Old Arithmetic Books: Mathematics in Spain in the First Half of the Sixteenth Century

María José Madrid; Alexander Maz-Machado; Carmen López; Carmen León-Mantero

doi:10.29333/iejme/5935

Full Text (PDF)

María José Madrid ¹, Alexander Maz-Machado ² ^* , Carmen López ³, Carmen León-Mantero ²

More Detail

¹ Universidad Pontificia de Salamanca, SPAIN² Universidad de Córdoba, SPAIN³ Universidad de Salamanca, SPAIN^* Corresponding Author

Abstract

During the sixteenth century, a relevant number of books related to practical arithmetic were published in Spain. This paper presents a comparative study that aims to identify the object and target of five old mathematics books and the main contents of these books. In order to do so, all the contents and all the examples found in five arithmetic books written during the first half of the 16th century were identified and categorised. A historical-mathematical analysis using a content analysis technique was then applied. The results show the authors’ concerns about mathematics at the time and the different contents that were included in some arithmetic books of this century.

Keywords

history of mathematics education
mercantile arithmetic
old mathematics books
sixteenth century

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 15, Issue 1, January 2020, Article No: em0553

https://doi.org/10.29333/iejme/5935

Publication date: 24 Sep 2019

Article Views: 2885

Article Downloads: 2490

Open Access References How to cite this article

References

Andres, J. (1515). Sumario breve de la practica de la arithmetica [Brief summary of practical arithmetic]. Valencia: Juan Joffre.
Ausejo, E. (2015). New Perspectives on Commercial Arithmetic in Renaissance Spain. In D. E. Rowe & W. Horng (Eds.), A Delicate Balance: Global Perspectives on Innovation and Tradition in the History of Mathematics (pp. 181-207). Basel: Springer. https://doi.org/10.1007/978-3-319-12030-0_9
Blanco, M. (2013). The Mathematical Courses of Pedro Padilla and Étienne Bézout: Teaching Calculus in Eighteenth-Century Spain and France. Science & Education, 22(4), 769-788. https://doi.org/10.1007/s11191-012-9537-6
Burke, P. (2000). A Social History of Knowledge: From Gutenberg to Diderot. Cambridge: Polity Press. https://doi.org/10.1353/jsh.2000.0001
Carabias, A. M. (2012). Salamanca y la medida del tiempo [Salamanca and the time measurement]. Salamanca: Ediciones Universidad de Salamanca.
Carpenter, D. I. (2013). Adam Riese. In F. J. Swetz (Ed.), The European Mathematical Awakening: A Journey Through the History of Mathematics from 1000 to 1800 (pp. 45-49). New York: Dover Publications.
Caunedo, B. (2009). Un manual de aritmética mercantil de Mosén Juan de Andrés [A manual of mercantil arithmetic by Mosén Juan de Andrés]. Pecvnia: Revista de la Facultad de Ciencias Económicas y Empresariales, Universidad de León, 8, 71-96. https://doi.org/10.18002/pec.v0i8.675
Choppin, A. (2000). Los manuales escolares de ayer a hoy: el ejemplo de Francia [School handbooks from yesterday to today: the french example]. Historia De La Educación, 19, 13-37.
Clark, K., & Robson, E. (2008). Ancient accounting in the modern mathematics classroom. BSHM Bulletin, 23(3), 129-142. https://doi.org/10.1080/17498430802304008
Cockcroft, W. H. (1982). Mathematics counts. London: HM Stationery Office.
De Ortega, J. (1512). Conpusicion de la arte de la arismetica y Juntamente de geometria [Composition of the art of arithmetic and together with geometry]. Lyon: casa de Maistro Nicolau de Benedictis.
De Texeda, G. (1546). Suma de Arihtmetica Practica y de todas Mercaderias con la horden de contadores [Sum of practical arithmetic and all merchandise with the order of accountants]. Valladolid: Oficina de Francisco Fernández de Córdoba.
De Yciar, J. (1549). Arithmetica Practica [Practical arithmetic]. Zaragoza: Casa de Pedro Bernuz.
Fauvel, J. (1991). Using history in mathematics education. For the Learning of Mathematics, 11(2), 3-6.
Fauvel, J., & van Maanen, J. A. (Eds.). (2000). History in mathematics education: The ICMI study. Dordrecht: Kluwer Academic Publishers.
Frejd, P. (2012). Old algebra textbooks: a resource for modern teaching. BSHM Bulletin: Journal of the British Society for the History of Mathematics, 28(1), 25-36. https://doi.org/10.1080/17498430.2012.676963
Garciadiego, A. R. (2002). History of Mathematics, an Intuitive Approach. Humanistic Mathematics Network Journal, 26, 6-11. https://doi.org/10.5642/hmnj.200201.26.05
