Avances en la caracterización del pensamiento variacional emergente en el contexto del planteo y resolución de problemas en profesores de matemáticas en formación

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dc.contributor.advisorFalk de Losada, Maryspa
dc.contributor.authorMariño, Luis Fernandospa
dc.creator.cedula13642624spa
dc.creator.cvlachttps://scienti.minciencias.gov.co/cvlac/EnRecursoHumano/inicio.dospa
dc.creator.cvlachttp://scienti.colciencias.gov.co:8081/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000049255spa
dc.creator.googlescholarhttps://scholar.google.es/citations?hl=es&user=Nw62cWYAAAAJspa
dc.creator.orcidhttps://orcid.org/0000-0002-3438-6963spa
dc.creator.orcidhttps://orcid.org/0000-0002-6380-0481spa
dc.date.accessioned2021-03-02T16:57:14Z
dc.date.available2021-03-02T16:57:14Z
dc.date.issued2020-11-20spa
dc.descriptionPropiaes_ES
dc.description.abstractVariational thinking has been categorized from different contexts and perspectives; to some researchers, reasoning is a way of thinking and they refer to variational thinking in terms of variational, co-variational, quantitative and parametric reasoning. To other authors, thinking is functional and representational. The aim of this research was to contribute to the characterization of variational thinking arising from the formulation and resolution of problems in a group of 24 trainee mathematics professors following a qualitative perspective from a grounded theory approach. Three processes of intervention were implemented composed of ten didactic activities, one retrospective interview, three codification cycles and data analysis focused on the constant comparison method which leads up to the sampling and theory saturation. A theory was built based on the data which characterizes variational thinking as a process of formulation and problem resolution as well as a process used to understand and think about problems. Among the findings, the participants’ variational thinking is highlighted when it addresses how the values of the variable x change following a pattern while the values of the variable y change following another pattern but both values change at the same time among infinite solutions to problems that involve Diophantic equations of the form ax+by=c. Along with the evolution of students’ thinking, the results suggest that it is possible to keep moving forward in the characterization of variational thinking from the contexts studied.eng
dc.description.abstractEl pensamiento variacional ha sido caracterizado desde diferentes contextos y perspectivas. Para algunos investigadores el razonamiento es una forma de pensar y se refieren al pensamiento variacional como razonamiento variacional, covariacional, cuantitativo y paramétrico. Para otros autores el pensamiento es funcional y representacional. El objetivo de la investigación fue aportar en la caracterización del pensamiento variacional emergente del planteo y resolución de problemas en un grupo 24 de profesores de matemáticas en formación siguiendo un enfoque cualitativo desde la teoría fundamentada. Se implementó un proceso de tres intervenciones compuesto por diez actividades didácticas, una entrevista retrospectiva, tres ciclos de codificación y análisis de datos centrado en el método de comparación constante que condujo al muestreo y saturación teórica. Se construyó una teoría desde los datos, que caracteriza al pensamiento variacional como proceso en el planteo y resolución de problemas y como proceso al entender y pensar sobre problemas. Entre los hallazgos se destaca la forma de pensar variacional de los participantes acerca de cómo los valores de la variable x cambian siguiendo un patrón, mientras los de la variable y cambian siguiendo otro patrón, pero ambos cambian al mismo tiempo en las infinitas soluciones a problemas que involucran ecuaciones diofánticas de la forma ax+by=c. Junto a la evolución en el desarrollo del pensamiento de los estudiantes, los resultados implican que es posible seguir avanzando en caracterizar el pensamiento variacional desde estos contextos.spa
dc.description.degreelevelDoctoradospa
dc.description.degreenameDoctor(a) en Educación Matemáticaspa
dc.description.notesPresencialspa
dc.identifier.bibliographicCitationBlanton , M., & Kaput, J. (2011). Functional Thinking as a Route Into Algebra in the Elementary Grades. En J. Cai , & E. Knuth (Edits.), Early Algebraization. Advances in Mathematics Education. Berlin,Heidelberg: Springer.spa
