la déplétion continue des femmes dans les programmes et les carrières en mathématiques à un taux plus élevé que leurs homologues masculins. Un élément important dans le choix des femmes de persévérer dans les mathématiques semble être la capacité de s'identifier comme mathématiquement capables, or la culture populaire construit souvent des concepts de «mathématiciens» et de «féminité» de manière à les rendre difficiles à concilier. Cette recherche explore les rapports narratifs d'étudiantes canadiennes au baccalauréat dans des programmes intensifs en mathématiques afin de mieux comprendre comment elles négocient des identités tel que «féminine» et mathématiquement capable. Quatre étudiantes d'une université canadienne ont été recrutées pour participer à des entrevues de recherche narrative. En utilisant le concept de «figured worlds» de Holland et al. (2003), cette étude utilise une analyse thématique des données pour examiner comment les participantes utilisent, adaptent ou rejettent les discours pour réaliser des identités comme féminines et mathématiquement capables.
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Kunert, Rachel. "Number Sense Intervention: A Comparison of a Packaged Program and a Research-Based Strategy." University of Dayton / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=dayton1405513267.

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Stone, Jason C. "The Formation of Self-Constructed Identity as Advanced Mathematical Thinker Among Some Female PhD Holders in Mathematics and the Relationship to the "Three-Worlds" Cognitive Model of Advanced Mathematical Thinking." Kent State University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=kent1436975429.

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Books on the topic "Tall's worlds of mathematics"

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Worlds without content: Against formalism. London [England]: New York, 1991.

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P, Restivo Sal, Bendegem, Jean Paul van, 1953-, and Fischer Roland 1945-, eds. Math worlds: Philosophical and social studies of mathematics and mathematics education. Albany: State University of New York Press, 1993.

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Michel, Cécile, and Karine Chemla, eds. Mathematics, Administrative and Economic Activities in Ancient Worlds. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48389-0.

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Padma, T. V. Mathematwist: Number tales from around the world. Chennai, India: Tulika Publishers, 2007.

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The worlds of Oronce Fine: Mathematics, instruments, and print in Renaissance France. Donington: Shaun Tyas, 2009.

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Ronald, Abler, Marcus Melvin G. 1929-, Olson Judy M, and Association of American Geographers, eds. Geography's inner worlds: Pervasive themes in contemporary American geography. New Brunswick, N.J: Rutgers University Press, 1992.

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Reeves, Byron. Total engagement: How games and virtual worlds will change the way we work. Boston, Mass: Harvard Business Press, 2009.

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Leighton, Read J., ed. Total engagement: How games and virtual worlds will change the way we work. Boston, Mass: Harvard Business Press, 2009.

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1835-1912, Skeat Walter W., ed. The Canterbury tales. New York: Avenel Books, 1985.

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Peter, Mack, Walton Chris, and Chaucer Geoffrey 1340?-1400, eds. General prologue to the Canterbury Tales. Oxford: Oxford University Press, 1994.

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Book chapters on the topic "Tall's worlds of mathematics"

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van Atten, Mark. "Gödel, Mathematics, and Possible Worlds." In Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer, 147–55. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10031-9_7.

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Just, Winfried, and Hannah Callender Highlander. "Vaccination Strategies for Small Worlds." In Foundations for Undergraduate Research in Mathematics, 223–64. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66065-3_10.

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Alznauer, Amy. "The Worlds of George Andrews, a Daughter’s Take." In Trends in Mathematics, 3–7. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-57050-7_1.

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Senechal, Marjorie. "Parallel Worlds: Escher and Mathematics, Revisited." In M.C. Escher’s Legacy, 83–91. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-28849-x_8.

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Giorgadze, Gia, and Vladimir Mityushev. "Bogdan Bojarski in Complex and Real Worlds." In Springer Proceedings in Mathematics & Statistics, 123–43. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-97127-4_5.

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Hartnett, Kevin. "Mathematicians Explore Mirror Link between Two Geometric Worlds." In The Best Writing on Mathematics 2019, edited by Mircea Pitici, 74–80. Princeton: Princeton University Press, 2019. http://dx.doi.org/10.1515/9780691197944-007.

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Maniatty, William A., Thomas Caraco, Niles Lehman, and Boleslaw K. Szymański. "Spatial Models of Persistence in RNA Worlds: Exploring the Origins of Life." In Parallel Processing and Applied Mathematics, 896–903. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-48086-2_100.

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Michel, Cécile, and Karine Chemla. "Mathematics, Administrative and Economic Activities in Ancient Worlds: An Introduction." In Mathematics, Administrative and Economic Activities in Ancient Worlds, 1–48. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48389-0_1.

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Michel, Cécile. "Computation Practices of the Assyrian Merchants During the Nineteenth Century BCE." In Mathematics, Administrative and Economic Activities in Ancient Worlds, 399–433. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48389-0_10.