Gómez, B. (2001). La justificación de la regla de los signos en los libros de texto: ¿Por qué menos por menos es más? [Justification of the rule of signs in textbooks: why negative times negative is positive?]. In P. Gómez & L. Rico (Eds.), Iniciación a la investigación en didáctica de la matemática. Homenaje al profesor Mauricio Castro (pp. 257-275). Granada: Universidad de Granada.
González, J. M. (1956). Gaspar de Texeda, precursor de la teneduría de libros en España [Gaspar de Texeda, precursor of the bookkeeping in Spain]. Técnica Económica: Administración y dirección de empresas, 2, 36-43.
Grattan-Guinness, I. (2004). The mathematics of the past: distinguishing its history from our heritage. Historia Mathematica, 31, 163-185. https://doi.org/10.1016/S0315-0860(03)00032-6
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. https://doi.org/10.1023/A:1014539212782
Gutiérrez, J. (1564). Arte Breve y muy provechoso de quenta castellana y Arithmetica [Brief and very useful art of Castilian count and arithmetic]. Zaragoza: casa de Pedro Bernuz.
Hallez, M. (1992). Teaching Huygens in the rue Huygens: Introducing the history of 17th-century mathematics in a junior secondary school. Science & Education, 1(3), 313-328. https://doi.org/10.1007/BF00430279
Jahnke, H. N. (2001). Cantor’s Cardinal and Ordinal Infinities: an Epistemological and Didactic View. Educational Studies in Mathematics, 48(2), 175-197. https://doi.org/10.1023/A:1016052726876
Jankvist, U. T. (2009). A categorization of the “whys” and “hows” of using history in mathematics education. Educational studies in Mathematics, 71(3), 235-261. https://doi.org/10.1007/s10649-008-9174-9
Kiliari, E. Gagatsis, A., & Papadaki, I. (2015). The first Greek printed mathematics book: The famous book of arithmetic Accounting of Manolis Glyzounis. International Journal for the History of Mathematics Education, 10(1), 25-53.
Kilpatrick, J. (1994). Historia de la investigación en educación matemática [History of research in mathematics education]. In J. Kilpatrick, L. Rico & M. Sierra (eds), Educación matemática e investigación (pp. 13-96). Madrid: Síntesis.
Kjeldsen, T. H. (2011). Uses of history in mathematics education: development of learning strategies and historical awareness. In M. Pytlak, T. Rowland and E. Swoboda (eds), Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (CERME 7, February 9- 13, 2011) (pp. 1700-1709). Rzeszów, Poland: University of Rzeszów and ERME.
López, J. M. (1979). Ciencia y técnica en la sociedad española de los siglos XVI y XVII [Science and technique in the Spanish society of the 16th and 17th centuries]. Barcelona: Labor.
Madrid, M. J. (2016). Los libros de aritmética en España a lo largo del siglo XVI [Arithmetic books in Spain during the 16th century]. Doctoral dissertation, Salamanca: Universidad de Salamanca.
Madrid, M. J., Maz-Machado, A., León-Mantero, C., & López-Esteban, C. (2017). Aplicaciones de las matemáticas a la vida diaria en los libros de aritmética españoles del siglo XVI [Applications of mathematics to everyday life in Spanish arithmetic books published in the 16th century]. Bolema: Boletim de Educação Matemática, 31(59), 1082-1100. https://doi.org/10.1590/1980-4415v31n59a12
Marco-Buzunáriz, M. A., Muñoz-Escolano, J. M., & Oller-Marcén, A. M. (2016). Investigación sobre libros de texto en los simposios de la SEIEM (1997-2015) [Research on textbooks on the Symposia of the SEIEM (1997-2015)]. In A. Berciano, C. Fernández, T. Fernández, J. L. González, P. Hernández, A. Jiménez, J. A. Macías, F. J. Ruiz, M. T. Sánchez (Eds.), Investigación en Educación Matemática XX (pp. 325-334). Malaga, Spain: Universidad de Málaga.
Maz, A. (2005). Los números negativos en España en los siglos XVIII y XIX [Negative numbers in Spain in the 18th and 19th centuries]. Doctoral dissertation, Granada: Universidad de Granada.
Maz, A. (2009), Investigación histórica de conceptos en los libros de matemáticas [Historical research of concepts in mathematics books]. In M.J. González, M.T. González & J. Murillo (Eds.), Investigación en Educación Matemática XIII (pp. 5-20). Santander: SEIEM.
Maz, A., & Rico, L. (2009). Negative numbers in the 18th and 19th centuries: phenomenology and representations. Electronic Journal of Research in Educational Psychology, 17(1), 537-554.
