Potencial formativo de la historia de la teoría euclidiana de la proporción en la constitución del conocimiento del profesor de matemáticas
Tipo de documento
Autores
Lista de autores
Guacaneme, Edgar Alberto
Resumen
La tesis ubica el papel de la Historia de las Matemáticas [HM] en la constitución del conocimiento del profesor de Matemáticas [CPM] como contexto general de investigación y dentro de este la pregunta ¿cuál es el potencial formativo de la historia de la teoría euclidiana de la razón y la proporción, contenida en el Libro V de Elementos, en la constitución del CPM? En procura de una respuesta, se establece la necesidad de lograr una aproximación al estado del arte de la reflexión e investigación en torno a la relación "Historia de las Matemáticas - Educación Matemática". A partir de tal estado del arte se procura explorar la relación "HM - CPM", guiado por las preguntas relacionadas con los argumentos que se esgrimen a favor de la integración de la HM en tales procesos, las intenciones que se persiguen con dicha integración, las características de la HM que se vincula a los procesos educativos de los profesores de Matemáticas y las estrategias metodológicas que se han diseñado e implementado para que los profesores de Matemáticas se apropien y usen los discursos históricos. Se construye así un marco de referencia para la relación mencionada. Se estudian entonces la teoría euclidiana de la razón y la proporción del Libro V de Elementos para obtener una perspectiva de esta. Así mismo se estudian los documentos que versan sobre la historia de la razón y proporción. A partir de esto se analiza la historia de la teoría euclidiana de la proporción a través de las categorías de análisis para las pregunta qué HM y para qué la HM. El resultado global muestra que el conjunto de documentos cubre la casi totalidad de las categorías de análisis. Finalmente, se establece el potencial formativo que los documentos que versan sobre la teoría euclidiana de la proporción tienen a favor del CPM.
Fecha
2017
Tipo de fecha
Estado publicación
Términos clave
Enfoque
Idioma
Revisado por pares
Formato del archivo
Tipo de tesis
Institución (tesis)
Departamento
Referencias
Abdeljaouad, M. (2012). Teaching European mathematics in the Ottoman Empire during the eighteenth and nineteenth centuries: between admiration and rejection. ZDM, 44(4), 483-498. doi: 10.1007/s11858-012-0381-6 Acerbi, F. (2003a). Drowning by Multiples. Remarks on the Fifth Book of Euclid’s Elements, with Special Emphasis on Prop. 8. Archive for History of Exact Sciences, 57(3), 175- 242. Acerbi, F. (2003b). Drowning by Multiples: Remarks on the Fifth Book of Euclid's Elements, with Special Emphasis on Prop.8. Archive for History of Exact Sciences, 57(3), 175. doi: 10.1007/s00407-002-0061-y Alpaslan, M., Işıksal, M., & Haser, Ç. (2014). Pre-service Mathematics Teachers’ Knowledge of History of Mathematics and Their Attitudes and Beliefs Towards Using History of Mathematics in Mathematics Education. Science & Education, 23(1), 159-183. doi: 10.1007/s11191-013-9650-1 Alsina Català, C. (2010). El club de la hipotenusa. Un paseo por la Historia de las Matemáticas a través de sus anécdotas más divertidas. México, D.F.: Ediciones Culturales Paidós, S.A. Álvarez Jiménez, C. (s.f). Razones y variaciones. El papel de la teoría de proporciones en el estudio galileano del movimiento. Departamento de Matemáticas. Facultad de Ciencias. UNAM. México, D. F. Allen, H. D. (2000). Gauss. [Book Review]. Mathematics Teacher, 93(8), 726. An, S., Kulm, G., & Wu, Z. (2004). The Pedagogical Content Knowledge of Middle School, Mathematics Teachers in China and the U.S. Journal of Mathematics Teacher Education, 7(2), 145-172. Anacona, M. (2003). La Historia de las Matemáticas en la Educación Matemática. Revista EMA. Investigación e innovación en educación matemática, 8(1), 30-46. Aranda Ballesteros, F. D., & Gómez Lara, M. (2011). Algunos hechos históricos en la resolución de problemas, sobre el origen del cálculo integral. Épsilon. Revista de Educación Matemática, 28(1), 155-164. Arboleda, L. C. (1984). Historia y enseñanza de las matemáticas. Quipu. Revista Latinoamericana de Historia de las Ciencias y la Tecnología, 1(2), 167-194. Arcavi, A. (1991). The experience of history in mathematics education: Two benefits of using history. For the Learning of Mathematics. An International Journal of Mathematics Education, 11(2), 11. Arcavi, A., Bruckheimer, M., & Ben-Zvi, R. (1982). Maybe a mathematics teacher can profit from the study of the history of mathematics. For the Learning of Mathematics. An International Journal of Mathematics Education, 3(1), 30-37. Arcavi, A., Bruckheimer, M., & Ben-Zvi, R. (1987). History of Mathematics for teachers: the case of irrational numbers. For the Learning of Mathematics. An International Journal of Mathematics Education, 7(2), 18-23. Arcavi, A., & Isoda, M. (2007). Learning to listen: from historical sources to classroom practice. Educational Studies in Mathematics, 66(2), 111-129. Askew, M. (2008). Mathematical Discipline Knowledge Requeriments for Prospective Primary Teachers, and the Structure and Teaching Approaches of Programs Designed to Develop that Knowledge. In P. Sullivan & T. Wood (Eds.), The International Handbook of Mathematics Teacher Education. Knowledge and Beliefs in Mathematics Teaching and Teaching Development (Vol. 1, pp. 13-35). Rotterdam: Sense Publishers. Aujac, G. (1986). Le rapport di isou (Euclide V, definition 17): Definition, utilisation, transmission. Historia Mathematica, 13(4), 370-386. Bagni, G. T. (2004). Prime numbers are infinitely many: Four proofs from history for mathematics education. Mediterranean Journal for Research in Mathematics Education, 3(1-2), 21-36. Bagni, G. T. (2008). A Theorem and Its Different Proofs: History, Mathematics Education, and the Semiotic-Cultural Perspective. Canadian Journal of Science, Mathematics and Technology Education, 8(3), 217-232. Ball, D. L. (1988). The Subject Matter Preparation of Prospective Mathematics Teachers: Challenging the Myths: National Center for Research on Teacher Education, 116 Erickson Hall, College of Education, Michigan State University, East Lansing, MI 48824-1034. Barabash, M., & Guberman-Glebov, R. (2004). Learning-and-teaching project in the history of mathematics for pre-service teachers: Educational and multicultural enrichment of their academic curriculum. Mediterranean Journal for Research in Mathematics Education, 3(1-2), 73-88. Barbin, É. (1991). The experience of history in mathematics education: The Reading of original texts: how and why to introduce a historical perspective. For the Learning of Mathematics. An International Journal of Mathematics Education, 11(2), 12-13. Barbin, É. (1996). The role of problems in the history of mathematics and mathematics teaching. In R. Calinger (Ed.), Vita mathematica: historical research and integration with teaching (pp. 17-25). Washington: Mathematical Association of America. Barbin, É. (2000). The Historicity of the Notion of What is Obvious in Geometry. In V. J. Katz (Ed.), Using History to Teach Mathematics: An International Perspective (pp. 89-98). Washington: Mathematical Association of America. Barbin, É. (2007). On the argument of simplicity in Elements and schoolbooks of Geometry. Educational Studies in Mathematics, 66(2), 225-242. Barbin, É., Bagni, G., Grugnetti, L., Kronfellner, M., Lakoma, E., & Menghini, M. (2000). Integrating history: research perspectives In J. Fauvel & J. van Maanen (Eds.), History in mathematics education. The ICMI Study (pp. 63-90). Dordrecht: Kluwer Academic Publishers. Barbin, É., & Bénard, D. (Eds.). (2007). Histoire et enseignement des mathématiques. Rigueurs, erreurs, raisonnements. Clermont-Ferrand: Institut National de Recherche Pédagogique Université Blaise-Pascal de Clermont-Ferrand (IREM). Barbin, É., Stehlikova, N., & Tzanakis, C. (Eds.). (2008). Proceedings of the 5th European Summer University on the History and Epistemology in Mathematics Education. Prague: Vydavatelsky servis, Plzeñ. Bardin, L. (1986). Análisis de contenido: Ediciones Akal. Barnett, J., Lodder, J., & Pengelley, D. J. (2014). The Pedagogy of Primary Historical Sources in Mathematics: Classroom Practice Meets Theoretical Frameworks. Science & Education, 23(1), 7-27. doi: 10.1007/s11191-013-9618-1 Barón Bocanegra, O., & Barragán Sánchez, P. J. (2013). Una teoría antigua vista con los ojos de hoy: influencia sobre el profesor de Matemáticas. Licenciatura en Matemáticas Trabajo de grado no publicado, Universidad Pedagógica Nacional, Bogotá, D.C. Barrow-Green, J. (1998). History of mathematics: resources on the World Wide Web. Mathematics in School, 27(4), 16-22. Barry, D. T. (2000). Mathematics in search of history. Mathematics Teacher, 93(8), 647-650. Bartolini Bussi, M., & Maschietto, M. (2008). Machines as Tools in Teacher Education. In D. Tirosh & T. Wood (Eds.), The International Handbook of Mathematics Teacher Education. Tools and Processes in Mathematics Teacher Education (Vol. 2, pp. 183-208). Rotterdam: Sense Publishers. Baumgart, J. K. (1994). Tópicos de História da Matemática para uso em sala de aula. Álgebra (H. H. Domingues, Trans. Vol. 4). Sao Paulo: Atual Editora Ltda. Baumgart, J. K., Deal, D. E., Vogeli, B. R., & Hallerberg, A. E. (1969). Preface Historical Topics for the Mathematics Classroom. Thirty-first Yearbook (pp. ix-xiv). Washington, D.C.: National Council of Teacher of Mathematics. Becker, O. (1933). Eudoxus-Studien I: Eine voreudoxische Proportionenlehre und ihre Spuren bei Aristoteles und Euklid Quellen und Studien zur Geschichte der Mathematik, Astronomie und Phyik B. II (pp. 311-330): Springer- Verlag. (Reprinted from: Jean Christianidis, ed. Classics in the history of Greek Mathematics, Boston Studies in the Philosophie of Science, vol. 240, Dordrecht/Boston: 2004, 191–209). Belisario, A., & González, F. E. (2012). Historia Social de la Educación Matemática en Iberoamérica. Historia de la Matemática, Educación Matemática e Investigación en Educación Matemática. UNIÓN. Revista Iberoamericana de Educación Matemática,31, 161-182. Berghout, R. F. (1974). The Historical Development of Magnitudes, Ratios and Proportions. Australian Mathematics Teacher, 30(5), 184-196. Berghout, R. F. (1975). The Historical Development of Magnitudes, Ratios and Proportions. Australian Mathematics Teacher, 31(2), 66-76. Berlinghoff, W. P., & Gouvêa, F. Q. (2004). Math through the Ages. A Gentle History for Teacher and Others (Expanded Edition ed.). Washington & Farmington: Oxton House Piblishers & The Mathematical Association of America. Bero, P. (1996). Pupils' perception of the continuum In R. Calinger (Ed.), Vita mathematica: historical research and integration with teaching (pp. 303-307). Washington: Mathematical Association of America. Biard, J. (2003). Mathématiques et philosophie dans les "Questions" de Blaise de Parme sur le "Traité des rapports" de Thomas Bradwardine. Revue d'histoire des sciences, 56(2), 383-400. doi: 10.2307/23634023 Bishop, A. J. (2001). Lo que una perspectiva cultural nos cuenta sobre la historia de las matemáticas. Uno. Revista de Didáctica de las Matemáticas, 26, 61-72. Bishop, J. P., Lamb, L. L., Philipp, R. A., Whitacre, I., Schappelle, B. P., & Lewis, M. L. (2014). Obstacles and Affordances for Integer Reasoning: An Analysis of Children's Thinking and the History of Mathematics. Journal for Research in Mathematics Education, 45(1), 19-61. Bkouche, R. (1997). Epistémologie, histoire et enseignement de mathématiques. For the Learning of Mathematics. An International Journal of Mathematics Education, 17(1), 34-42. Bkouche, R. (2000). Sur la notion de perspective historique dans l'enseignement d'une science. Repères - IREM, 39, 35-59. Blanco, L. (2004). Problem Solving and the Initial Practical and Theoretical Education of Teachers in Spain. Mathematics Teacher Education and Development, 6, 31-42. Blanton, M. L. (2002). Using an undergraduate geometry course to challenge pre-service teachers' notions of discourse. Journal of Mathematics Teacher Education, 5(2), 117-152. Boero, P. (1989). Utilización de la Historia de las Matemáticas en clase con alumnos de 6 a 13 años. Suma: Revista sobre Enseñanza y Aprendizaje de las Matemáticas, 2, 17- 28. Boero, P., & Guala, E. (2008). Development of Mathematical Knowledge and Beliefs of Teachers: The Role of Cultural Analysis of the Content to be Taught. In P. Sullivan & T. Wood (Eds.), Knowledge and Beliefs in Mathematics Teaching and Teaching Development (Vol. 1, pp. 223-244). Rotterdam: Sense Publishers. Bongiovanni, V. (2005). As duas maiores contribuições de Eudoxo de Cnido “a teoria das proporções e o método de exaustão”. UNIÓN. Revista Iberoamericana de Educación Matemática 2, 91-110. Bonsangue, M. V. (2000). A mathematical mystery tour. [Book Review]. Mathematics Teacher, 93(8), 726. Bos, H. J. M. (1984). Mathematics and its social context; a dialogue in the staff room, with historical episodes. For the Learning of Mathematics. An International Journal of Mathematics Education, 4(3), 2-9. Boyer, C. B. (1993). Tópicos de História da Matemática para uso em sala de aula. Cálculo (H. H. Domingues, Trans. Vol. 6). Sao Paulo: Atual Editora Ltda. Bradwardine, T., & Crosby, H. L. (1955). Thomas of Bradwardine, his Tractatus de proportionibus; its significance for the development of mathematical physics. Madison,: University of Wisconsin Press. Bradwardine, T., Rommevaux, S., & Oresme, N. (2009). Traité des rapports entre les rapidités dans les mouvements. Paris: Les Belles lettres. Brentjes, S. (2001). Two comments on Euclid's Elements? On the relation between the Arabic text attributed to al-Nayrızı and the Latin text ascribed to Anaritius. Centaurus, 43(1), 17-55. doi: 10.1034/j.1600-0498.2001.t01-1-430102.x Brentjes, S. (2008). Elements: Reception of Euclid's Elements in the Islamic World. In H. Selin (Ed.), Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures (pp. 741-743): Springer Netherlands. Brousseau, G. (1990). ¿Qué pueden aportar a los enseñantes los diferentes enfoques de la didáctica de las matemáticas? Primera Parte. Enseñanza de las Ciencias. Revista de investigación y experiencias didácticas, 8(3), 259-268. Brown, D. (2003). The School of Pythagoras. Mathematics in School, 32(1), 29-34. Brown, G. (1991). The experience of history in mathematics education: Integrating the history and philosophy of math into core curriculum math courses from a cultural and humanistic viewpoint. For the Learning of Mathematics. An International Journal of Mathematics Education, 11(2), 13-14. Bruckheimer, M., & Arcavi, A. (2000). Mathematics and its History: An Educational Partnership. In V. J. Katz (Ed.), Using History to Teach Mathematics: An International Perspective (pp. 135-146). Washington: Mathematical Association of America. Buendia Abalos, G., & Montiel Espinosa, G. (2011). From History to Research in Mathematics Education: Socio-Epistemological Elements for Trigonometric Functions. In V. J. Katz & C. Tzanakis (Eds.), Recent Developments on Introducing a Historical Dimension in Mathematics Education (1 ed., Vol. 78, pp. 67-82): Mathematical Association of America. Buendia, G. (2006). Una socioepistemología del aspecto periodico de las funciones. Revista Latinoamericana de Investigación en Matemática Educativa, 9(2), 227-252. Buendía, G. (2008). Historia y Pedagogía de las Matemáticas (HMP 2008). Revista Latinoamericana de Investigación en Matemática Educativa, 20(3), 125-127. Burn, B. (2003). The hyperbola: some 17th century arguments. Mathematics in School, 32(1), 27-28. Burn, R. P. (1998a). Is the number line full? Mathematics in School, 27(4), 55. Burn, R. P. (1998b). Napier's logarithms. Mathematics in School, 27(4), 32-33. Busard, H. L. L. (1996). Einiges über die Handschrift Leiden 399,1 und die arabischlateinische Ü bersetzung von Gerhard von Cremona. In J. Dauben, M. Folkerts, E. Knobloch & H. Wussing (Eds.), History of Mathematics: States of the Art (pp. 173-205). San Diego: Academic Press. Byers, V. (1982). Why study the history of mathematics? International Journal of Mathematical Education in Science and Technology, 13(1), 59 - 66. Cable, J. (2014). La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy. Science & Education, 23(1), 223-240. doi: 10.1007/s11191-013-9628-z Cajori, F. (1928). Ciruelo on the Names "Arithmetical" and "Geometrical" Proportions and Progressions. Isis, 10(2), 363-366. Calinger, R. (Ed.). (1996). Vita mathematica. Historical research and integration with