Publicado dic 6, 2017



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Soledad Estrella http://orcid.org/0000-0002-4567-2914

Arturo Mena-Lorca http://orcid.org/0000-0002-8150-2832

Raimundo Olfos-Ayarza http://orcid.org/0000-0002-9886-4282

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Resumen

El estudio ofrece una visión amplia del proceso de evolución de las ideas sobre tablas, su connotación de herramienta, surgimiento y desarrollo en diversas sociedades y culturas en diferentes momentos de la historia, cuestiones que aportan al conocimiento sobre este objeto y sus alcances didácticos. La reflexión sobre la trayectoria de la tabla y su presencia como herramienta de almacenamiento, como herramienta de cálculo en sistemas de numeración y de metrología, y como herramienta de análisis en ámbitos científicos y ma­temáticos, ayuda a precisar su origen y naturaleza como objeto matemático.

Keywords

Visual representation, epistemology, statistical data, storage of information, mathematics, statisticsRepresentación visual, epistemología, datos estadísticos, almacenamiento de la información, matemáticas, estadística

References
Aaboe, Asger (1964). Episodes from the Early History of Mathematics. Washington, DC: The Mathematical Association of America.

Anellis, Irving H. (1995). Peirce Rustled, Russell Pierced: How Charles Peirce and Bertrand Russell Viewed Each Other's Work in Logic, and an Assessment of Russell's Accuracy and Role in the Historiography of Logic. Modern Logic, 5 (3), 270-328. Disponible en: http://www.iupui.edu/~arisbe/menu/library/aboutcsp/ANELLIS/csp&br.htm

Anellis, Irving H. (2012). Peirce's Truth-functional Analysis and the Origin of the Truth Table. History and Philosophy of Logic, 33 (1), 87-97.

Arad, Zvi; Bangteng, Xu; Chen, Guiyun; Cohen, Effi; Hussam, Arisha HajIhia & Muzychuk, Mikhail (2011). On Normalized Integral Table Algebras (Fusion Rings): Generated by a Faithful Non-real Element of Degree 3. London: Springer.

Arad, Zvi & Blau, Harvey I. (1991). On Table Algebras and Applications to Finite Group Theory. Journal of Algebra, 138 (1), 137-185.

Arad, Zvi; Fisman, Elsa & Muzychuk, Misha (1999). Generalized Table Algebras. Israel Journal Mathematics, 114 (1), 29-60.

Bertoloni-Meli, Domenico (2004). The Role of Numerical Tables in Galileo and Mersenne. Perspectives on Science, 12 (2), 164-190. Disponible en: https://pdfs.semanticscholar.org/7b83/70eb76988606f2b0307799a1a5f56caf8927.pdf

Blau, Harvey I. & Zieschang, Paul-Hermann (2004). Sylow Theory for Table Algebras, Fusion Rule Algebras, and Hypergroups. Journal of Algebra, 273 (2), 551-570. Disponible en: http://www.sciencedirect.com/science/article/pii/S0021869303007087

Bocheński, Innocentius M. (1961). A History of Formal Logic. South Bend, Indiana: University of Notre Dame Press.

Campbell-Kelly, Martin; Croarken, Mary; Flood, Raymond & Robson, Eleanor (eds.) (2003). The History of Mathematical Tables. From Sumer to Spreadsheets. Oxford: Oxford University Press.

Chevallard, Yves (1991). La transposición didáctica. Del saber sabio al saber enseñado. Buenos Aires: Aique Grupo Editor S. A.

Estrella, Soledad (2014). El formato tabular: una revisión de literatura. Revista Actualidades Investigativas en Educación, 14 (2), 1-23. Disponible en: http://www.redalyc.org/pdf/447/44731371016.pdf

Estrella, Soledad; Mena-Lorca, Arturo & Olfos, Raimundo (2014). Desarrollo de una taxonomía de comprensión tabular. En Patricia Lestón (ed.). ALME, Acta Latinoamericana de Matemática Educativa, 27, 1041-1048. México: Colegio Mexicano
de Matemática Educativa A. C., Comité Latinoamericano de Matemática Educativa A. C. Disponible en: http://www.clame.org.mx/documentos/alme27.pdf

Euler, Leonhard (1748/1988). Introduction to Analysis of the Infinite. Book I. Berlin: Birkhäuser.

Friberg, Jöran (2007). A Remarkable Collection of Babylonian Mathematical Texts. Manuscripts in the Schøyen Collection: Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer.