Maz-Machado, A., Madrid, M. J., León-Mantero, C., & Jiménez-Fanjul, N. (2017). Research trends in the history of mathematics education: the Spanish case. In K. Patterson (Ed.), Focus on mathematics education research (pp. 150-182). New York: Nova.
Meavilla, V., & Oller, A.M. (2014). El simbolismo algebraico en tres álgebras españolas del siglo XVI [Algebraic symbolism in three Spanish books on Algebra from the 16th century]. Números, 87, 59-68.
Meavilla, V., & Oller, A.M. (2014). La extracción de raíces en el Tratado de Mathematicas (1573) del bachiller Juan Pérez de Moya [The extraction of roots in the Tratado de Mathematicas (1573) of the bachelor Juan Pérez de Moya]. Epsilon, 88(33-1), 71-88.
O’Connor, J. J., & Robertson, E. F. (2019). MacTutor History of Mathematics archive. Scotland: University of St Andrews. Retrieved on 6 March 2019 from http://www-history.mcs.st-andrews.ac.uk/index.html
Paradís, J., & Malet, A. (1989), La génesis del álgebra simbólica. (Vol. I). Los orígenes del álgebra: de los árabes al renacimiento [The genesis of symbolic algebra (Vol. I). The origins of algebra: from the Arabs to the Renaissance]. Barcelona: PPU.
Picado, M. E. (2012). El sistema métrico decimal en libros de texto de matemáticas en España durante la segunda mitad del siglo XIX (1849-1892) [The metric system in mathematics textbooks in Spain during the second half of the 19th century (1849-1892)]. Doctoral dissertation, Granada: Universidad de Granada.
Picado, M., & Rico, L. (2012). La introducción del sistema métrico decimal y los libros de texto en España [The Introduction of Metric System and the Textbooks in Spain]. Suma: Revista Sobre Enseñanza y Aprendizaje De Las Matemáticas, 71, 9-18.
Picatoste, F. (1891). Apuntes para una biblioteca científica española del siglo XVI: estudios biográficos y bibliográficos de ciencias exactas, físicas y naturales y sus inmediatas aplicaciones en dicho siglo [Notes for a Spanish scientific library of the 16th century: biographical and bibliographic studies of exact, physical and natural sciences and their immediate applications in this century]. Madrid: Manuel Tello.
Puig, L., & Fernández, A. (2013). La Arithmetica Algebratica de Marco Aurel, primer álgebra impresa escrita en español. Preliminares para su estudio [Arithmetica Algebratica by Marco Aurel, the first printed algebra written in Spanish. Preliminaries for its study]. In L. Rico, M. C. Cañadas, J. Gutiérrez, M. Molina, I. Segovia (eds.), Investigación en Didáctica de la Matemática. Homenaje a Encarnación Castro (pp. 143- 150). Granada, España: Editorial Comares.
Rey, J. (1934). Los matemáticos españoles del siglo XVI [Spanish mathematicians of the 16th century]. Madrid: Junta de Investigaciones Histórico-Bibliográficas.
Salavert, V. (1990). Introducción a la historia de la aritmética práctica en la Corona de Aragón en el siglo XVI [Introduction to the history of practical arithmetic in the kingdom of Aragon in the 16th century]. Dynamis: Acta Hispanica Ad Medicinae Scientiarumque. Historiam Illustrandam, 10, 63-91.
Salavert, V. L. (1994), Aritmética y sociedad en la España del siglo XVI [Arithmetic and society in Spain in the 16th century. In S. Garma, V. Navarro, D. Flament (Eds.), Contra los gigantes de la rutina. Investigaciones sobre Historia y Filosofía de las Matemáticas. (pp. 51-69). Madrid: CSIC.
Schubring, G. (1987). On the methodology of analysing historical textbooks: Lacroix as textbook author. For the Learning of Mathematics, 7(3), 41-50.
Schubring, G. (2006). Researching into the History of Teaching and Learning Mathematics: the State of the Art. Paedagogica Historica, 42(4-5), 665-677. https://doi.org/10.1080/00309230600806955
Schubring, G. (2014). On Historiography of Teaching and Learning Mathematics. In A. Karp & G. Schubring (Eds.), Handbook on the history of mathematics education (pp. 3-8). New York: Springer. https://doi.org/10.1007/978-1-4614-9155-2_1
Sierra, M., Rico, L., & Gómez, B. (1997). El número y la forma: libros e impresos para la enseñanza del cálculo y la geometría [The number and the form: books and printed texts for teaching calculation and geometry]. In A. Escolano (Ed.), Historia ilustrada del libro escolar en España: del Antiguo Régimen a la Segunda República (pp. 373-398). Fundación Germán Sánchez Ruipérez: Ediciones Pirámide.
Swetz, F. (1992). Fifteenth and sixteenth century arithmetic texts: What can we learn from them? Science & Education, 1, 365-378. https://doi.org/10.1007/BF00430963