teaching. [Washington, D.C.]: Mathematical Association of America. Camp, D. R. (2000). Benoit Mandelbrot: the Euclid of fractal geometry. Mathematics Teacher, 93(8), 708-712. Campistrous, L. A., López Fernández, J. M., & Rizo Cabrera, C. (2011). Historia y didáctica: el caso del escrito de L'Hôpital Analyse des Infiniment Petits pour L’intelligence Des lignes Courbes. Épsilon. Revista de Educación Matemática, 28(1), 51-64. Campos, A. (1994a). Axiomática y Geometría desde Euclides hasta Hilbert y Bourbaki. Bogotá. Campos, A. (1994b). Introducción a la Lógica y la Geometría griegas anteriores a Euclides. Bogotá. Cantoral, R., Fasanelli, F., Garciadiego, A., Stein, B., & Tzanakis, C. (Eds.). (2008). Proceedings of HPM 2008, The satellite meeting of ICME 11. Mexico City: CDROM. Cardeñoso, J. M., Flores, P., & Azcárate, C. (2001). El desarrollo profesional de los profesores de matemáticas como campo de investigación. In P. Gómez & L. Rico (Eds.), Iniciación a la investigación en didáctica de la matemática. Homenaje al profesor Mauricio Castro (pp. 233-244). Granada: Universidad de Granada. Carss, M. (Ed.). (1986). Proceedings of the Fifth International Congress on Mathematical Education. New York: Springer Science+Business Media, LLC. Carvalho, J. B. P., & Dassie, B. A. (2012). The history of mathematics education in Brazil. ZDM, 44(4), 499-511. doi: 10.1007/s11858-012-0439-5 Castañeda, A. (2002). Estudio de la evolución didáctica del punto de inflexión: una aproximación socioepistemológíca Revista Latinoamericana de Investigación en Matemática Educativa, 5(1), 27-44. Caveing, M. (1994). La proportionnalité des grandeurs dans la doctrine de la nature d'Aristote. Revue d'histoire des sciences, 47(2), 163-188. CBMS. (2001). The Mathematical Education of Teachers: American Mathematical Society - Mathematical Association of America. CBMS. (2012). The Mathematical Education of Teachers II: American Mathematical Society - Mathematical Association of America. Celeyrette, J. (2008). Bradwardine’S Rule: A Mathematical Law? In W. Laird & S. Roux (Eds.), Mechanics and Natural Philosophy Before the Scientific Revolution (Vol. 254, pp. 51-66): Springer Netherlands. Celeyrette, J., & Mazet, E. (2003). Le mouvement du point de vue de la cause et le mouvement du point de vue de l'effet dans le "Traité des rapports" d'Albert de Saxe. Revue d'histoire des sciences, 56(2), 419-437. doi: 10.2307/23634025 Clark, K. M. (2011). Reflections and Revision: Evolving Conceptions of a Using History Course. In V. J. Katz & C. Tzanakis (Eds.), Recent Developments on Introducing a Historical Dimension in Mathematics Education (1 ed., Vol. 78, pp. 211-220): Mathematical Association of America. Clark, K. M. (2012). History of mathematics: illuminating understanding of school mathematics concepts for prospective mathematics teachers. Educational Studies in Mathematics, 81(1), 67-84. doi: 10.1007/s10649-011-9361-y Clark, K. M. (2014). History of Mathematics in Mathematics Teacher Education. In R. M. Matthews (Ed.), International Handbook of Research in History, Philosophy and Science Teaching (pp. 755-791). Dordrecht: Springer Netherlands. Cooper, M. (1992). Who Named the Radian? The Mathematical Gazette, 76(475), 100-101. Cordero, F., & Flores, R. (2007). El uso de las gráficas en el discurso matemático escolar. Un estudio socioepistemológico en el nivel básico a través de los libros de texto. (Spanish). Revista Latinoamericana de Investigación en Matemática Educativa, 10(1), 7-38. Corry, L. (1994). La teoría de las proporciones de Eudoxio interpretada por Dedekind. Mathesis. Filosofía e Historia de las Matemáticas, 10(1), 1-24. Cortez Godinez, R. A., Ponce Ocegueda, C. E., Flores Robles, J. F., Muñoz Carrillo, S., & Reynaga Luna, C. M. (2009). Historia, Matemáticas y Profesores en la UAN. In P. Lestón (Ed.), Acta Latinoamericana de Matemática Educativa (Vol. 22, pp. 1529- 1533). México, D.F.: Colegio Mexicano de Matemática Educativa A. C. y Comité Latinoamericano de Matemática Educativa A. C. Cousquer, É. (1994, 27-28 mai ). De la théorie des proportions à la théorie des nombres réels. Paper presented at the 10ème colloque Inter-IREM d’épistémologie & d’histoire des mathématiques. La mémoire des nombres, Université de Caen - Cherbourg. Craik, A. D. D. (2009). A proportional view: The mathematics of James Glenie (1750-1817). Historia Mathematica, 36(3), 247-272. Crilly, T. (1992). A Gemstone in Matrix Algebra. The Mathematical Gazette, 76(475), 182-188. Curchin, L., & Fischler, R. (1981). Hero of Alexandria's Numerical Treatment of Division in Extreme and Mean Ratio and Its Implications. Phoenix, 35(2), 129-133. doi: 10.2307/1087332 Chan, Y.-C., & Siu, M.-K. (2012). Facing the change and meeting the challenge: mathematics curriculum of Tongwen Guan in China in the second half of the nineteenth century. ZDM, 44(4), 461-472. doi: 10.1007/s11858-012-0427-9 Charalambous, C., Panaoura, A., & Philippou, G. (2009). Using the history of mathematics to induce changes in preservice teachers’ beliefs and attitudes: insights from evaluating a teacher education program. Educational Studies in Mathematics, 71(2), 161-180. Charbonneau, L., & Fernández, S. (1998). History of Mathematics and the Teaching of Mathematics. In C. Alsina, J. M. Álvarez, M. Niss, A. Pérez, L. Rico & A. Sfard (Eds.), Proceedings of 8th International Congress of Mathematics Education (Vol. 1, pp. 339). Sevilla: Sociedad Andaluza de Educación Matemática Thales. Charette, R. J. (2004). Integrating the history of mathematics in the teaching of mathematics: A possible link between Pythagoras and King Tut. Mediterranean Journal for Research in Mathematics Education, 3(1-2), 115-124. Chassapis, D. (2007). Integrating the Philosophy of Mathematics in Teacher Training Courses Philosophical Dimensions in Mathematics Education (pp. 61-79). Chassapis, D., & Kotsakosta, M. (2003). Crossing the Bridges of Konigsberg in a Primary Mathematics Classroom. Mathematics in School, 32(1), 11-13. Chechile, R. A. (2006). From calculus to computers: Using the last 200 years of mathematics history in the classroom. Journal of Mathematical Psychology, 50(6), 584-584. Chelma, K. (2012). The History of Mathematical Proof in Ancient Traditions. New York: Cambridge University Press. Chevallard, Y., & Joshua, M. A. (1982). Un exemple d’analyse de la transposition didactique. La notion de distance. Recherches en Didactique des Mathématiques, 3(1), 159-239. Chinnappan, M. (2003). Schema Construction among Pre-Service Teachers and the Use of IT in Mathematics Teaching: A Case Study. Mathematics Teacher Education and Development, 5, 32-44. Chinnappan, M., & Lawson, M. J. (2005). A framework for analysis of teachers' geometric content knowledge and geometric knowledge for teaching. Journal of Mathematics Teacher Education, 8(3), 197-221. Christianidis, J. (1998). Une interpretation byzantine de Diophante. Historia Mathematica, 25(1), 22-28. D'Ambrosio, U., & Lázsló, F. (1988). International Study Group on the relations between History and Pedagogy of Mathematics (HPM). In A. Hirst & K. Hirst (Eds.), Proceedings of the Sixth International Congress on Mathematical Education (pp. 389-391). Budapest: János Bolyai Mathematical Society. D’Ambrosio, U. (2009). Some Reflections on Education, Mathematics, and Mathematics Education. In R. Even & D. Ball (Eds.), The Professional Education and Development of Teachers of Mathematics. The 15th ICMI Study (pp. 239-244). New York: Springer Science+Business Media. d’Enfert, R. (2012). Mathematics teaching in French écoles normales primaires, 1830– 1848: social and cultural challenges to the training of primary school teachers. ZDM, 44(4), 513-524. doi: 10.1007/s11858-012-0416-z da Ponte, J. P., Oliveira, H., & Varandas, J. M. (2002). Development of pre-service mathematics teachers' professional knowledge and identity in working with information and communication technology. Journal of Mathematics Teacher Education, 5(2), 93-115. Darden, L. (1991). Theory Change in Science: Strategies from Mendelian Genetics. New York: Oxford University Press. Davis, B. (1999). Basic irony: Examining the foundations of school mathematics with preservice teachers. Journal of Mathematics Teacher Education, 2(1), 25-48. Davitt, R. M. (2000). The evolutionary character