Skip to main content

History of Teaching Arithmetic

  • Chapter
  • First Online:
Handbook on the History of Mathematics Education

Abstract

The history of teaching arithmetic is traced back to the early-Modern Age Italian reckoning masters and their arithmetic textbooks – libri di abbaco – based on the Hindu-Arabic numeral system. After the introduction of printing, arithmetic textbooks were printed in a variety of European languages. The textbooks had standard content until the twentieth century: mainly the four arithmetic operations in whole numbers and fractions and proportions in the form of the Rule of Three. The first books were aimed at self-study, while the gradual establishment of schools changed their use, as did impacts from influential educators such as Comenius and Pestalozzi. After the mid-twentieth century, radical changes in arithmetic teaching were made in the worldwide introduction of the new math.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 299.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 379.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 379.99
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

Institutional subscriptions

Notes

  1. 1.

    Wenn mein Leben einen Wert hat, so besteht er darin, dass ich das Quadrat zum Fundamente einer Anschauung erhob, die das Volk nie hatte.

References

  • Allard, André (ed.). 1992. Muhammad Ibn Mūsā al-Khwārizmī. Le Calcul Indien. Paris: Societé des Études Classiques/Librairie scientifique et technique.

    Google Scholar 

  • Andresen, Lembit. 1985. Eesti kooli vanem ajalugu. Tallinn: Valgus.

    Google Scholar 

  • Arnalds, Ari. 1949. Minningar. Reykjavík: Hlaðbúð.

    Google Scholar 

  • Becker, Joanne Rossi, and Teri Perl. 2003. The mathematics community’s response to a diverse and changing population. In A history of school mathematics, vol. 1, ed. George M.A. Stanic and Jeremy Kilpatrick, 1085–1142. Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Bjarnadóttir, Kristín. 2006. Mathematical education in Iceland in historical context – Socio-economic demands and influences. Reykjavík: Háskólaútgáfan.

    Google Scholar 

  • Bjarnadóttir, Kristín. 2011. Seventeenth and eighteenth century European arithmetic in an eighteenth century Icelandic manuscript. In History and epistemology in mathematics education. Proceedings of the Sixth European Summer University, ESU 6 Wien, Austria 19–23 July 2010. Vienna: Verlag Holzhausen GmbH.

    Google Scholar 

  • Boyer, Carl, and Uta Merzbach. 1991. A history of mathematics. New York: Wiley.

    MATH  Google Scholar 

  • Briem, Eiríkur. 1880. Reikningsbók. 2nd ed, revised. Reykjavík: Einar Þórðarson and Eiríkur Briem.

    Google Scholar 

  • Briscoe Center for American History. n.d. A guide to the school mathematics study group records, 1958–1977. https://www.lib.utexas.edu/taro/utcah/00284/00284-P.html. Accessed 1 Nov 2012.

  • Bruner, Jerome. 1960. The process of education. New York: Vintage Books.

    Google Scholar 

  • Bullynck, Marteen. 2008. The transmission of numeracy: Integrating reckoning in Protestant North-German elementary education (1770–1810). Paedagogica Historica 44(5): 568–585.

    Article  Google Scholar 

  • Bundgaard, Agnete. 1969–1972. Stærðfræði. Reikningur. 3a, 3b, 4a, 4b, 5a, 5b, 6. Reykjavík: Ríkisútgáfa námsbóka.

    Google Scholar 

  • Clements, McKenzie A., and Nerida Ellington. 2012. Early history of school mathematics in North America 1607–1861. In Preproceedings of 12th international congress on mathematical education, 6916–6925, Topic study group, vol. 35, Seoul, 8–15 Jul 2012.

    Google Scholar 

  • Cocker, Edward. 1703. Cocker’s decimal arithmetick. Perused, corrected and published by John Hawkins. London: Georg Sawbridge.

    Google Scholar 

  • Cohen, Patricia Cline. 2003. Numeracy in nineteenth-century America. In A history of school mathematics, vol. 1, ed. George M.A. Stanic and Jeremy Kilpatrick, 43–76. Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Cooper, Barry. 1985. Renegotiating secondary school mathematics. A study of curriculum change and stability. London: The Falmer Press.