dc.identifier.bibliographicCitationBreckler, S. (1984). Empirical validation of affect, behavior, and cognition as distinct components of attitude. Journal of personality and social psychology, 47(6), 1191.spa
dc.identifier.bibliographicCitationBrown, S., & Walter , M. (2005). The Art of problem posing (3 ed.). (L. Hawver, Ed.) Londres, UK: Lawrence Erlbaum Associates, Publisherspa
dc.identifier.bibliographicCitationBryant, A., & Charmaz, K. (2019). The SAGE Handbook of Current Developments in Grounded Theory. 55 City Road, London: SAGE Publications. doi:10.4135/9781526485656spa
dc.identifier.bibliographicCitationBurton, L. (1984). Mathematical Thinking: The Struggle for Meaning. Journal for Research in Mathematics. Education, 15(1), 35-49. doi:10.2307/748986spa
dc.identifier.bibliographicCitationCaballero, M., & Cantoral, R. (2013). Una caracterización de los elementos del pensamiento y lenguaje variacional. En R. Flores (Ed.), Acta latinoamericana de Matemática Educativa (págs. 1197-1205). México, DF: Comité Latinaoamaericano de Matemática Educativa.spa
dc.identifier.bibliographicCitationCai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. The Journal of Mathematical Behavior, 21(4), 401-421.spa
dc.identifier.bibliographicCitationCai, J., & Hwang, S. (2019). Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research.spa
dc.identifier.bibliographicCitationCai, J., Hwang, S., & Silber, S. (2015). Problem-posing research in mathematics education: Some answered and unanswered questions. En Mathematical problem posing (págs. 3-34). New York, NY: Springer.spa
dc.identifier.bibliographicCitationCai, J., Jiang, C., Hwang, S., & Hu, D. (2016). How do textbooks incorporate mathematical problem posing? An international comparative study. En Posing and solving mathematical problems (págs. 3-22). Cham: Springer.spa
dc.identifier.bibliographicCitationCarlson, M. (1998). A cross-sectional investigation of the development of the function concept. Research in collegiate mathematics education. III. CBMS issues in mathematics education,, 114-162.spa
dc.identifier.bibliographicCitationCarlson, M., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events: A framework and a study. Journal for Research in Mathematics Education,, 352-378. doi:10.2307/4149958spa
dc.identifier.bibliographicCitationCarlson, M., Larsen, S., & Jacobs, S. (2001). An investigation of covariational reasoning and its role in learning the concepts of limit and accumulation. En Education, Proceedings of the 23rd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics (Vol. 1, págs. 145-153)spa
dc.identifier.bibliographicCitationCastillo-Garsow, C. (2010). Teaching the Verhulst model: A teaching experiment in covariational reasoning and exponential growth. Tempe, AZ: Arizona State University.spa
dc.identifier.bibliographicCitationCastillo-Garsow, C. (2012). Continuous quantitative reasoning. En R. Mayes, R. Bonilla, L. Hatfield, & S. Belbase (Edits.), Quantitative reasoning: Current state of understanding, (Vol. 2, págs. 55-73). Laramie: University of Wyoming.spa
dc.identifier.bibliographicCitationCastillo-Garsow, C., Johnson, H., & Moore, K. (2013). Chunky and smooth images of change. For the Learning of Mathematics, 33(3), 31-37spa
dc.identifier.bibliographicCitationCharmaz, K. (2006). Constructing grounded theory: A practical guide through qualitative analysis. London: Sage Publicationsspa
dc.identifier.bibliographicCitationCharmaz, K. (2014). Constructing grounded theory (2 ed.). Thousand Oaks, CA: Sage.spa
dc.identifier.bibliographicCitationCobb, P., Confrey , J., DiSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational researcher, 32(1), 9-13.spa
dc.identifier.bibliographicCitationConfrey, J. (1991). The concept of exponential functions: A student’s perspective. En L. Steffe (Ed.), Epistemological Foundations of Mathematical Experience. Recent Research in Psychology (págs. 124-159). New York, NY: Springerspa
dc.identifier.bibliographicCitationConfrey, J., & Smith, E. (1994). Exponential functions, rates of change, and the multiplicative. Educational Studies in Mathematics, 26, 135-164.spa
dc.identifier.bibliographicCitationConfrey, J., & Smith, E. (1995). Splitting, covariation and their role in the development of exponential function. Journal for Research in Mathematics Education, 26, 66-86spa