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Middeke-Conlin, Robert. "Connecting a Disconnect Can Evidence for a Scribal Education Be Found in a Professional Setting During the Old Babylonian Period?" In Mathematics, Administrative and Economic Activities in Ancient Worlds, 435–62. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48389-0_11.

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Conference papers on the topic "Tall's worlds of mathematics"

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Durrer, Ruth, Marcus Ruser, Marc Vonlanthen, Peter Wittwer, Kerstin E. Kunze, Marc Mars, and Miguel Angel Vázquez-Mozo. "Graviton production in brane worlds by the dynamical Casimir effect." In PHYSICS AND MATHEMATICS OF GRAVITATION: Proceedings of the Spanish Relativity Meeting 2008. AIP, 2009. http://dx.doi.org/10.1063/1.3141336.

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Samuels, Peter Charles. "Design of a Mobile Mathematics Creativity Laboratory for Contemporary Learners." In 2009 Conference in Games and Virtual Worlds for Serious Applications (VS-GAMES). IEEE, 2009. http://dx.doi.org/10.1109/vs-games.2009.34.

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Surith, Dhanya. "Understanding students’ transition in mathematical thinking in algebra: The three worlds of mathematics." In 2022 Advances in Science and Engineering Technology International Conferences (ASET). IEEE, 2022. http://dx.doi.org/10.1109/aset53988.2022.9734941.

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Gonçalves, Clara. "The perfect dwelling is any place in the heavens: Platonism, mathematics and music: On Kepler’s thoughts and the theory of architecture in the Renaissance." In The 2nd International Multidisciplinary Congress Phi 2016 – Utopia(S) – Worlds and Frontiers of the Imaginary. CRC Press, 2016. http://dx.doi.org/10.1201/9781315265322-11.

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Rodriguez, Demy, Leslie Trevizo, Arturo Rodriguez, Julio Aguilar, Clinton Chijioke, Brandon Paez, Rafael Baez, V. M. Krushnarao Kotteda, and Vinod Kumar. "Learning and Engaging Through Transformative Informal Setting Driven by COVID Induced Leading Edge Virtual Technology for Advanced Fluid Mechanics Modeling and Simulations Seminar Series." In ASME 2022 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/fedsm2022-87409.

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Abstract COVID-19 pandemic has forced students to learn about advanced scientific concepts, such as Fluid Mechanics and Modeling and Simulations, in a completely virtual setting. Such advanced concepts have traditionally been taught in face-to-face settings partially because these concepts require rigorous mathematical derivation and discussions. Pandemic has brought new challenges to educators to create engaging learning materials for students. The study indicates that students unconsciously absorb information that triggers motivation and endurance in students’ desire to pursue a lifelong research career. Pandemic however has brought new attention to technology development and created effective technology-driven solutions to learning needs for such concepts. Using the leading-edge technology, we have conducted extensive learning sessions for engineering undergraduate and graduate students for the last two years. In this paper, we will present a qualitative study aimed to understand the benefits of informal learning via advanced modeling and simulations seminar series. In this study, world-renowned STEM experts have given 45-minute seminar talks accompanied by 15-minute Q&A sessions to engineering graduate and undergraduate students, primarily from the University of Texas at El Paso. The seminar discussions, feedback, and comments were recorded using the Microsoft Teams video conferencing platform. We created this seminar series aimed to enhance and mitigate motivation losses faced during the COVID-19 pandemic. The goal lies in bringing students closer to new ways of learning, enhancing their knowledge not only in traditional classroom settings but also to motivate students and convince leaders to create dual engineering partnership study programs among the United States’ top universities for diverse groups of students to foster an atmosphere of collaboration and inclusion among the United States higher education systems. This study indicates that students unconsciously absorb information that triggers motivation and endurance in students’ desire to pursue a lifelong research career.
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Яшин, Б. Л. "Mathematical ideas in Russian philosophy of the XIX–XX centuries." In Современное социально-гуманитарное образование: векторы развития в год науки и технологий: материалы VI международной конференции (г. Москва, МПГУ, 22–23 апреля 2021 г.). Crossref, 2021. http://dx.doi.org/10.37492/etno.2021.79.38.059.