    Google Scholar 

  • D’Ambrosio, Ubiratan. 2006. Ethnomathematics: Link between traditions and modernity. Rotterdam: Sense Publishers.

    Google Scholar 

  • D’Enfert, Renaud. 2003. L’enseignement mathématique à l’école primaire de la Révolution à nos jours. Tome 1: 1791–1914. Paris: Institut National de Recherche Pédagogique.

    Google Scholar 

  • Educational Encyclopedia. n.da. Elementary education. http://education.stateuniversity.com/pages/1950/Elementary-Education.html. Accessed 24 Jul 2012.

  • Educational Encyclopedia. n.db. Progressive education – Philosophical foundations, pedagogical progressivism, administrative progressivism, life-adjustment progressivism. http://education.stateuniversity.com/pages/2336/Progressive-Education.html. Accessed 21 Jun 2012.

  • Euler, Leonhard. 1738. Einleitung zur Rechenkunst zum Gebrauch des Gymnasii bey der Kayserlichen Academie der Wissenschafften in St. Petersburg. Gedruckt in der Academischen Buchdruckerey 1738. St. Petersburg. http://www.math.dartmouth.edu/~euler. Accessed Oct 12 2013

  • Euler, Leonhard. 1822. Elements of algebra. London: Longman, Hurst, Rees, Orme.

    Google Scholar 

  • Fey, James T. 1978. Change in mathematics education since the late 1950s – Ideas and realisation. U.S.A. Educational Studies in Mathematics 9(3): 339–353.

    Article  Google Scholar 

  • Frege, Gottlob. 1953. The Foundations of Arithmetic. A Logico-Mathematical Enquiry into the Concept of Number. Trans. J.L. Austin. Oxford: Basil Blackwell.

    Google Scholar 

  • Furinghetti, Fulvia. 2008. Mathematics education in the ICMI perspectives. The International Journal for the History of Mathematics Education 3(2): 47–56.

    MathSciNet  Google Scholar 

  • Furinghetti, Fulvia, Marta Menghini, Ferdinando Arzarello, and Livia Giacardi. 2008. ICMI renaissance: The emergence of new issues in mathematics education. In The first century of the international commission on mathematics instruction (1908–2008). Reflecting and shaping the world of mathematics education, ed. Marta Menghini, Fulvia Furinghetti, Livia Giacardi, and Ferdinando Arzarello, 131–147. Rome: Instituto della Enciclopedia Italiana.

    Google Scholar 

  • Gjone, Gunnar. 1983. “Moderne matematikk” i skolen. Internasjonale reformbestrebelser og nasjonalt læreplanarbeid, vol. I–VIII. Oslo: Author.

    Google Scholar 

  • Griffiths, Hubert Brian, and A. Geoffrey Howson. 1974. Mathematics, society and curricula. London: Cambridge University Press.

    MATH  Google Scholar 

  • Grosse, Hugo. 1901. Historische Rechenbücher des 16. und 17. Jahrhunderts und die Entwicklung ihrer Grundgedanken bis zur Neuzeit: ein Beitrag zur Geschichte d. Methodik des Rechenunterrichts mit 5 Titelabbildungen. Bad Godesberg: Genehmigung des Verlages Dürrsche Buchhandlung. Neudruck der Ausgabe in 1965 in Wiesbaden: Dr. Martin Sändig oHG.

    Google Scholar 

  • Gunnlaugsson, Björn. 1865. Tölvísi. Reykjavík: Hið íslenska bókmenntafélag.

    Google Scholar 

  • Hansen, Hans Christian. 2002. Fra forstandens slibesten til borgerens værktøj. Regning og matematik i folkets skole 1739–1958. Aalborg: Aalborg Universitet.

    Google Scholar 

  • Hatami, Reza. 2007. Reguladetri. En retorisk räknemetod speglad i svenska läromedel från 1600-tallet til början av 1900-tallet. Växsjö: MSI Växsjö University. http://lnu.diva-portal.org/smash/record.jsf?pid=diva2:205218. Accessed Oct 12 2013.