dc.identifier.bibliographicCitationConfrey, J., & Smith, E. (1995). Splitting, covariation and their role in the development of exponential function. Journal for Research in Mathematics Education, 26, 66-86spa
dc.identifier.bibliographicCitationCorbin, J., & Strauss, A. (1990). Basics of qualitative research. Sage publications.spa
dc.identifier.bibliographicCitationCorbin, J., & Strauss, A. (2008). Basics of qualitative research: Techniques and procedures for developing grounded theory. Thousand Oaks, CA, USA: Sage Publications, Inc.spa
dc.identifier.bibliographicCitationCorbin, J., & Strauss, A. (2014). Conceptos básicos de la investigación cualitativa: técnicas y procedimientos para desarrollar la teoría fundamentada (4 ed.). Thousand Oaks, California, United States of America: SAGE Publications.spa
dc.identifier.bibliographicCitationCorbin, J., & Strauss, A. (2017). Conceptos básicos de la investigación cualitativa: técnicas y procedimientos para desarrollar la teoría fundamentada (4 ed.). Thousand Oaks, California, United States of America: SAGE Publications.spa
dc.identifier.bibliographicCitationDenzin, N. K., & Lincoln, Y. S. (2018). Introduction: The discipline and practice of qualitative. En N. Denzin, & Y. Lincon (Edits.), The Sage handbook of qualitative research (5 ed.). Thousand Oaks, CA, USA: SAGE Publications.spa
dc.identifier.bibliographicCitationDreyfus, T. (2002). Advanced mathematical thinking processes. En T. David (Ed.), Advanced mathematical thinking (Vol. 11, págs. 25-41). Springer, Dordrecht.spa
dc.identifier.bibliographicCitationEllis, A. (2007). The influence of reasoning with emergent quantities on students' generalizations. Cognition and Instruction, 25(4), 439-478.spa
dc.identifier.bibliographicCitationErnest, P. (1993). Constructivism, the psychology of learning, and the nature of mathematics: Some critical issues. Science & Education, 2(1), 87-93.spa
dc.identifier.bibliographicCitationFalk de Losada, M. (1994). Enseñanzas acerca de la naturaleza y el desarrollo del pensamiento matemático extraídas de la historia del álgebra. Boletín de Matemáticas, 1(1), 35-59spa
dc.identifier.bibliographicCitationFelmer, P., Pehkonen, E., & Kilpatrick, J. (2016). Posing and solving mathematical problems. Springer International Publishing.spa
dc.identifier.bibliographicCitationGinsburg, H. (1981). The clinical interview in psychological research on mathematical thinking: Aims, rationales, techniques. For the learning of mathematics, 1(3), 4-11.spa
dc.identifier.bibliographicCitationGlaser, B. (1978). Theoretical sensitivity: Advances in the methodology of grounded theory. Mill Valley, CA: Sociology Press.spa
dc.identifier.bibliographicCitationGlaser, B., & Strauss, A. (2017). Discovery of grounded theory: Strategies for qualitative research. New York, USA: Routledge.spa
dc.identifier.bibliographicCitationGlasser, B., & Strauss, A. (1967). The development of grounded theory. Chicago: IL: Alden.spa
dc.identifier.bibliographicCitationGravemeijer, K. (2004). Local instruction theories as a means of support for teachers in reform mathematics education. Mathematical Thinking and Learning, 6, 105-128. doi:10.1207/s15327833mtl0602_3spa
dc.identifier.bibliographicCitationHarel, G. (2008a). DNR Perspective on Mathematics Curriculum and Instruction: Focuson Proving,Part I. ZDM—The International Journal on Mathematics Education, 47, 487-500.spa
dc.identifier.bibliographicCitationHarel, G. (2008b). DNR Perspective on Mathematics Curriculum and Instruction, Part II. ZDM—The International Journal on Mathematics Education.spa
dc.identifier.bibliographicCitationHarel, G. (2010). DNR-based instruction in mathematics as a conceptual framework. En Theories of mathematics education (págs. 343-367). Berlin, Heidelberg: Springer.spa
dc.identifier.bibliographicCitationHarel, G., & Sowder, L. (2005). Advanced Mathematical-Thinking at Any Age: Its Nature and Its Development. 7(1), 27-50. doi:10.1207/s15327833mtl0701_3spa
dc.identifier.bibliographicCitationHeath, T. (1910). Diophantus of Alexandria: A study in the history of Greek algebra. CUP Archive.spa
dc.identifier.bibliographicCitationHunting, R. (1997). Clinical interview methods in mathematics education research and practice. The Journal of Mathematical Behavior, 16(2), 145-165.spa
dc.identifier.bibliographicCitationJohnson, B., & Christensen, L. (2013). Educational research: Quantitative, qualitative and mixed approaches. Thousand Oaks, CA: Sage.spa