of mathematics. Mathematics Teacher, 93(8), 692-694. De Groot, J. (2000). Aspects of Aristotelian statics in Galileo's dynamics. Studies In History and Philosophy of Science Part A, 31(4), 645-664. de la Fuente Martínez, C. (2011). Historia de las matemáticas e investigaciones matemáticas en secundaria. Algunos fundamentos y ejemplos para la clase. Épsilon. Revista de Educación Matemática, 28(1), 133-151. de la Torre, A. (1997). Anotaciones a una lectura de Arquímedes. Medellín: Universidad de Antioquia. De Morgan, A. (1836). The connexion of number and magnitude: an attempt to explain the fifth book of Euclid. London: Taylor and Walton. de Parme, B. (2005). Questiones circa Tractatum Proportionum Magistri Thome Braduardini. Paris: Vrin. De Young, G. (1984). The Arabic textual traditions of Euclid's elements. Historia Mathematica, 11(2), 147-160. De Young, G. (1992). Ishaq ibn Hunayn, Hunayn ibn Ishaq, and the third Arabic translation of Euclid's Elements. Historia Mathematica, 19(2), 188-199. De Young, G. (1995). Euclidean geometry in the mathematical tradition of Islamic India. Historia Mathematica, 22(2), 138-153. De Young, G. (2005). Diagrams in the Arabic Euclidean tradition: A preliminary assessment. Historia Mathematica, 32(2), 129–179. Deakin, M. (2001). Using History to teach mathematics. ZDM, 33(5), 137-138. del Río Sánchez, J. (1997). Historia de la Matemática: implicaciones didácticas. Suma: Revista sobre Enseñanza y Aprendizaje de las Matemáticas, 26, 33-38. Despeaux, S. E. (2014). Collective Research Projects in the History of Mathematics Classroom. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 24(8), 684-697. doi: 10.1080/10511970.2014.905810 Dhombres, J. (1978). Nombre, mesure et continu. Épistémologie et histoire. Paris: CEDIC/FERNAND NATHAN. Dhombres, J., & Giusti, E. (1989). Ratio La theorie des proportions de l'antiquite au XIXeme siecle : Trento, Italia, 9-13 Janvier 1989. Historia Mathematica, 16(1), 88-89. Dhombres, J., & Giusti, E. (1990). Colloque: Ratio--La theorie des proportions de l'Antiquite au XIXeme siecle : Centro Internazionale per la Ricerca Matematica, Trento, 9-13 janvier 1989. Historia Mathematica, 17(1), 73-75. Díaz Fernández, L. M., & Moreno Escobar, K. L. (2012). Caracterización de la régula falsa como método de solución de ecuaciones de primer grado Licenciatura en Matemáticas Trabajo de grado no publicado, Universidad Pedagógica Nacional, Bogotá, D.C. Dimitric, R. M. (2001). Using less calculus in teaching calculus: an historical approach. Mathematics Magazine, 74(3), 201-211. Downes, S. (1997). Women mathematicians--male mathematics: a history of contradiction? Mathematics in School, 26(3), 26-27. doi: 10.2307/30215286 Drake, S. (1973). Medieval Ratio Theory vs Compound Medicines in the Origins of Bradwardine's Rule. Isis, 64(1), 67-77. doi: 10.2307/229870 Duckworth, G. E. (1962). Structural Patterns and Proportions in Vergil's Aeneid: A Study in Mathematical Composition: University of Michigan Press. Dummett, M. (1991). Frege. Philosophy of Mathematics. Cambridge, Massachusetts: Harvard University Press. Eagle, R. (1998). A typical slice. Mathematics in School, 27(4), 37-39. Ernest, P. (1991). The Philosophy of Mathematics Education (1st Edition ed.): Routledge. Ernest, P. (1998). The history of mathematics in the classroom. Mathematics in School, 27(4), 25-31. Ernest, P. (Ed.). (1994). Mathematics, Education and Philosophy: An International(Vol. 3). London: The Falmer Press. Estepa Castro, A., Gea Serrano, M. M., Cañadas de la Fuente, G. R., & Contreras García, J.M. (2012). Algunas notas históricas sobre la correlación y regresión y su uso en el aula. Números. Revista de Didáctica de las Matemáticas, 81, 5-14. Euser, M. (2000). Pythagorean Triangles and Musical Proportions. Nexus Network Journal, 2(1-2), 33-40. doi: 10.1007/s00004-999-0006-8 Evans, G. (1927). The Greek Idea of Proportion The American Mathematical Monthly, 34(7), 354-357. Even, R. (1999). The Development of Teacher Leaders and Inservice Teacher Educators. Journal of Mathematics Teacher Education, 2(1), 3-24. Even, R., & Ball, D. L. (2009). The Professional Education and Development of Teachers of Mathematics. The 15th ICMI Study Springer. Eves, H. (1994). Tópicos de História da Matemática para uso em sala de aula. Geometría (H. H. Domingues, Trans. Vol. 3). Sao Paulo: Atual Editora Ltda. Farmaki, V., & Paschos, T. (2007). Employing genetic ‘moments’ in the history of mathematics in classroom activities. Educational Studies in Mathematics, 66(1), 83- 106. Fauvel, J. (1991a). Editorial. For the Learning of Mathematics. An International Journal of Mathematics Education, 11(2), 2. Fauvel, J. (1991b). Using History in Mathematics Education. For the Learning of Mathematics. An International Journal of Mathematics Education, 11(2), 3-6. Fauvel, J. (1992). Mathematical People: John Fauvel. The Mathematical Gazette, 76(475), 199-203. Fauvel, J. (1998). Algorithms in the pre-calculus classroom: who was Newton-Raphson? Mathematics in School, 27(4), 45-47. Fauvel, J., Cousquer, É., Furinghetti, F., Heiede, T., Lit, C., Smid, H., . . . Tzanakis, C. (2000). Bibliography for further work in the area In J. Fauvel & J. van Maanen (Eds.), History in mathematics education. The ICMI Study (pp. 371-418). Dordrecht: Kluwer Academic Publishers. Fauvel, J., & van Maanen, J. (1997a). The role of the history of mathematics in the teaching and learning of mathematics. ZDM, 29(4), 138-140. Fauvel, J., & van Maanen, J. (1997b). The role of the History of Mathematics in the Teaching and Learning of Mathematics: Discussion Document for an ICMI Study (1997-2000). Mathematics in School, 26(3), 10-11. doi: 10.2307/30215282 Fauvel, J., & van Maanen, J. (1997c). The role of the history of mathematics in the teaching and learning of mathematics: Discussion Document for an ICMI Study (1997–2000). Educational Studies in Mathematics, 34(3), 255-259. Fauvel, J., & van Maanen, J. (2000). History in Mathematics Education. The ICMI Study. Dordrecht/Boston/London: Kluwer Academic Publisher. Fenaroli, G., Furinghetti, F., & Somaglia, A. (2014). Rethinking Mathematical Concepts with the Lens of the History of Mathematics: An Experiment with Prospective Secondary Teachers. Science & Education, 23(1), 185-203. doi: 10.1007/s11191-013-9651-0 Fernandez, E. (1994). A Kinder, Gentler Socrates: Conveying New Images of Mathematics Dialogue. For the Learning of Mathematics. An International Journal of Mathematics Education, 14(3), 43-47. Fernández Fernández, S. (1988). La proporción y la Historia de las Matemáticas. Números. Revista de Didáctica de las Matemáticas, 18, 45-49. Fernández Fernández, S. (2001). La historia de las matemáticas en el aula. Uno. Revista de Didáctica de las Matemáticas, 26, 9-27. Fernández González, M., & Rondero Guerrero, C. (2004). El inicio histórico de la ciencia del movimiento: Implicaciones epistemológicas y didácticas. Revista Latinoamericana de Investigación en Matemática Educativa, 7(2), 145-156. Ferrari, M., y Farfán, R.M. (2008). Un estudio socioepistemológico de lo logaritmico: la construcción de una red de modelos. Revista Latinoamericana de Investigación en Matemática Educativa, 11(3), 309-354. Fett, B. (2006). An In-depth Investigation of the Divine Ratio. Montana Mathematics Enthusiast, 3(2), 157-175. Filep, L. (1999). Pythagorean side and diagonal numbers. Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, 15, 1-7. Filep, L. (2003). Proportion Theory in Greek Mathematics. Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, 19, 167-174. Filep, L. (2004). How the Greeks might have discovered and aproximate irrational numbers. Paper presented at the 3rd Conference on History of Mathematics and Teaching of Mathematics, Miskolc. Fine, H. (1917). Ratio, Proportion and Measurement in the Elements of Euclid. The Annals of Mathematics, Second Series, 19(1), 70-76. Fiss, A. (2014). Cultivating Parabolas in the Parlor Garden: Reconciling Mathematics Education and Feminine Ideals in Nineteenth-Century America. Science & Education, 23(1), 241-250. doi: 10.1007/s11191-013-9638-x Foley, G. D. (2000). Notable mathematicians. [Book Review]. Mathematics Teacher, 93(8), 726-728. Fowler, D. H. (1979). Ratio in Early Greek Mathematics. Bulletin (New Series) of the Amrican Mathematical Society, 1(6), 807-846. Fowler, D. H. (1980). Book II of Euclid's Elements and a pre-Eudoxan theory of ratio. Archive for History of Exact Sciences, 22(1), 5-36. Fowler, D. H. (1981). Anthyphairetic ratio and Eudoxan proportion. Archive for History of Exact Sciences, 24(2), 69-72. Fowler, D. H. (1982a). Book II of Euclid's Elements and a pre-Eudoxan theory of ratio part 2: Sides and diameters. Archive for History of Exact Sciences, 26(3), 193-209. Fowler, D. H. (1982b). A generalization of the golden section. Fibonacci Quart, 20(2), 146- 158. Fowler, D. H. (1991). The experience of history in mathematics education: Perils and pitfalls of history. For the Learning of Mathematics. An International Journal of Mathematics Education, 11(2), 15-16. Fowler, D. H. (1992). A Final-Year University Course on the History of Mathematics: Actively Confronting the Past. The Mathematical Gazette, 76(475), 46-48. Fowler, D. H. (1999). The Mathematics of Plato’ Academy: A New Reconstruction (2 ed.). Oxford Oxford University Press. Fowler, D. H., & Rawlins, D. (1983). Eratosthenes' Ratio for the Obliquity of the Ecliptic. Isis, 74(4), 556-562. doi: 10.2307/232212 François, K., & Van Bendegem, J. P. (Eds.). (2007). Philosophical Dimensions in Mathematics Education (Vol. 42): Springer. French, D. (1997). New sins for old sines. Mathematics in School, 26(3), 23-25. doi: 10.2307/30215285 Freudenthal, H. (1981). Should a Mathematics Teacher Know Something about the History of Mathematics? For the Learning of Mathematics. An International Journal of Mathematics Education, 2(1), 30-33. Fried, M. (2001). Can Mathematics Education and History of Mathematics Coexist? Science & Education, 10(4), 391-408. Fried, M. (2007). Didactics and History of Mathematics: Knowledge and Self-Knowledge. Educational Studies in Mathematics, 66(2), 203-223. Frykholm, J. A. (1999). The Impact of Reform: Challenges for Mathematics Teacher Preparation. Journal of Mathematics Teacher Education, 2(1), 79-105. Führer, L. (1991). Historical stories in the mathematics classroom. For the Learning of Mathematics. An International Journal of Mathematics Education, 11(2), 24-31. Führer, L. (1992). Historical Stories in the Mathematics Classroom. The Mathematical Gazette, 76(475), 127-138. Fung, C.-I. (2004). How history fuels teaching for mathematising: Some personal reflections. Mediterranean Journal for Research in Mathematics Education, 3(1-2), 125-146. Furinghetti, F. (1992). The Ancients and the Approximated Calculation: Some Examples and Suggestions for the Classroom. The Mathematical Gazette, 76(475), 139-142. Furinghetti, F. (1997). History of Mathematics, Mathematics Education, School Practice: Case Studies in Linking Different Domains. For the Learning of Mathematics. An International Journal of Mathematics Education, 17(1), 55-61. Furinghetti, F. (2000). The history of mathematics as a coupling link between secondary and university teaching. International Journal of Mathematical Education in Science and Technology, 31(1), 43-51. Furinghetti, F. (2004). History and mathematics education: A look around the world with particular reference to Italy. Mediterranean Journal for Research in Mathematics Education, 3(1-2), 1-20. Furinghetti, F. (2007). Teacher education through the history of mathematics. Educational Studies in Mathematics, 66(2), 131-143. Furinghetti, F., & Barnett, C. (1998). Teacher Education Around the World. Journal of Mathematics Teacher Education, 1(3), 341-356. Furinghetti, F., & Giacardi, L. (2012). Secondary school mathematics teachers and their training in pre- and post-unity Italy (1810–1920). ZDM, 44(4), 537-550. doi: 10.1007/s11858-012-0396-z Furinghetti, F., Kaijer, S., & Vretblad, A. (Eds.). (2004). Proceedings of the HPM 2004: History and Pedagogy of Mathematics ICME 10 Satellite Meeting and 4th European Summer University on the History and Epistemology in Mathematics Education. Uppsala: Uppsala University. Furinghetti, F., & Paola, D. (2003). History as a Crossroads of Mathematical Culture and Educational Needs in the Classroom. Mathematics in School, 32(1), 37-41. Furinghetti, F., & Somaglia, A. (1998). History of mathematics in school across disciplines. Mathematics in School, 27(4), 48-51. Gagatsis, A., & Thomaidis, I. (1993). Le concept de valeur absolue, une étude multidimensionnelle. PLOT, 67, 12-16. Gálvez Socarrás, A. M., & Maldonado Guinea, A. F. (2012). El papel de la historia de la Aritmética en un curso de Didáctica para la formación inicial de profesores. Maestría en Docencia de la Matemática Tesis no publicada, Universidad Pedagógica Nacional, Bogotá, D.C. Gandon, S. (2009). La théorie des rapports chez Augustus De Morgan. Revue d'histoire des sciences, 62(1), 285-311. doi: 10.2307/23634494 Gardies, J.-L. (1988). L'Héritage épistémologique d'Eudoxe de Cnide. Un essai de reconstitution. Paris: Librairie Philosophique J. Vrin. Gardies, J.-L. (1991). La proposition 14 du livre V dans l'économie des "Eléments" d'Euclide. Revue d'histoire des sciences, 44(3/4), 457-467. doi: 10.2307/23632874 Gardies, J.-L. (1997). L'organisation des mathématiques grecques de Théétète à Archimède. Paris: Librairie Philosophique J. Vrin. Gardies, J.-L. (2004). Du mode d'existence des objects de la mathématique. Paris: Librairie Philosophique J. Vrin. Gardiner, T. (1992a). Once upon a Time. The Mathematical Gazette, 76(475), 143-150. Gardiner, T. (1992b). Rigorous Thinking and the Use of Instruments. The Mathematical Gazette, 76(475), 179-181. Gardner, J. H. (1991). How Fast Does the Wind Travel?;: History in the Primary Mathematics Classroom. For the Learning of Mathematics. An International Journal of Mathematics Education, 11(2), 17-20. Gazit, A. (2013). What do mathematics teachers and teacher trainees know about the history of mathematics? International Journal of Mathematical Education in Science and Technology, 44(4), 501-512. doi: 10.1080/0020739x.2012.742151 Giusti, E. (2008). La théorie des proportions au XVe siécle: entre philologie et mathématiques. In P. Radelet-de Grave (Ed.), Liber Amicorum Jean Dhombres (pp. 173-193). Louvain-la-Neuve: Breplos Publisher. Glenie, J. (1777). The General Mathematical Laws Which Regulate and Extend Proportion Universally; Or, a Method of Comparing Magnitudes of Any Kind Together, in All the Possible Degrees of Increase and Decrease. By James Glenie, A. M. and Lieutenant in the Royal Regiment of Artillery. Philosophical Transactions of the Royal Society of London, 67(ArticleType: research-article / Full publication date: 1777 /), 450-457. doi: 10.2307/106247 Goldstein, J. A. (2000). A Matter of Great Magnitude: The Conflict over Arithmetization in 16th-, 17th-, and 18th-Century English Editions of Euclid's Elements Books I Through VI (1561-1795). Historia Mathematica, 27(1), 36-53. Gómez, B. (2011). Marco preliminar para contextualizar la investigación en historia y educación matemática. Épsilon. Revista de Educación Matemática, 28(1), 9-22. González Astudillo, M. T. (2011). Revisitando los conceptos de máximo y mínimo a través del libro de L'Hôpital. Épsilon. Revista de Educación Matemática, 28(1), 83-97. González Urbaneja, P. M. (1991). Historia de la matemática, integración cultural de las matemáticas, génesis de los conceptos y orientación de su enseñanza. Enseñanza de las Ciencias, 9(3), 28 21-289. González Urbaneja, P. M. (2004). La historia de las matemáticas como recurso didáctico e instrumento para enriquecer culturalmente su enseñanza. Suma: Revista sobre Enseñanza y Aprendizaje de las Matemáticas(45), 17-28. González Urbaneja, P. M. (2008). La solución de Eudoxo a la crisis de los inconmensurables. La teoría de la proporción y el método de exhaución. Sigma(33), 101-129. Goulding, M., Hatch, G., & Rodd, M. (2003). Undergraduate mathematics experience: Its significance in secondary mathematics teacher preparation. Journal of Mathematics Teacher Education, 6(4), 361-393. Grant, E. (1960). Nicole Oresme and His De Proportionibus Proportionum. Isis, 51(3), 293- 314. doi: 10.2307/226509 Grant, E. (1972). Nicole Oresme and the medieval geometry of qualities and motions. A treatise on the uniformity and difformity of intensities known as `tractatus de configurationibus qualitatum et motuum' : Marshall Clagett (ed. and