  • Howson, A. Geoffrey. 1995. Mathematics textbooks: A comparative study of grade 8 texts, TIMSS monograph, vol. 3. Vancouver: Pacific Educational Press.

    Google Scholar 

  • Høyrup, Jens. 1979. Historien om den nye matematik i Danmark – en skitse. In Den ny Matematik i Danmark, ed. Peter Bollerslev, 49–65. Copenhagen: Gyldendal.

    Google Scholar 

  • Høyrup, Jens. 2007. Jacopo da Firenze’s Tractatus Algorismi and Early Italian Abacus Culture. Science networks: Historical studies, vol. 34. Basel: Birkhäuser. doi: 10.1007/978-3-7643-8391-6.

  • Jänicke, Eduard. 1888. Geschichte des Rechenunterrichts. In Geschichte der Methodik des deutschen Volksschulunterrichts, vol. 3, ed. Carl Kehr. Gotha: Verlag Von E.F. Thienemanns Hofbuchhandlung.

    Google Scholar 

  • Karp, Alexander. 2013. From the local to the international in mathematics education. In Third international handbook of mathematics education, ed. McKenzie A. Clements, Alan J. Bishop, Christine Keitel, Jeremy Kilpatrick, and Frederick K.S. Leung. New York: Springer.

    Google Scholar 

  • Kästner, Abraham G. 1792. Anfangsgründe der Arithmetik, Geometrie, ebenen und sphärischen Trigonometrie und Perspective. 5th ed, 1st ed, 1758. Göttingen: Vandenhoeck und Ruprecht.

    Google Scholar 

  • Katz, Victor J. 1993. A history of mathematics. An introduction. New York: Harper Collins.

    MATH  Google Scholar 

  • Kilpatrick, Jeremy. 1992. A history of research in mathematics education. In Handbook of research on mathematics teaching and learning, ed. D. Grouws, 3–38. New York: Macmillan.

    Google Scholar 

  • Kliebard, Herbert M., and Barry M. Franklin. 2003. The ascendance of practical and vocational mathematics 1893–1945: Academic mathematics under siege. In A history of school mathematics, vol. 1, ed. George M.A. Stanic and Jeremy Kilpatrick, 399–440. Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Kruze, Aida, Iveta Kestere, Väino Sirk, and Ona Tijuneliene. 2009. History of education and pedagogical thought in the Baltic countries up to 1940: An overview. Riga: RaKa.

    Google Scholar 

  • Lbs 408, 8vo. Professor J. M. Geuss Collegium, over Arithmetiken, holdet Anno C.N. 1781 & 1782. [Professor J. M. Geuss lectures on arithmetic, held Anno Domini 1781 and 1782]. National and University Library of Iceland, manuscript department.

    Google Scholar 

  • Lüneburg, Heinz. 2008. Von Zahlen und Grössen. Dritthalbtausend Jahre Theorie und Praxis, vol. 1. Basel: Birkhäuser Verlag.

    Google Scholar 

  • Menghini, Marta. 2012. Rational approaches to arithmetic and real numbers in the Italian textbooks and programmes for the classical and the scientific curricula. In Proceedings of the second international conference on the history of mathematics education, ed. Kristín Bjarnadóttir, Fulvia Furinghetti, José M. Matos, and Gert Schubring. Lisbon: New University of Lisbon.

    Google Scholar 

  • Michalowicz, Karen D., and A.C. Howard. 2003. Pedagogy in text: An analysis of mathematics texts from the 19th century. In A history of school mathematics, vol. 1, ed. George M.A. Stanic and Jeremy Kilpatrick, 77–109. Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • OEEC. 1961. New thinking in school mathematics, 2nd ed. Paris: OEEC Publications.

    Google Scholar 

  • Osborne, A.R., and F.J. Crosswhite. 1970. Forces and issues related to curriculum and instruction. In A history of mathematics education in the United States and Canada. Thirty-second yearbook, ed. Philip S. Jones, 7–12. Washington, DC: National Council of Teachers of Mathematics. 155–297.

    Google Scholar 

  • Prinits, Olaf. 1992. Eesti koolimatemaatika ajalugu [The history of Estonian school mathematics]. Tartu: University of Tartu.

