Formación matemática: reflexiones y recursos directos (y contextuales) al diseño curricular de un programa en matemáticas, nivel licenciatura. Se incluyen también algunos aspectos sobre desarrollo matemático profesional (ver p. j. Halmos (1970, 1974)).

[rev. 2023.10.08]

Referencias preliminares:

  1. Andrews, Paul; Hatch, Gillian (2001) Hungary and Its Characteristic Pedagogical Flow. In Winter, J. (Ed.) Proceedings of BCME5. [acc. 2020.07.27]
  2. Bressoud, D. et al. (2016) Teaching and Learning of Calculus. ICME-13. SpringerOpen. @2021.10.31
  3. Byers, B. (1984) ⇒Dilemmas in Teaching and Learning Mathematics. For The Learning of Mathematics 4:1 [acc. 2015.05.29]
  4. Doorman, Michiel et al. (2007) Problem solving as a challenge for mathematics education in The Netherlands.  ZDM Mathematics Education. {2020.06.13}
  5. Earl, Richard; et al. (2014) How do undergraduates do mathematics? A guide to studying mathematics at Oxford University. [2020.07.29]
  6. Gerovitch, Slava (2016) ♥Creative Discomfort: The Culture of the Gelfand Seminar at Moscow University. In B. Larvor (ed.), Mathematical Cultures, Trends in the History of Science, pp. 51-70. Springer. {acc. 2019.12.26} [extra: Mathematics as an adequate language, por Israel Gelfand]
  7. Halmos, Paul R. (1970) Cómo escribir matemáticas. {Biblioteca Digital del ILCE. Título original: How to write Mathematics. © De la traducción: Emilio Méndez Pinto. Publicado originalmente en L’ Enseignement Mathématique, Vol. 16, Fasc. 2, 123-152} (También publicado por AMS, 1973) [2020.08.29]
  8. Halmos, Paul R. (1974) ¿Cómo hablar matemáticas?. {Traducción Jackeline Cupitra Gómez. Título original: How to talk mathematics, AMS Notices 21 (1974), 155–158} [2020.08.29]
  9. Henrich, Allison K. et al. (2019) Living Proof: Stories of Resilience Along the Mathematical Journey.  AMS-MAA. @08.17
  10. Klymchuk, Sergiy; Susan Staples (2013) ⇒Paradoxes and Sophisms in Calculus. Classroom Resource Materials. MAA {From: STEM-TEC, A multidisciplinary centre of AUT University} [acc. 2015.07.02]
  11. MacDonald, Rita; et al. (2014) Doing and Talking Mathematics: A Teacher’s Guide to Meaning-Making with
    English Learners. [acc. 2020.07.29]
  12. Siegel, M. et al. (2015) ⇒2015 CUPM Curriculum Guide Steering Committee, MAA. [acc. 2015.03.21]
  13. Steen, L. A. et al. (1990) ⇒Challenges for College Mathematics: An Agenda for the Next Decade. [acc. 2015.03.21]
  14. Steen, L. A. (1992) ⇒Heeding the Call for Change: Suggestions for Curricular Action. MAA [acc. 2015.03.21]
  15. Streefland, Leen; van den Heuvel-Panhuizen, Marja (1999) Uncertainty, a Metaphor for Mathematics Education? {2020.06.13}
  16. Wagener, L. L. (2010) ⇒Affective Socialization Processes in Mathematics Doctoral Study: Gaining Insight from Successful Students. UT [acc. 2015.05.29]
  17. [Wageningen] (c. 2019) ⇒WGS Guide for Supervisors [of PhD Projects]. Wageningen University & Research. (ver también: Rules and Regulations for PhD Candidates.) {2019.10.11}
  18. Webb, D. C. (2009) Designing Professional Development for Assessment. (⇒PDF) Educational Designer, 1(2). {2019.10.16}
  19. Weiss, M. K. (2009) ⇒Mathematical Sense, Mathematical Sensibility: the role of the secondary geometry course in teaching students to be like mathematicians. UM [acc. 2015.05.29]
  20. Williner, Betina (2019) La comprensión de conceptos involucrados en problemas de optimización. Un estudio en primer año de ingeniería a partir de ideas variacionales y diferentes sistemas de representación. Tesis doctoral. Univ. Nacional de Comahue, Argentina [acc. 2022.02.01]
  21. Williner, Betina, et al. (2019) La Comprensión a través de las Concepciones Proceso-Objeto. Un Estudio sobre de los Conceptos que Intervienen en la Resolución de Problemas de Optimización. Bolema, Rio Claro (SP), v. 33, n. 65, p. 1549-1569. [acc. 2022.02.01]
  22. Yackel, Erna (2001) Explanation, justification and argumentation in mathematics classrooms.  PME25. {2020.06.13}
  23. Zahner, William C. (2011) How to do math with words: Learning algebra through peer discussions. Doctoral dissertation. University of California, Santa Cruz. [2020.07.29]

