Skip to main content
SpringerLink
Log in
Book cover

Mathematics, Education and History pp 193–208Cite as

Missing Curious Fraction Problems

The Unknown Inheritance and the Unknown Number of Heirs

  • Chapter
  • First Online:

  • 945 Accesses

Part of the book series: ICME-13 Monographs ((ICME13Mo))

Abstract

In this paper we present a study of one of the best-known types of descriptive word fraction problems. These problems have disappeared from today’s textbooks but are hugely important for developing arithmetic thinking. The aim of this paper is to examine the historical solution methods for these problems and discuss the analytical readings suggested by the authors. On the basis of this analysis we have conducted a preliminary study of the performance of 35 Spanish students who are highly trained in mathematics. Our results show that these students have a preference for algebraic reasoning, are reluctant to use arithmetic methods, and have reading comprehension difficulties that are reflected in their translations, from literal language to symbolic language, of the relationship between the parts expressed in the problem statement.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   119.00
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    A collection originally compiled by Metrodorus, probably around the 6th century and later on greatly enriched by C. Cephalas in the 10th century and M. Planudes in the 13th century.

References

  • Aurel, M. (1552). Libro primero, de arithmetica algebraica. Valencia: En casa de Ioan de Mey Flandro.

    Google Scholar 

  • Bachet C. G. (1612). Problêmes plaisans et délectables qui se font par les nombres. Alton: Chez Pierre Rigaud.

    Google Scholar 

  • Bruño, G. (1940). Aritmética Razonada. Curso Superior. Madrid: Editorial Bruño.

    Google Scholar 

  • Cerdán, F. (2008). Estudios sobre la Familia de Problemas Aritmético-Algebraicos. València: Servei de Publicacions de la Universitat de València.

    Google Scholar 

  • Chemla, K., & Guo, S. (Eds.). (2005). Les Neuf Chapitres, le classique mathématique de la Chine ancienne et ses commentaires. Paris: Dunod.

    Google Scholar 

  • Colebrooke, H. T. (Trans.). (1817). Algebra, with arithmetic and mensuration: From the Sanscrit of Brahmegupta and Bhascara. London: John Murray (Original: 1150 AD).

    Google Scholar 

  • De Ortega, J. (1552). Tractado subtilissimo de Arismetica y de Geometria. Compuesto por el reverendo padre fray Juan de Hortega de la orden de los predicadores. Ahora de nuevo enmendado con mucha diligencia por Gonzalo Busto de muchos errores que havia en algunas impressiones pasadas. Sevilla: Juan Canalla.

    Google Scholar 

  • Descartes, R. (1701). Opuscula posthuma physica et mathematica. Amsterdam: Typographia P. & J. Blaev.

    Google Scholar 

  • Euler, L. (1822). Elements of algebra. Translated from the French with the notes of M. Bernouilli, &c and the additions of M. De La Grange. Third edition, carefully revised and corrected (J. Hewlett, Trans.). London: Longman, Hurst, Rees, Orme, and Co (Original work published in 1770).

    Google Scholar 

  • Goldin, G. A., & McClintock, C. E. (1979). Task variables in mathematical problem solving. Philadelphia: Franklin Institute Press.

    Google Scholar 

  • Gómez, B. (2003). La investigación histórica en didáctica de las matemáticas. In E. Castro, P. Flores, T. Ortega, L. Rico, & A. Vallecillos A. (Eds.), Proceedings VII Simposio de la Sociedad Española de Investigación en Educación Matemática (SEIEM): Investigación en Educación Matemática (pp. 79–85). Granada: Universidad de Granada.

    Google Scholar 

  • Gómez, B., Sanz, M., & Huerta, I. (2016). Problemas Descriptivos de fracciones. Boletim de Educaçao Matematica (Bolema), 30(55), 586–604.

    Google Scholar 

  • Hutton, C. (1844). Recreation in science and natural philosophy: Dr. Hutton’s translation of Montucla’s edition of Ozanam. The present new edition of this celebrated work is revised by Edward Riddle, master of the mathematical school, Royal Hospital, Greenwich, who has corrected it to the present era, and made numerous additions. London: Thomas Tegg (Original work of Ozanam published in 1692).

    Google Scholar 

  • Jacobs, F. (Trans.). (1863). Anthologie Grecque. Traduite sur le texte publié d’après le manuscrit palatin par Fr. Jacobs avec des notices biographiques et littéraires sur les poètes de l’anthologie. Tome second. Paris: Hachette.

    Google Scholar 

  • Migne, J. P. (Ed.). (1850). Venerabilis Bedae Opera Omnia: Patrologia Cursus Completus, Series Latina (Vol. 90, columns 665–676). Paris: Petit-Montrouge (Original work from 641 AD).