    Google Scholar 

  • Quartararo, Anne T. 1995. Women teachers and popular education in nineteenth-century France. Social values and corporate identity at the normal school institution. London: Associated University Presses.

    Google Scholar 

  • Schröder, Ebenhard. 1988. Das Bamberger Rechenbuch von 1483. In Das Bamberger Rechenbuch von 1483, ed. Ulrich Wagner. Berlin: Akademie-Verlag.

    Google Scholar 

  • Schubring, Gert. 2005. Conflicts between generalization, rigor, and intuition. New York: Springer.

    MATH  Google Scholar 

  • Schubring, Gert. 2012. From the few to the many: Historical perspectives on who should learn mathematics. In Proceedings of the second international conference on the history of mathematics education, ed. Kristín Bjarnadóttir, Fulvia Furinghetti, José M. Matos, and Gert Schubring. Lisbon: New University of Lisbon.

    Google Scholar 

  • Schugurensky, Daniel, ed. n.d. 1919 – The Winnetka Plan. History of education: selected moments of the 20th century. http://legacy.oise.utoronto.ca/research/edu20/moments/1919winnetka.html. Accessed 21 Jun 2012.

  • Seppala-Holzman, David. 2007. Ancient Egyptians, Russian peasants foretell the digital age. Mathematics Teacher 100(9): 632–635.

    Google Scholar 

  • Sigler, Lawrence E. (ed.). 2003. Fibonacci’s liber abaci. New York: Springer.

    MATH  Google Scholar 

  • Silber, Kate. 1976. Pestalozzi: The man and his work. 4th revised ed. London/Henley: Routledge/Kegan Paul.

    Google Scholar 

  • Stedall, Jaqueline. 2012. History of mathematics: A very short introduction. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Stefánsson, Ólafur Stephensen. 1785. Stutt Undirvísun í Reikníngslistinni og Algebra. Samantekin og útgefin handa Skóla-lærisveinum og ødrum ýnglíngum á Íslandi. Copenhagen: Author. http://baekur.is/is/bok/000302457/. Accessed Oct 12 2013.

  • Suevus, Sigismund. 1593. Arithmetica Historica. Die löbliche Rechenkunst. Durch alle Species und fürnembste Regeln mit schönen gedenckwirdigen Historien und Exempeln; auch mit Hebraischer, Griechischer, und Römischer Münze, Gewicht und Mass, deren in heiliger Schrifft und gutten Geschichtbüchern gedacht wird … Breslaw: G Bawman. http://www.archive.org/details/arithmeticahisto00suev. Accessed Oct 12 2013.

  • Swetz, Frank J. 1987. Capitalism and arithmetic: The new math of the fifteenth century, including the full text of the Treviso arithmetic of 1478. La Salle: Open Court.

    Google Scholar 

  • Swetz, Frank J. 1992. Fifteenth and sixteenth century arithmetic texts: What can we learn from them? Science and Education 1: 365–378.

    Article  MATH  MathSciNet  Google Scholar 

  • Tropfke, Johannes. 1980. Geschichte der Elementarmathematik, Vol. 1: Arithmetik und Algebra. Berlin: Walter de Gruyter.

    Google Scholar 

  • van Egmond, Warren. 1980. Practical mathematics in the Italian Renaissance: A catalog of Italian abbacus manuscripts and printed books to 1600. In Annali dell’Istituto e Museo di Storia della Scienza. Monografia N. 4, 3–36. Firenze: Istituto e Museo di Storia della Scienza.

    Google Scholar 

  • von Clausberg, Christlieb. 1732, 1748, 1762. Demonstrative Rechenkunst oder Wissenshaft, gründlich und kurz zu rechnen … Leipzig: Breitkopf. Second volume available at http://www.zvdd.de/dms/load/met/?PPN=PPN604553676; third volume available at http://archive.org/details/demonstrativere00claugoog. Accessed Oct 12 2013.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kristín Bjarnadóttir .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this chapter

Cite this chapter

Bjarnadóttir, K. (2014). History of Teaching Arithmetic. In: Karp, A., Schubring, G. (eds) Handbook on the History of Mathematics Education. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9155-2_21

Download citation

Publish with us

Policies and ethics