Friendly, Michael & Denis, Daniel J. (2009). Milestones in the History of Thematic Cartography, Statistical Graphics, and Data Visualization. Natural Sciences and Engineering Research Council. Canada: Grant OGP0138748. Disponible en http://www.math.yorku.ca/SCS/Gallery/milestone/milestone.pdf, http://www.datavis.ca/milestones/

Friendly, Michael & Kwan, Ernest (2003). Effect Ordering for Data Displays. Computational Statistics & Data Analysis, 43 (4), 509-539. Disponible en: http://citeseerx.ist.psu.edu/viewdoc/download? doi=10.1.1.445.2938&rep=rep1&type=pdf

Garrow, John S. & Webster, Joan (1984). Quetelet's Index (W/H2) as a Measure of Fatness. International Journal of Obesity, 9 (2), 147-153.

Goody, Jack (1976). Civilisation de l'écriture et classification ou l'art de jouer sur les tableaux. Actes de la Recherche en Sciences Sociales, 2 (1), 87-101. Disponible en: http://www.persee.fr/doc/arss_0335-5322_1976_num_2_1_3384

Goody, Jack (1977). La domesticación del pensamiento salvaje. Madrid: Ediciones Akal.

Hallo, William W. (1964). The Road to Emar. Journal of Cuneiform Studies, 18 (3), 57-88.

Hitotsumatsu, Shin; Okada, Yoshio & Machida, Shouichiro (eds.). (2008). Study with Your Friends Mathematics for Elementary School, 3rd grade, vol. 1, 65-66. Tokyo: Gakko Tosho Co.

Lardner, Dionysius (1834). Babbage's Calculating Engine. Edinburgh Review, 120, 263-327.

Merzbach, Uta C. (1977). Georg Scheutz and the First Printing Calculator. Smithsonian Studies in History and Technology, 36, 1-74. Disponible en http://hdl.handle.net/10088/2435

Neugebauer, Otto & Hoesen, Henry B. van (1959). Greek Horoscopes. En Memoirs of the American Philosophical Society. Baltimore, Maryland: J. H. Furst Company.

Parnas, David Lorge; Asmis, G. J. Kurt & Madey, Jan (1991). Assessment of Safety-Critical Software in Nuclear Power Plants. Nuclear Safety, 32 (2), 189-198. Disponible en: https://www.researchgate.net/publication/242413466_Assessment_of_safety-critical_software_in_nuclear_power_plants

Pearson, Karl (1904). On the Theory of Contingency and its Relation to Association and Normal Correlation; on the General Theory of Skew Correlation and Non-linear Regression. Cambridge: Cambridge University Press.

Pecharromán-Gómez, Cristina (2013). Naturaleza de los objetos matemáticos: representación y significado. Enseñanza de las Ciencias, Revista de Investigación y Experiencias Didácticas, 31 (3), 121-134. Disponible en: http://www.raco.cat/index.php/Ensenanza/article/view/285795/373798

Pedersen, Olaf (1974). Logistics and Theory of Function: An Essay in the History of Greek Mathematics. Archives Internationales d'Histoire des Sciences, ARIHS, 24 (94), 29-50.

Peirce, Charles Sanders (1931). Division of Signs. En Charles Hartshorne & Paul Weiss (eds.). Collected Papers of Charles Sanders Peirce, Volume II, Chapter 2. Cambridge, Massachusetts: Harvard University Press.

Peirce, Charles Sanders (1931-1958). Collected Papers of Charles Sanders Peirce. Cambridge, Massachusetts: Harvard University Press.

Proust, Christine (2005). Le calcul sexagésimal en Mésopotamie. Disponible en http://culturemath.ens.fr/histoire%20des%20maths/pdf/Calcul%20sexa_Proust.pdf

Proust, Christine (2008). Quantifier et calculer: usages des nombres à Nippur. Revue d'Histoire des Mathématiques, 14 (2), 143-209. Disponible en: http://smf4.emath.fr/Publications/RevueHistoireMath/14/pdf/smf_rhm_14_143-209.pdf

Proust, Christine (2009). Numerical and Metrological Graphemes: From Cuneiform to Transliteration. Cuneiform Digital Library Journal, 1, 1-27. Disponible en: http://cdli.ucla.edu/files/publications/cdlj2009_001.pdf, http://www.cdli.ucla.edu/pubs/cdlj/2009/cdlj2009_001.html

Proust, Christine (2010). Mesopotamian Metrological Lists and Tables: Forgotten Sources. En Florence Bretelle-Establet (ed.). Looking at it from Asia: The Processes that Shaped the Sources of History of Science, 245-276. New York: Springer.