tr.), edited with an introduction, English translation and commentary by Marshall Clagett. University of Wisconsin Press: Madison, Milwaukee, 1968; and London, 1969. xiii+713pp. [pound sign]7.75. Studies In History and Philosophy of Science Part A, 3(2), 167-182. Grant, E. (1975). Nicole Oresme and the commensurability or incommensurability of the celestial motions. Archive for History of Exact Sciences, 1(4), 420-458. Grattan-Guinness, I. (1978). On the relevance of the history of mathematics to mathematical education. International Journal of Mathematical Education in Science and Technology, 9(3), 275 - 285. Grattan-Guinness, I. (1996). Numbers, Magnitudes, Ratios, and Proportions in Euclid's Elements: How Did He Handle Them? Historia Mathematica, 23(4), 355-375. Grattan-Guinness, I. (1997). Numbers, Magnitudes, Ratios, and Proportions in Euclid'sElements: How Did He Handle Them?: Volume 23, Number 4 (1996), pages 355-375. Historia Mathematica, 24(2), 213-213. Grattan-Guinness, I. (2004a). History or Heritage? An Important Distinction in Mathematics and for Mathematics Education. American Mathematical Monthly, 111(1), 1-12. Grattan-Guinness, I. (2004b). The mathematics of the past: Distinguishing its history from our heritage. Historia Mathematica, 31(2), 163–185. Gravemeijer, K. (2008). RME Theory and Mathematics Teacher Education. In D. Tirosh & T. Wood (Eds.), The International Handbook of Mathematics Teacher Education. Tools and Processes in Mathematics Teacher Education (Vol. 2, pp. 283-302). Rotterdam: Sense Publishers. Gray, S. B. (2000). Mathematics in the age of Jane Austen: essential skills of 1800. Mathematics Teacher, 93(8), 670-679. Griesel, H. (2007). Reform of the construction of the number system with reference to Gottlob Frege. ZDM, 39(1), 31-38. Grosholz, E. (1987). Some uses of proportion in Newton's principia, book I: A case study in applied mathematics. Studies In History and Philosophy of Science Part A, 18(2), 209-220. Grossman, P. L. (1990). The Making of a Teacher. Teacher Knowledge and Teacher Education. New York Teachers College, Columbia University. . Groth, R. E. (2005/2006). Analysis of an Online Case Discussion about Teaching Stochastics. Mathematics Teacher Education and Development, 7, 53–71. Grugnetti, L. (2000). The History of Mathematics and its Influence on Pedagogical Problems. In V. J. Katz (Ed.), Using History to Teach Mathematics: An International Perspective (pp. 29-35). Washington: Mathematical Association of America. Guacaneme, E. A. (2000). ¿Es posible "sumar" razones? Revista EMA. Investigación e innovación en educación matemática, 5(3), 284-289. Guacaneme, E. A. (2001). Estudio Didáctico de la proporción y la proporcionalidad: Una aproximación a los aspectos matemáticos formales y a los textos escolares de matemáticas. Magister en Educación - Énfasis en Educación Matemática Tesis no publicada, Universidad del Valle, Cali. Guacaneme, E. A. (2002). Una mirada al tratamiento de la proporcionalidad en los textos escolares de matemáticas. Revista EMA. Investigación e innovación en educación matemática, 7(1), 3-42. Guacaneme, E. A. (2003). Estudio de la variación conjunta en la identificación de funciones. In G. Pentagogía (Ed.), Matemática educativa: Fundamentos de la matemática universitaria (pp. 129-136). Bogotá: Editorial Escuela Colombiana de Ingeniería. Guacaneme, E. A. (2006). El conocimiento histórico en la formación integral de un profesor de matemáticas: Estudio del caso de la proporcionalidad. Anteproyecto. Guacaneme, E. A. (2007a). La Historia de las matemáticas y el conocimiento histórico de las Matemáticas Ensayo no publicado. Universidad del Valle. Guacaneme, E. A. (2007b). La razón y la proporción en la Historia de las Matemáticas. Paper presented at the XVIII Encuentro de Geometría y sus aplicaciones y VI Encuentro de Aritmética, Bogotá, Colombia. Guacaneme, E. A. (2009). Dificultades para precisar el conocimientos disciplinar del profesor de matemáticas. Ensayo. Guacaneme, E. A. (2010). ¿Qué tipo de Historia de las Matemáticas debe ser apropiada por un profesor? Revista Virtual Educyt, 2, 136-148. Guacaneme, E. A. (2011). La Historia de las Matemáticas en la educación de un profesor: razones e intenciones. Paper presented at the XIII Conferencia Interamericana de Educación Matemática, Recife - Brasil. Guacaneme, E. A. (2012a). Aspectos de la teoría euclidiana de la proporción que favorecen la educación del profesor de Matemáticas. In L. Sosa Moguel, E. Aparicio Landa & F. M. Rodríguez Vásquez (Eds.), Memoria de la XV Escuela de Invierno en Matemática Educativa. Desarrollo de la Matemática Educativa y los Cimates (pp. 3- 11). México, D. F.: Red de Centros de Investigación en Matemática Educativa A.C. Guacaneme, E. A. (2012b). La educación del profesor como campo de investigación. Paper presented at the X Encuentro de Matemáticas Aplicada & VII Encuentro de Estadística, San José de Cúcuta. Guacaneme, E. A. (2012c). Significados de los conceptos de razón y proporción en el Libro V de los Elementos. In O. L. León (Ed.), Pensamiento, epistemología y lenguaje matemático (pp. 99-135). Bogotá: Fondo de Publicaciones Universidad Distrital Francisco José de Caldas. Guacaneme, E. A. (2012d). Teoría euclidiana de la proporción en la construcción de los números reales: ¿un asunto útil para un profesor? Revista TED. Tecné, Episteme y Didaxis, 31, 113-131. Guacaneme, E. A. (2013a). Conflictos para precisar el conocimiento disciplinar del profesor de Matemáticas. In C. Dolores Flores, M. d. S. García González, J. A. Hernández Sánchez & L. Sosa Guerrero (Eds.), Matemática Educativa: La formación de profesores (pp. 77-95). Chilpancingo, Guerrero: Ediciones Díaz de Santos, S. A. Guacaneme, E. A. (2013b). Tres ejemplos para discutir la existencia de objetos geométricos. In P. Perry (Ed.), Memorias del 21º Encuentro de Geometría y sus Aplicaciones (pp. 23-34). Bogotá, Colombia: Universidad Pedagógica Nacional. Guacaneme, E. A. (2015). ¿Versiones históricas no multiplicativas de la proporcionalidad? In P. R. Scott, Á. Ruiz & S. González (Eds.), Educación Matemática en las Américas 2015 (Vol. 17: Talleres y minicursos, pp. 380-390). Tuxtla Gutiérrez (México): Comité Interamericano de Educación Matemática. Guacaneme, E. A., Andrade, L., Perry, P., & Fernández, F. (2003). ¿Confía en sus conocimientos geométricos para construir figuras semejantes? In P. Perry, E. A. Guacaneme, F. Fernández & L. Andrade (Eds.), Transformar la proporcionalidad en la escuela: Un hueso duro de roer (pp. 55-92). Bogotá: una empresa docente. Guacaneme, E. A., Ángel, J. L., & Bello, J. H. (2013). Una experiencia de formación en “Historia de las Matemáticas en la educación en Matemáticas”. Paper presented at the I Congreso de Educación Matemática de América Central y El Caribe, Santo Domingo, República Dominicana. Guacaneme, E. A., & Mora, L. C. (2012a). El campo "Educación del profesor de Matemáticas". Ensayo no publicado. Departamento de Matemáticas. Universidad Pedagógica Nacional. Bogotá. Guacaneme, E. A., & Mora, L. C. (2012b). La educación del profesor de Matemáticas como campo de investigación. Paper presented at the Primer Simposio Internacional de Educación en competencias docentes, Bogotá, D.C. . Gulikers, I., & Blom, K. (2001). `A historical angle’, a survey of recent literature on the use and value of history in geometrical education. Educational Studies in Mathematics, 47(2), 223-258. Gundlach, B. H. (1994). Tópicos de História da Matemática para uso em sala de aula. Números e numerais (H. H. Domingues, Trans. Vol. 1). Sao Paulo: Atual Editora Ltda. Guyot, T., Cerizola, N., & Giordano, V. (1993). Matemática e Historia: Una articulación para la enseñanza. Enseñanza de las Ciencias, 11(Número Extra), 329-330. Hadley, J., & Singmaster, D. (1992). Problems to Sharpen the Young. The Mathematical Gazette, 76(475), 102-126. Heath, T. L. (1908). The Thirteen Books of Euclid’s Elements (Vol. II. Books III-IX). Cambridge, UK: Cambridge University Press. Heeffer, A. (2007). Learning Concepts Through the History of Mathematics Philosophical Dimensions in Mathematics Education (pp. 83-103). Hefendehl-Hebeker, L. (1991). Negative Numbers: Obstacles in Their Evolution from Intuitive to Intellectual Constructs. For the Learning of Mathematics. An International Journal of Mathematics Education, 11(1), 26-32. Heiede, T. (1992). Why Teach History of Mathematics? The Mathematical Gazette, 76(475), 151-157. Heiede, T. (1996). History of mathematics and the teacher. In R. Calinger (Ed.), Vita mathematica: historical research and integration with teaching (pp. 231-243). Washington: Mathematical Association of America. Helfgott, M. (1995). Improved teaching of the Calculus through the use of historical materials. In F. Swetz, J. Fauvel, O. Bekken, B. Johansson & V. J. Katz (Eds.), Learn from the Masters! (pp. 135-144). Washington, D.C.: The Mathematical Association of America. Helfgott, M. (2004). Two examples from the natural sciences and their relationship to the history and pedagogy of mathematics. Mediterranean Journal for Research in Mathematics Education, 3(1-2), 147-166. Henry, M. (2000). Evolution and Prospects of Preservice Secondary Mathematics Teacher Education in France. Journal of Mathematics Teacher Education, 3(3), 271-279. Hickman, F., & Kapadia, R. (1983). A History of Mathematics course for teachers. International Journal of Mathematical Education in Science and Technology, 14(6), 753 - 761. Hill, H. c., Ball, D. L., & Schilling, S. G. (2008). Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers' Topic-Specific Knowledge of Students. [Feature]. Journal for Research in Mathematics Education, 39(4), 372-400. Hill, M. J. M. (1900). The contents on the fifth and sixth books of Euclid. London: Cambridge University Press Warehouse. Hill, M. J. M. (1912a). The Mathematical Association. London Branch. Presidential Address on the Theory of Proportion. The Mathematical Gazette, 6(99), 324-332. doi: 10.2307/3605021 Hill, M. J. M. (1912b). Presidential Address on the Theory of Proportion. The Mathematical Gazette, 6(100), 360-368. Hill, M. J. M. (1914). The Theory of Proportion. London: Constable and Company Ltd. Hill, M. J. M. (1923). A Critical Account of Euclid's Exposition of the Theory of Proportion in the Fifth Book of the "Elements". The Mathematical Gazette, 11(162), 213-220. Hill, M. J. M. (1928). The Logical Eye and the Mathematical Eye. Their Outlook on Euclid's Theory of Proportion. Presidential Address to the Mathematical Association, 1928. The Mathematical Gazette, 14(193), 36-56. Hitchcock, G. (1997). Teaching the Negatives, 1870-1970: A Medley of Models. For the Learning of Mathematics. An International Journal of Mathematics Education, 17(1), 17-25, 42. Hogendijk, J. P. (2002). Anthyphairetic Ratio Theory in Medieval lslamic Mathematics. In Y. Dold-Samplonius, J. W. Dauben, M. Folkerts & B. van Dalen (Eds.), From China to Paris: 2000 Years Transmission of Mathematical Ideas (pp. 187-202). Stuttgart: Franz Steiner Verlag. Horn, J., Zamierowski, A., & Barger, R. (2000). Correspondence from mathematicians. Mathematics Teacher, 93(8), 688-691. Horng, W.-S., & Lin, F. L. (Eds.). (2000). Proceedings of the HPM 2000 Conference History in mathematics education. Challenges for a new millennium. Taipei: National Taiwan Normal University. Howson, A. G. (Ed.). (1973). Developments in Mathematical Education. Proceedings of the Second International Congress on Mathematical Education. Exeter: Cambridge University Press. Høyrup, J. (2006). Reviews: Busard, H. L. L., Campanus of Novara and Euclid’s Elements (Stuttgart: Franz Steiner Verlag, 2005), 2 vols. 768 pp. Centaurus, 48(4), 329-330. doi: 10.1111/j.1600-0498.2006.00051.x Høyrup, J. (2007). The roles of Mesopotamian bronze age mathematics tool for state formation and administration – carrier of teachers’ professional intellectual autonomy. Educational Studies in Mathematics, 66(2), 257-271. Huisjes, J., & Langeland, J. (1992). Wat deed een Egyptenaar 4000 jaar geleden met een differentiaalvergelijking? Nieuwe wiskrant, 11(4), 32-35. Isaac, I., Ram, V. M., & Richards, A. (1996). A historical approach to developing the cultural significance of mathematics amongst first year preservice primary school teachers. Paper presented at the HEM Meeting, Braga, Portugal. Isaac, I., Ram, V. M., & Richards, A. (2000). A Historical Approach to Developing the Cultural Significance of Mathematics Among First Year Pre-Service Primary School Teachers. In V. J. Katz (Ed.), Using History to Teach Mathematics: An International Perspective (pp. 123-128). Washington: Mathematical Association of America. J. (1920). Review: The Theory of Proportion. Isis, 3(2), 307. doi: 10.2307/224031 Jahnke, H. N. (1996). Mathematikgeschichte für Lehrer: Gründe und Beispiele. Mathematische Semesterberichte, 43, 21-46. Jankvist, U. T. (2009a). A categorization of the “whys” and “hows” of using history in mathematics education. Educational Studies in Mathematics, 71(3), 235-261. Jankvist, U. T. (2009b). On empirical research in the field of using History in Mathematics Education. Revista Latinoamericana de Investigación en Matemática Educativa, 12(1), 67-101. Jankvist, U. T., & Iversen, S. M. (2014). ‘Whys’ and ‘Hows’ of Using Philosophy in Mathematics Education. Science & Education, 23(1), 205-222. doi: 10.1007/s11191-013-9616-3 Jardine, D., & Shell-Gellasch, A. (Eds.). (2011). Mathematical Time Capsules. Historical Modules for the Mathematics Classroom: The Mathematical Association of America. Jaworski, B., & Wood, T. (Eds.). (2008). The International Handbook of Mathematics Teacher Education. The Mathematics Teacher Educator as a Developing Professional. (Vol. 4). Rotterdam: Sense Publishers. Jiménez, D. (2006). ¿Qué era un irracional para un matemático griego antiguo? Boletín de la Asociación Matemática Venezolana, XIII(1), 87-103. Joseph, G. G. (1997). What is a square root? A study of geometrical representation in different mathematical traditions. Mathematics in School, 26(3), 4-9. doi: 10.2307/30215281 Kahan, J. A., Cooper, D. A., & Bethea, K. A. (2003). The role of mathematics teachers' content knowledge in their teaching: A framework for research applied to a study of student teachers. Journal of Mathematics Teacher Education, 6(3), 223-252. Kappraff, J. (2000). The Arithmetic of Nicomachus of Gerasa and its Applications to Systems of Proportion. Nexus Network Journal, 2(1-2), 41-56. doi: 10.1007/s00004- 999-0007-7 Karp, A. (2012). Soviet mathematics education between 1918 and 1931: a time of radical reforms. ZDM, 44(4), 551-561. doi: 10.1007/s11858-012-0430-1 Karp, A., & Schubring, G. (Eds.). (2014). Handbook on the History of Mathematics Education New York: Springer. Katz, V. J. (1986). Using History in Teaching Mathematics. For the Learning of Mathematics. An International Journal of Mathematics Education, 6(3), 13-19. Katz, V. J. (1993). Using the history of calculus to teach calculus. Science & Education, 2(3), 243-249. Katz, V. J. (1997). Some Ideas on the Use of History in the Teaching of Mathematics. For the Learning of Mathematics. An International Journal of Mathematics Education, 17(1), 62-63. Katz, V. J. (2000a). The nothing that is. [Book Review]. Mathematics Teacher, 93(8), 728. Katz, V. J. (Ed.). (2000b). Using History to Teach Mathematics: An International Perspective: The Mathematical Association of America. Katz, V. J., & Barton, B. (2007). Stages in the History of Algebra with Implications for Teaching. Educational Studies in Mathematics, 66(2), 185-201. Katz, V. J., Jankvist, U. T., Fried, M. N., & Rowlands, S. (2014). Special Issue on History and Philosophy of Mathematics in Mathematics Education. Science & Education, 23(1), 1-6. doi: 10.1007/s11191-013-9660-z Katz, V. J., & Michalowicz, K. D. (Eds.). (2004). Historical Modules for the Teaching and Learning of Mathematics. Washington: Mathematical Association of America. Katz, V. J., & Tzanakis, C. (Eds.). (2011). Recent Developments on Introducing a Historical Dimension in Mathematics Education: Mathematical Association of America. Kellogg, A. (2005). Integration of the History of Mathematics Into the Elementary Classroom. Southern Connecticut State University. Kilpatrick, J. (2012). The new math as an international phenomenon. ZDM, 44(4), 563-571. doi: 10.1007/s11858-012-0393-2 Kjeldsen, T. H., & Blomhøj, M. (2009). Integrating history and philosophy in mathematics education at university level through problem-oriented project work. ZDM, 41(1- 2), 87-103. Kjeldsen, T. H., & Blomhøj, M. (2012). Beyond