    Google Scholar 

  • Migne, J. P. (Ed.). (1863). Beati Flacci Albini seu Alcuini Opera Omnia: Patrologia Cursus Completus, Series Latina (Vol. 101, columns 1143–1160). Paris: Petit-Montrouge (Original work from 775 AD).

    Google Scholar 

  • Ministerio de Educación y Cultura (MEC). (2014). Real Decreto 126/2014, de 28 de febrero, por el que se establece el currículo de la Educación Primaria. Boletin Oficial del Estado (BOE), 52, 19349–19420.

    Google Scholar 

  • Pérez de Moya, J. (1562). Arithmetica practica y speculativa. Salamanca: Mathias Gast.

    Google Scholar 

  • Phadke, N. H., Patwardhan, K. S., Naimpally, S. A., & Singh, S. L. (Eds.). (2001). Līlāvatī of Bhāskarācārya: A treatise of mathematics of Vedic tradition: With rationale in terms of modern mathematics largely based on N.H. Phadke’s Marāthī translation of Līlāvatī (Bhāskarācārya, book 1). Delhi: Motilal Banarsidass.

    Google Scholar 

  • Polya, G. (1966). Mathematical discovery (2 Vols.). New York: Wiley.

    Google Scholar 

  • Puig, A. (1715). Arithmetica especulativa y practica y Arte de Algebra. Barcelona: Joseph Giralt. Impresor, y Librero.

    Google Scholar 

  • Puig, L. (2003). Historia de las ideas algebraicas: componentes y preguntas de investigación desde el punto de vista de la matemática educativa. In E. Castro, P. Flores, T. Ortega, L. Rico, & A. Vallecillos A. (Eds.), Proceedings VII Simposio de la SEIEM: Investigación en Educación Matemática (pp. 97–108). Granada: Universidad de Granada.

    Google Scholar 

  • Sánchez, E., & Cobos, J. M. (Trans.). (1996). Juan Martínez Silíceo. Ars Arithmética. Madrid: Universidad de Extremadura, Servicio de Publicaciones (Original work published in 1513).

    Google Scholar 

  • Sarasvati, S. S. P., & Jyotishmati U. (Eds.). (1979). The Bakhshali manuscript. An ancient treatise of Indian arithmetic. Allahabad: Arvind Printer (Original work from 300).

    Google Scholar 

  • Shen, K., Crossley, J. N., & Lun, A. W.-C. (1999). The nine chapters on the mathematical art: Companion and commentary. Oxford and Beijing: Oxford University Press and Beijing Science Press.

    Google Scholar 

  • Sigler L. E. (2002). Fibonacci’s Liber Abaci: A translation into modern English of Leonardo Pisano’s book of calculation. New York: Springer (Original work from 1202).

    Google Scholar 

  • Singmaster, D. (1998). Chronology of recreational mathematics. http://utenti.quipo.it/base5/introduz/singchro.htm. Accessed August 9, 2017.

  • Swetz, F. J. (2014). Expediciones matemáticas. La aventura de los problemas matemáticos a través de la historia (J. Migual Parra, Trad.). Madrid: La esfera de los libros.

    Google Scholar 

  • Tahan, M. (1993). The man who counted: A collection of mathematical adventures (L. Clark & A. Reid, Trans.). New York: W. W. Norton.

    Google Scholar 

  • Vinot, J. (1860). Récréations mathématiques. Paris: Larousse et Boyer.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento Didáctica de la Matemática, Facultad de Magisterio, Universidad de Valencia, Av. dels Tarongers, 4, 46022, València, Spain

    Maria T. Sanz & Bernardo Gómez

Authors
  1. Maria T. Sanz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bernardo Gómez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Maria T. Sanz .

Editor information

Editors and Affiliations

  1. School of Teacher Education, Florida State University, Tallahassee, Florida, USA

    Kathleen M. Clark

  2. Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark

    Tinne Hoff Kjeldsen

  3. Institut Didaktik der Mathematik, Justus-Liebig-Universität Gießen, Giessen, Hessen, Germany

    Sebastian Schorcht

  4. Department of Education, University of Crete, Rethymnon, Greece

    Constantinos Tzanakis

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Sanz, M.T., Gómez, B. (2018). Missing Curious Fraction Problems. In: Clark, K., Kjeldsen, T., Schorcht, S., Tzanakis, C. (eds) Mathematics, Education and History . ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-73924-3_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-73924-3_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73923-6

  • Online ISBN: 978-3-319-73924-3

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics

Search

Navigation