dc.identifier.bibliographicCitationJoshua, S., Musgrave, S., Hatfield, N., & Thompson, P. (2015). Conceptualizing and reasoning with frames of reference. En 2015, T. Fukawa-Connelly, N. Infante, K. Keene , & M. Zandieh (Edits.), Proceedings of the 18th Meeting of the MAA Special Interest Group on Research in Undergraduate Mathematics Education (págs. 31-44). Pittsburgh, RA: RUME.spa
dc.identifier.bibliographicCitationKilpatrick, J. (1987). Formulating the problem: Where do good problems come from? En A. Schoenfeld (Ed.), Cognitive Science and Mathematics Education (págs. 123-147). Hillsdale, NJ: Lawrence Erlbaum Associates.spa
dc.identifier.bibliographicCitationLakatos, I. (1978). The Metodology of Scientif Reaseerch programmes-Philosophical Papers (Vol. 1). (J. Worrall, & G. Currie, Edits.) New York, USA: Cambridge University Press.spa
dc.identifier.bibliographicCitationLakatos, I., & Alcañiz, J. (1982). La crítica y la metodología de programas científicos de investigación. Instituto de Lógica y Metodología, Facultad de Filosofía. Universidad de Valencia.spa
dc.identifier.bibliographicCitationLeung, S. (2016). Mathematical problem posing: A case of elementary school teachers developing tasks and designing instructions in Taiwan. En Posing and Solving Mathematical Problems (págs. 327-344). Springer, Cham.spa
dc.identifier.bibliographicCitationLikert, R. (1932). A technique for the measurement of attitudes. Archives of Psychology, 22 140, 55.spa
dc.identifier.bibliographicCitationMason, J., Burton, L., & Stacey, K. (2010). Thinking Mathematically (2 ed.). Harlow, UK: Pearson Education Limited.spa
dc.identifier.bibliographicCitationMcGuire, W. (1989). The structure of individual attitudes and attitude systems. Attitude structure and function, 37-69.spa
dc.identifier.bibliographicCitationMinisterio de Educación Nacional de Colombia. (2006). Estándares Básicos de Competencias en Lenguaje, Matemáticas, Ciencias y Ciudadanas. Recuperado el 30 de 05 de 2020, de http://cms.mineducacion.gov.co/static/cache/binaries/articles-340021_recurso_1.pdf?binary_rand=1223spa
dc.identifier.bibliographicCitationPaoletti, T., & Moore, K. (2017). The parametric nature of two studens´ covariational reasoning. The journal of Mathematical Behavoir, 48, 137-151.spa
dc.identifier.bibliographicCitationPolya, G. (1945). Cómo plantear y resolver problemas. Editorial Trillas. México: Editorial Trillas.spa
dc.identifier.bibliographicCitationQSR, International. (2002). NVivo. Version 12. Análisis de datos cualitativos (QDA).spa
dc.identifier.bibliographicCitationRolfe, G. (2006). Validity, trustworthiness and rigour: quality and the idea of qualitative research. Journal of advanced nursing, 53(3), 304-310.spa
dc.identifier.bibliographicCitationRosenberg, M. (1960). A structural theory of attitude dynamics. Public Opinion Quarterly, 24(2), 319-340.spa
dc.identifier.bibliographicCitationSaldanha, L., & Thompson, P. (1998). Re-thinking covariation from a quantitative perspective: Simultaneous continuous variation. En Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education.spa
dc.identifier.bibliographicCitationSchoenfeld, A. (2000). Purposes and methods of research in mathematics education. Notices of the AMS, 47(6), 641-649.spa
dc.identifier.bibliographicCitationSchoenfeld, A. H. (2016). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics (Reprint). Journal of Education, 196(2), 1- 38.spa
dc.identifier.bibliographicCitationSilver, E. A. (2013). Problem-posing research in mathematics education: Looking back, looking around, and looking ahead. Educational Studies in Mathematics, 83(1), 157-162.spa
dc.identifier.bibliographicCitationSimon , M. (1995). Reconstructing Mathematics Pedagogy from a Constructivist Perspective. Journal for Research in Mathematics Educatio, 26(2), 114-145.spa
dc.identifier.bibliographicCitationSimon , M., & Tzur, R. (2004). Explicating the Role of Mathematical Tasks in Conceptual Learning: An Elaboration of the Hypothetical Learning Trajectory. Mathematical Thinking and Leraning, 6(2), 91-104.spa
dc.identifier.bibliographicCitationSmith, E. (2008). Representational thinking as a framework for introducing functions in the elementary curriculum. En J. J. KAPUT (Ed.), Algebra in the Early Grades (págs. 133-160). New York, USA: Routledge Publishers.spa