motivation: history as a method for learning meta-discursive rules in mathematics. Educational Studies in Mathematics, 80(3), 327-349. doi: 10.1007/s10649-011-9352-z Kjeldsen, T. H., & Petersen, P. H. (2014). Bridging History of the Concept of Function with Learning of Mathematics: Students’ Meta-Discursive Rules, Concept Formation and Historical Awareness. Science & Education, 23(1), 29-45. doi: 10.1007/s11191-013- 9641-2 Klein, J. (1968). Greek Mathematical Thought and the Origin of Algebra (E. Brann, Trans.). New York: Dover Publications, Inc. Kleiner, I. (1991). Rigor and proof in mathematics: a historical perspective. [Feature]. Mathematics Magazine, 64, 291-314. Kleiner, I. (1996). A history-of-mathematics course for teachers, based on great quotations In R. Calinger (Ed.), Vita mathematica: historical research and integration with teaching (pp. 261-268). Washington: Mathematical Association of America. Kleiner, I. (1998). A historically focused course in abstract algebra. Mathematics Magazine, 71(2), 105-111. Knoebel, A., Lodder, J., Laubenbacher, R. C., & Pengelley, D. J. (2007). Mathematical Masterpieces: Further Chronicles by the Explorers. New York: Springer. Knorr, W. R. (1975). The evolution of the Euclidean Elements. A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry. Dordrecht-Holland / Boston-U.S.A.: D. Reidel Publishing Company. Knorr, W. R. (1978). Archimedes and the Pre-Euclidean Proportion Theory. Archives internationales d'histoire des sciences, 28, 183-244. Knorr, W. R. (1992). De exhaución a cortaduras: primeras etapas de la teoría griega de las proporciones. Mathesis. Filosofía e Historia de las Matemáticas, 8, 1-12. Knorr, W. R. (2001). The impact of modern mathematics on ancent mathematics. Revue d'histoire des mathématiques, 7(1), 121-135. doi: 1262-022X / 1777-568X Knuth, E. J. (2002). Teachers' conceptions of proof in the context of secondary school mathematics. Journal of Mathematics Teacher Education, 5(1), 61-88. Kool, M. (1992). Dust Clouds from the Sixteenth Century. The Mathematical Gazette, 76(475), 90-96. Kool, M. (2003). An extra student in your classroom: How the history of mathematics can enrich interactive mathematical discussions at primary school. Mathematics in School, 32(1), 19-22. Krainer, K., & Wood, T. (Eds.). (2008). The International Handbook of Mathematics Teacher Education. Participants in Mathematics Teacher Education: Individuals, Teams, Communities and Networks. (Vol. 3). Rotterdam: Sense Publishers. Kronfellner, M. (1996). The history of the concept of function and some implications for classroom teaching. In R. Calinger (Ed.), Vita mathematica: historical research and integration with teaching (pp. 317-320). Washington: Mathematical Association of America. Kronfellner, M., Tzanakis, C., & Barbin, É. (Eds.). (2011). History and Epistemology in Mathematics Education. Proceedings of the 6th European Summer University (Firts ed.). Vienna: Verlag Holzhausen GmbH. Lagarto, M. J., Viera, A., & Veloso, E. (Eds.). (1996). Proceedings of the 2nd European Summer University on the History and Epistemology in Mathematics Education and the ICME 8 Satellite Meeting of HPM. Braga: Portuguese Association of the Teachers of Mathematics & Department of Mathematics, University of Minho. Lalande, F., Jaboeuf, F., & Nouazé, Y. (Eds.). (1995). Actes de la première Université d’ Été Européenne sur l’ Histoire et Épistémologie dans l’ Éducation Mathématique. Montpelier: IREM de Montpellier, Université Montpellier II. Lamandé, P. (2013). Quelques conceptions de la théorie des proportions dans des traités de la seconde moitié du dix septième siècle. Archive for History of Exact Sciences, 67(6), 595-636. doi: 10.1007/s00407-013-0120-6 Larsen, M. E. (1984). On the Possibility of a Pre-Euclidean Theory of Proportions. Centaurus, 27(1), 1-25. doi: 10.1111/j.1600-0498.1984.tb00752.x Lasher, P. (2000). Georg Cantor. [Book Review]. Mathematics Teacher, 93(8), 726. Laubenbacher, R. C., & Pengelley, D. J. (1996). Mathematical masterpieces: teaching with original sources In R. Calinger (Ed.), Vita mathematica: historical research and integration with teaching (pp. 257-260). Washington: Mathematical Association of America. Laubenbacher, R. C., & Pengelley, D. J. (1999). Mathematical Expeditions: Chronicles by the Explorers. New York: Springer. Lee, H. S. (2005). Facilitating students' problem solving in a technological context: Prospective teachers' learning trajectory. Journal of Mathematics Teacher Education, 8(3), 223-254. Leikin, R. (2008). Teams of Prospective Mathematics Teachers: Multiple Problems and Multiple Solutions. In K. Krainer & T. Wood (Eds.), The International Handbook of Mathematics Teacher Education. Participants in Mathematics Teacher Education: Individuals, Teams, Communities and Networks (Vol. 3, pp. 63-88). Rotterdam: Sense Publishers. Leikin, R., & Winicki-Landman, G. (2001). Defining as a Vehicle for Professional Development of Secondary School Mathematics Teachers. Mathematics Teacher Education and Development, 3, 62-73. Levi, B. (2003). Leyendo a Euclides (Tercera ed.). Buenos Aires: Libros del Zorzal. Li, S., Huang, R., & Shin, H. (2008). Discipline Knowledge Preparation for Prospective Secondary Mathematics Teachers: An East Asian Perspective. In P. Sullivan & T. Wood (Eds.), The International Handbook of Mathematics Teacher Education. Knowledge and Beliefs in Mathematics Teaching and Teaching Development (Vol. 1, pp. 63-86). Rotterdam: Sense Publishers. Lightner, J. E. (2000). Mathematicians are human too. Mathematics Teacher, 93(8), 696- 699. Lingard, D. (2000). The History of Mathematics: An Essential Component of the Mathematics Curriculum At All Levels. Australian Mathematics Teacher, 56(1), 40- 44. Lit, C.-K., Siu, M.-K., & Wong, N.-Y. (2001). The use of History in the Teaching of Mathematics: Theory, Practice, and Evaluation of Effectiveness. Education Journal, 29(1), 17-31. Loats, J., White, D., & Rubino, C. (2014). History of Mathematics: Three Activities to Use with Undergraduate Students and In-service Teachers. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 24(8), 698-709. doi: 10.1080/10511970.2014.900157 Mackinnon, N. (1992a). Homage to Babylonia. The Mathematical Gazette, 76(475), 158- 178. Mackinnon, N. (1992b). Newton's Teaser. The Mathematical Gazette, 76(475), 2-27. Maher, P. (1998). From al-jabr to algebra. Mathematics in School, 27(4), 14-15. Manrique García, J. F., & Triana Yaya, J. A. (2013). El papel de la historia del Álgebra en un curso de Didáctica para la formación inicial de profesores. Maestría en Docencia de la Matemática Tesis no publicada, Universidad Pedagógica Nacional, Bogotá, D.C. Markowsky, G. (1992). Misconceptions about the Golden Ratio. The College Mathematics Journal, 23(1), 2-19. doi: 10.2307/2686193 Marshall, G. L., & Rich, B. S. (2000). The role of history in a mathematics class. Mathematics Teacher, 93(8), 704-706. Martiñón Cejas, A. (1992). La teoría de las proporciones en los Elementos de Euclides Actas del Seminario "Orotava" de Historia de la Ciencia. Historia de la Geometría Griega (Vol. 1, Año I). Canarias: Consejería de Educación, Cultura y Deportes del Gobierno de Canarias. Dirección General de Ordenación e Innovación Educativa. Ediciones Educativas Canarias. Martiñón Cejas, A. (2001). Abstracción máxima y aplicaciones universales: las matemáticas del siglo XX. Uno. Revista de Didáctica de las Matemáticas, 26, 50-60. Mason, J. (1998). Enabling teachers to be real teachers: Necessary levels of awareness and structure of attention. Journal of Mathematics Teacher Education, 1(3), 243-267. Massa Esteve, M. R. (1997). Mengoli on "Quasi Proportions". Historia Mathematica, 24(3), 257-280. Massa Esteve, M. R. (2003). La théorie euclidienne des proportions dans les "Geometriæ speciosæ elementa" (1659) de Pietro Mengoli. Revue d'histoire des sciences, 56(2), 457-474. doi: 10.2307/23634027 Mathews, G. B. (1915). Review: The Theory of Proportion. The Mathematical Gazette, 8(117), 87-89. doi: 10.2307/3604056 Matthews, R. M. (Ed.). (2014). International Handbook of Research in History, Philosophy and Science Teaching. Dordrecht: Springer Netherlands. McComas, K. K. (2000). Felix Klein and the NCTM's standards: a mathematician considers mathematics