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среди представителей русской философии XIX–XX вв. было немало тех, кто пытался выявить характер взаимосвязи в процессе познания мира философии и математики. М.С. Аксенов создал метагеометрическую концепцию пространственно-временной модели мироздания, где утверждал, что воспринимаемые человеком объекты как трехмерные на самом деле четырехмерны и существуют в четырехмерном пространстве в абсолютном покое. Идея иллюзорности движения, изменения, развития объективного мира была фундаментом в рассуждениях М.С. Аксенова. Человек, в его понимании, живет в неизменяющейся Вселенной, находясь в непрерывном движении во времени, воспринимаемом им не как свое собственное, а как изменения, происходящие с ней. Ярким представителем плеяды русских математиков-философов был и участник «Московской философско-математической школы» Н.В. Бугаев, разработавший оригинальное учение – аритмологию, которую вместе с математикой он считал специфической методологией, способной помочь в поиске ответов на сложные вопросы научно-философского понимания мира. Еще одной идеей Н.В. Бугаева, где проявилась связь математики и философии, была идея эволюционного развития природного, социального и духовного миров, воплощенная им в его монадологии. Философские работы М.С. Аксенова и Н.В. Бугаева, в которых они использовали математические модели для осмысления мироустройства, способствовали разработке и осознанию роли «философско-математического синтеза» как метода познания. Among the representatives of Russian philosophy of the XIX–XX centuries, there were many who tried to identify the nature of the relationship in the process of cognition of the world of philosophy and mathematics. One of them was M.S. Aksenov, who created the metageometric concept of the space-time model of the universe, where he argued that the objects perceived by man as three-dimensional are four-dimensional and exist in four-dimensional space in absolute rest. The idea of the illusory nature of movement, change, and the development of the objective world was the foundation of M.S. Aksenov's reasoning. Man, in his understanding, lives in an unchanging Universe, being in continuous motion in time, perceived by him not as his own, but as changes occurring with it. A prominent representative of Russian mathematicians and philosophers was also a member of the "Moscow Philosophical and Mathematical School" N.V. Bugaev, who developed an original teaching – arrhythmology, which, together with mathematics, he considered a specific methodology that could help in finding answers to complex questions of scientific and philosophical understanding of the world. Another idea of N.V. Bugaev, where the connection between mathematics and philosophy was manifested, was the idea of the evolutionary development of the natural, social, and spiritual worlds, embodied by him in his monadology. The philosophical works of M. S. Aksenov and N. V. Bugaev, in which they used mathematical models to understand the world order, contributed to the development and awareness of the role of "philosophical and mathematical synthesis" as a method of cognition.
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7

Franco, Jorge. "A Decolonized Mood of Creating a Three-dimensional Digital Space Based on Integrating Transdisciplinary Knowledge." In LINK 2021. Tuwhera Open Access, 2021. http://dx.doi.org/10.24135/link2021.v2i1.66.

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This experimental artwork has attempted to produce a decolonized mood of researching and creating Three-dimensional (3D) Virtual Reality (VR) digital spaces based on using and integrating transdisciplinary knowledge. These research and creative 3DVR digital spaces processes have been connected with applying the concept of Digital Transformation (DX) within Educative Computational Practice (ECP) proceedings, addressing the idea of empowering people. The mentioned ECP proceedings have occurred through designing and carrying out 3DVR digital spaces by using 3D computer graphics programming techniques, bringing about individuals’ developing digital and visual communication skills with support of employing Web3D-based technologies, such as the Extensible 3D (X3D) language and the X3Dom framework, as Open Educational Resources (OER). Low cost and accessible Web3D technologies have allowed practicing, analyzing and extending our open-ended long-term investigation at K-12 education levels referent to sharing 3DVR and computer graphics programming knowledge, aiming to inspire individuals’ engagement in computing practices encompassing coding and visual literacy skills. These educational processes have also been sustained by art and its learning and expressing opportunities in the digital age. With support of Web3D technologies and lifelong learning and teaching experiences, we have taken part of a course called “Projeto Espetáculo em Realidade Aumentada”, at Fabrica de Cultura Diadema. Through this course, there has been designed and implemented a 3DVR artwork which has extended our research and digital knowledge acquisition processes through producing a decolonized content by interconnecting conceptual knowledge referent to the visual artwork of Rubem Valentim’s mix of Afro-Brazilian, Amerindian and European cultures and Jacob Lawrence’s Afro-American culture symbolic representation. Both artists have trajectories of lifelong learning and using geometry and colorful forms in their artwork composition. Their artwork has expressed knowledge related to Afro-Brazilian and Afro-American cultures, contributing to reduce a gap, at official education, in the teaching of black culture contributions to the worlds of arts, sciences and technology. Interacting with these artists’ trajectories and artworks has lead to research, apply and share knowledge related to ancient Africa, having as reference the Egyptian civilization use of mathematics, geometry (at some extent sacred geometry) shapes and colors knowledge for building and decorating pyramids and other monuments. Such transdisciplinary knowledge confluence has made part of researching and forming the bases of computer graphics libraries and techniques in databases, allowing through educative 3D computer programming practices, to integrate in this 3DVR artwork features referent to digital sculpture, installation and net art, be it within a standalone way and/or through a blog based interface online. This knowledge confluence has brought about using 3D computer graphics programming proceedings for building and visualizing symbolic representation of Afro-Brazilian, European and Amerindian Enchanted Beings’ sacred adornments and instruments. It includes, based on the artwork another Brazilian educator and artist, Abdias do Nascimento, learning to research and utilize knowledge from people of the West Africa related to a writing system, the Adinkra, which is a group of symbols that express and represent ideas in proverbs. In addition, this artwork participatory development has stimulated individuals enhancing cognitive and technical skills, including their complex and spatial thinking abilities.
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