Referencias selectas para diseño curricular y Programas de estudios matemáticos

  1. AMATYC: Beyond crossroads. { Chap. 6 Curriculum and program development |  Chap. 7 Intruction }
  2. Mass.gov: Science physics high school curriculum map.
  3. Sañagua, Porfirio (2017) Plan Académico 2017: Licenciatura en Matemáticas. Universidad Mayor de San Andrés. La Paz. Bolivia. {acc. 2021.09.12}
  4. Saxe, K. & Braddy, L. (2015) A Common Vision for Undergraduate Mathematical Sciences Programs in 2025, MAA.
  5. Zwiers, J. et al. (2017) Principles for the Design of Mathematics Curricula: Promoting Language and Content Development. Stanford Graduate School of Education. {2019.10.11}

Referencias selectas para educación matemática en programas de ingeniería

Referencias selectas (a manera de ejemplos) para formación matemática profesional

Materias fundamentales para estudios avanzados*
[Área] Título
[Álgebra] Algebra Course Notes. Instituto de Matemáticas. Univ. de Leiden [acc. 2021.08.11]
[Análisis Real] YouTube Lectures in Real Analysis. Francis Su. Harvey Mudd College. [acc. 2021.08.11]
Nota: Adicionalmente, se pueden seleccionar cursos y materiales apropiados de: {Catálogo de cursos gratuitos en matemáticas. Cortesía de OpenCulture.com},  {Catálogo de matemáticas,  Cortesía de EdX.org}, o bien muy especialmente de {Cursos de Matemáticas, OpenCourseWare, cortesía del MIT} entre otras posibilidades. [acc. 2021.08.11]
*Para estudios avanzados (Maestría y Doctorado), se recomiendan muy especialmente los ofrecidos por: Fields Academy Shared Graduate Courses. [2023-2025]

Tópicos en educación matemática:

 Scaffolding & Metaphor
Anthony, Glenda; Walshaw, Margaret (2009) Effective pedagogy in mathematics. Educational Practices Series-19.  Int’l Academy of Education. IBE. UNESCO @2022.01.27
Bakker, Arthur, et al. (2015) Scaffolding and dialogic teaching in mathematics education: introduction and review. ZDM Mathematics Education 47:1047–1065. @2022.01.27
Borko, Hilda; Potari, Despina (2020) The Twenty-Fifth ICMI Study Teachers of M athematics Work ing and Learning in Collaborative Groups {Conference Proceedings}. Univ. de Lisboa. @2022.01.27
Dyrvold, A., Bergvall, I. (2019) Designing tasks with self-explanation prompts. In: U. T. Jankvist, M. van den Heuvel-Panhuizen, & M. Veldhuis (ed.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME. {Postprint} @2022.01.27
Larvor, Brendan (2018) Why ‘scaffolding’ is the wrong metaphor: the cognitive usefulness of mathematical representations. Synthese 197 pp.3743-3756. @2022.01.27
Liljekvist, Yvonne (2020) Sustainable mathematics education in a digitalized world.  Proceeddings of MADIF 12.
The twelfth research seminar of the Swedish Society for Research in Mathematics Education. @2022.01.27
Malik, S. A. (2017) Revisiting and re-representing scaffolding: The two gradient model. Cogent Education  4: 1331533. @2022.01.27
Miyazaki, M. et al. (2015) Flow-chart proofs with open problems as scaffolds for learning about geometrical proofs. ORE Open Research Exeter. @2022.01.27
van de Pol, Janneke, et al. (2010) Scaffolding in Teacher–Student Interaction: A Decade of Research. Educ Psychol Rev. 22:271–296. @2022.01.27
Postnikoff, Deter (2014) Metaphor and Mathematics. PhD Thesis. Univ. of  Saskatchewan. Canada. @2022.01.27
Sherin, Bruce, et al. (2004) Scaffolding Analysis: Extending the Scaffolding Metaphor to Learning Artifacts.  The J. of the Learning Sciences, 13(3), 387-421.   @2022.01.27
Williams, Gaye (2020) Attaining mathematical insight during a flow state: was there scaffolding? Hiroshima J. of Mathematics Education 13:31-56. @2022.01.27
Semiotic representations
Duval, Raymond (2017) Understanding the Mathematical Way of Thinking – The Registers of Semiotic Representations. Springer. @2022.08.23 (Obs. Libro accesible en Campus Universitarios selectos)

Referencias adicionales de matemáticas:

♦Cultura matemática
Courant, Richard; Robbins, Herbert; rev. by Ian Stewart (1996) What is Mathematics?: an elementary approach to ideas and methods (2/ed). Oxford Univ. Press. {acc. 2023.10.08}
♦Demostraciones matemáticas
Chartrand, Gary, et al. (2018) Mathematical Proofs: A Transition to Advanced Mathematics (4/ed). Pearson {acc. 2023.10.08}
Hammack, Richard. (2013) Book of Proof. {acc. 2023.10.08}
♦Economía
Sydsæter, Knut; Hammond, Peter J. (1995) Mathematics for Economic Analysis. Prentice-Hall, Inc. {acc. 2023.10.08}
 ♦Teoría de la medida
Galaz-García, Fernando (2007) Definiciones originales de la integral y medida de Lebesgue. Miscelánea Matemática 44, pp. 83-100. SMM. @2022.04.12