dc.identifier.bibliographicCitationSmith, E. (2017). Representational thinking as a framework for introducing functions in the elementary curriculum. En J. Kaput, D. Carraher, & M. Blanton (Edits.), Algebra in the early grades (págs. 155-182). Routledge.spa
dc.identifier.bibliographicCitationStacey, K. (2006). WHAT IS MATHEMATICAL THINKING AND WHY IS IT IMPORTANT?spa
dc.identifier.bibliographicCitationSteffe, K., Thompson, P., & Von Glasersfeld, E. (2000). Teaching experiment methodology: Underlying principles and essential elements. Handbook of research design in mathematics and science education, 267-306.spa
dc.identifier.bibliographicCitationStrauss, A., & Corbin, J. (1990). Basics of qualitative research. Sage publications.spa
dc.identifier.bibliographicCitationTallman, M., & Frank, K. (2020). Angle measure, quantitative reasoning, and instructional coherence: an examination of the role of mathematical ways of thinking as a component of teachers’ knowledge base. Journal of Mathematics Teacher Education, 23(1), 69-95.spa
dc.identifier.bibliographicCitationThompson, P. (1990). A theoretical model of quantity-based reasoning in arithmetic and algebraic. Center for Research in Mathematics & Science Education.spa
dc.identifier.bibliographicCitationThompson, P. (2011). Quantitative reasoning and mathematical modeling. En L. Hatfield, S. Chamberlain, & S. Belbase (Edits.), New perspectives and directions for collaborative research in mathematics education. WISDOMe Mongraphs (Vol. 1, págs. 33-57). Laramie, WY: University of Wyoming.spa
dc.identifier.bibliographicCitationThompson, P. W., & Carlson, M. (2017). Variation, covariation, and functions: Foundational ways of thinking mathematically. (J. Cai , Ed.) Compendium for research in mathematics education, 421-456.spa
dc.identifier.bibliographicCitationThompson, P., & Thompson, A. (1992, Abril). Images of rate. Paper presented at the Annual Meeting of the American Educational Research Association. San Francisco. Recuperado el 17 de 06 de 2020, de http://pat-thompson.net/PDFversions/1992Images.pdfspa
dc.identifier.bibliographicCitationThompson, P., Carlson, M., Byerley, C., & Hatfield, N. (2014). Schemes for thinking with magnitudes: A hypothesis about foundational reasoning abilities in algebra 1, 2, 3. En L. Steffe, L. Hatfield, & K. Moore (Ed.), Epistemic algebraic students: Emerging models of students' algebraic knowing, 4, págs. 1-24.spa
dc.identifier.bibliographicCitationThompson, P., Hatfield, N., Yoon, H., Joshua, S., & Byerley, C. (2017). Covariational reasoning among US and South Korean secondary mathematics teachers. The Journal of Mathematical Behavior, 48, 95-111.spa
dc.identifier.bibliographicCitationVasco, C. (2003). El pensamiento variacional y la modelación matemática. In Anais eletrônicos do CIAEM–Conferência Interamericana de Educação Matemática. 9, págs. 2009-2010. Blumenau: Brasil.spa
dc.identifier.bibliographicCitationYemen-Karpuzcu, S., Ulusoy, F., & Işıksal-Bostan, M. (2017). Prospective middle school mathematics teachers’ covariational reasoning for interpreting dynamic events during peer interactions. International Journal of Science and Mathematics, 15(1), 89-108.spa
dc.identifier.urihttp://repositorio.uan.edu.co/handle/123456789/2241
dc.language.isospaspa
dc.publisherUniversidad Antonio Nariñospa
dc.publisher.campusBogotá - Federmánspa
dc.publisher.facultyFacultad de Educaciónspa
dc.publisher.programDoctorado en Educación Matemáticaspa
dc.rightsAcceso abierto
dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.rights.coarhttp://purl.org/coar/access_right/c_abf2spa
dc.rights.licenseAttribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)spa
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/spa
dc.subjectPensamiento Variacional, Resolución de Problemas, Planteo de Problemas, Ecuaciones Diofánticas, Teoría Fundamentadaes_ES
dc.subject.keywordVariational Thinking, Problem Solving, Problem Posing, Diophantine Equations, Grounded Theoryes_ES
dc.titleAvances en la caracterización del pensamiento variacional emergente en el contexto del planteo y resolución de problemas en profesores de matemáticas en formaciónes_ES
dc.typeTesis y disertaciones (Maestría y/o Doctorado)spa
dc.type.coarhttp://purl.org/coar/resource_type/c_bdccspa
dc.type.coarversionhttp://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.versioninfo:eu-repo/semantics/acceptedVersionspa
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