Quetelet, Lambert Adolphe Jacques (1835). Sur l'homme et le développement de ses facultés, ou Essai de physique sociale. Paris: Bachelier. Disponible en https://archive.org/stream/surlhommeetled00quet#page/n5/mode/2up

Rashed, Roshdi (2003). History of Science and Diversity at the Beginning of the 21st Century. En Proceedings of the XXI International Congress of History of Science, vol. I, 15-29. Ciudad de México: Universidad Nacional Autónoma de México, UNAM, Sociedad Mexicana de Historia de la Ciencia y la Tecnología.

Robson, Eleanor (2001). The Tablet House: A Scribal School in Old Babylonian Nippur. Revue d'assyriologie et d'archéologie orientale, 93 (1), 39-66.

Robson, Eleanor (2003). Tables and Tabular Formatting in Sumer, Babylonia, and Assyria, 2500 BCE-50 CE. En Martin Campbell-Kelly, Mary Croarken, Raymond Flood & Eleanor Robson (eds.). The History of Mathematical Tables. From Sumer to Spreadsheets, 19-48. Oxford: Oxford University Press.

Roegel, Denis (2010). A Reconstruction of the Tables of Briggs and Gellibrand's. Trigonometria Britannica (1633). En The LOCOMAT Project: Recomputing Mathematical and Astronomical Tables. Technical Report. Nancy, France: LOCOMAT, The LOria COllection of MAthematical Tables. Disponible en: http://locomat.loria.fr/briggs1633/briggs1633doc.pdf

Ross, Micah T. (2011). Survey of Graphical and Numerical Tables in Egypt. Oberwolfach Reports, 12, 650-652. Disponible en: http://www.academia.edu/7451497/Survey_of_Graphical_and_Numerical_Tables_in_Egypt

Schubring, Gert (2005). Conflicts between Generalization, Rigor and Intuition. Number Concepts Underlying the Development of Analysis in 17th19th Century France and Germany. New York: Springer. Sources and Studies in the History of Mathematics and Physical Sciences, SHMP.

Schubring, Gert (2011). Conceptions for Relating the Evolution of Mathematical Concepts to Mathematics Learning - Epistemology, History, and Semiotics Interacting. Educational Studies in Mathematics, 77 (1), 79-104.

Sidoli, Nathan (2014). Mathematical Tables in Ptolemy's Almagest. Historia Mathematica, 41 (1), 13-37. Disponible en: http://individual.utoronto.ca/acephalous/Sidoli_2014b.pdf

Tournès, Dominique (2000). Pour une histoire du calculgraphique. Revue d'Histoire des Mathématiques, 6, 127-161. Disponible en: http://www.numdam.org/article/RHM_2000__6_1_127_0.pdf

Tournès, Dominique (2011). What is a Numerical Table? Milestones for a Historical Research Project. Oberwolfach Reports, European Mathematical Society, 8 (1), Mini-Workshop: History of Numerical and Graphical Tables, 643-645. Disponible en: https://www.academia.edu/30940430/What_is_a_numerical_table_Milestones_for_a_historical_research_project

Tournès, Dominique (2014). Mathematics of Engineers: Elements for a New History of Numerical Analysis. En Proceedings of the International Congress of Mathematicians, Vol. 4, 1255-1273. Disponible en: https://hal.archives-ouvertes.fr/hal-01479456/document

Vergnaud, Gérard (1990). La théorie des champs conceptuels. Recherches en Didactique des Mathématiques, RDM, 10 (23), 133-170.

Vergnaud, Gérard (2013). Pourquoi la theorie des champs conceptuels? Infancia y Aprendizaje, 36 (2), 131-161. Disponible en: http://www.tandfonline.com/doi/pdf/10.1174/021037013806196283

Wiese, Heike (2003). Iconic and Non-iconic Stages in Number Development: the Role of Language. Trends in Cognitive Sciences, 7 (9), 385-390.

Wussing, Hans (1998). Lecciones de historia de las matemáticas. Madrid: Siglo XXI.

Youschkevitch, Adolph-Andrei Pavlovich (1976). The Concept of Function up to the Middle of the 19th Century. Archive for History of Exact Sciences, 16 (1), 37-85.
Cómo citar
Estrella, S., Mena-Lorca, A., & Olfos-Ayarza, R. (2017). Naturaleza del objeto matemático “Tabla”. Magis, Revista Internacional De Investigación En Educación, 10(20), 105–122. https://doi.org/10.11144/Javeriana.m10-20.nomt
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