How to cite this article

APA

Madrid, M. J., Maz-Machado, A., López, C., & León-Mantero, C. (2020). Old Arithmetic Books: Mathematics in Spain in the First Half of the Sixteenth Century. International Electronic Journal of Mathematics Education, 15(1), em0553. https://doi.org/10.29333/iejme/5935

Vancouver

Madrid MJ, Maz-Machado A, López C, León-Mantero C. Old Arithmetic Books: Mathematics in Spain in the First Half of the Sixteenth Century. INT ELECT J MATH ED. 2020;15(1):em0553. https://doi.org/10.29333/iejme/5935

AMA

Madrid MJ, Maz-Machado A, López C, León-Mantero C. Old Arithmetic Books: Mathematics in Spain in the First Half of the Sixteenth Century. INT ELECT J MATH ED. 2020;15(1), em0553. https://doi.org/10.29333/iejme/5935

Chicago

Madrid, María José, Alexander Maz-Machado, Carmen López, and Carmen León-Mantero. "Old Arithmetic Books: Mathematics in Spain in the First Half of the Sixteenth Century". International Electronic Journal of Mathematics Education 2020 15 no. 1 (2020): em0553. https://doi.org/10.29333/iejme/5935

Harvard

Madrid, M. J., Maz-Machado, A., López, C., and León-Mantero, C. (2020). Old Arithmetic Books: Mathematics in Spain in the First Half of the Sixteenth Century. International Electronic Journal of Mathematics Education, 15(1), em0553. https://doi.org/10.29333/iejme/5935

MLA

Madrid, María José et al. "Old Arithmetic Books: Mathematics in Spain in the First Half of the Sixteenth Century". International Electronic Journal of Mathematics Education, vol. 15, no. 1, 2020, em0553. https://doi.org/10.29333/iejme/5935