Skip to main content
SpringerLink
Log in

History of Mathematics in German Mathematics Textbooks

Typology of Tasks

  • Chapter
  • First Online:
Mathematics, Education and History

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

Abstract

Student textbooks and the tasks that they feature play a crucial role in mathematical lessons (Hiebert et al. 2003). While there have been several international studies on the history of mathematics in textbooks (Lakoma 2000; Shen et al. 2013; Smestad 2000a; Smestad 2000b; Smestad 2002; Xenofontos and Papadopoulos 2015), a comparable German study has yet to be published. This study analyzes and classifies one hundred and fifty-one tasks associated with the history of mathematics in mathematics textbooks and groups each task into one of four dimensions: “connection between the present and the past,” “evolution of mathematics over time,” “people throughout mathematics history” and “the aims and purposes of mathematics.” The results show five types of tasks: informative present, acting present, informative past, acting past and personalization type.

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

Access this chapter

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

Institutional subscriptions

References

  • Bergmann, K. (2008). Geschichtsdidaktik: Beiträge zu einer Theorie historischen Lernens. Schwalbach: Wochenschau-Verlag.

    Google Scholar 

  • Biegel, G., Reich, K., & Sonar, T. (Eds.). (2008). Historische Aspekte im Mathematikunterricht an Schule und Universität. Termessos: Göttingen & Stuttgart.

    Google Scholar 

  • Böttner, J., Maroska, R., Olpp, A., Pongs, R., Stöckle, C., Wellstein, H., et al. (2008). Schnittpunkt 5: Mathematik. Stuttgart & Leipzig: Ernst Klett Verlag.

    Google Scholar 

  • De Morgan, A. (1865). Speech of Professor De Morgan. Proceedings of the London Mathematical Society, 1, 1–9.

    Article  Google Scholar 

  • Epple, M. (2000). Genies, Ideen, Institutionen, mathematische Werkstätten: Formen der Mathematikgeschichte. Mathematische Semesterberichte, 47, 131–163.

    Article  Google Scholar 

  • Fauvel, J., & van Maanen, J. (Eds.). (2000). History in mathematics education: The ICMI study. New ICMI Study Series (Vol. 6). Dordrecht: Kluwer.

    Google Scholar 

  • Fischer, R. (2006). Materialisierung und Organisation: Zur kulturellen Bedeutung der Mathematik. München: Profil-Verlag.

    Google Scholar 

  • Fried, M. (2001). Can mathematics education and history of mathematics coexist? Science & Education, 10, 391–408.

    Google Scholar 

  • 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, 1–20.

    Google Scholar 

  • Ganter, B., Stumme, G., & Wille, R. (Eds.). (2005). Formal concept analysis: Foundations and applications. Berlin: Springer.

    Google Scholar 

  • Heymann, H. W. (1996). Allgemeinbildung und Mathematik. Weinheim/Bergstr. & Basel: Beltz.

    Google Scholar 

  • Hersh, R. (1997). What is mathematics, really? New York: Oxford University Press.

    Google Scholar 

  • Hiebert, J., Gallimore, R., Garnier, H., Givvin, K. B., Hollingsworth, H., Jacobs, J., et al. (2003). Teaching mathematics in seven countries: Results from the TIMSS 1999 video study. Washington, DC: NCES.

    Google Scholar 

  • Hug, W. (1985). Geschichtsunterricht in der Praxis der Sekundarstufe I: Befragungen Analysen und Perspektiven. Frankfurt a. M.: Diesterweg

    Google Scholar 

  • Jahnke, H. N., & Habdank-Eichelsbacher, B. (1999). Authentische Erfahrungen mit Mathematik durch historische Quellen. In C. Selter & G. Walther (Eds.), Mathematikdidaktik als design science: Festschrift für Erich Christian Wittmann (pp. 95–104). Leipzig: Ernst Klett Grundschulverlag.

    Google Scholar 

  • Jahnke, H. N., Schoenbeck, J., Weber-Foerster, A., Roessing, R., Zimmermann, B., Rieche, A., et al. (1991). Historische Quellen für den Mathematikunterricht. Mathematik lehren, 47, 23–50.

    Google Scholar 

  • Jahnke, H. N., Gerber, F., Richter, K., Richter, K., van Maanen, J., Kaske, R., et al. (1999). Mathematik historisch verstehen. Mathematik lehren, 91.

    Google Scholar 

  • Jahnke, H. N., Arcavi, A., Barbin, E., Bekken, O., Furinghetti, F., El Idrissi, A., et al. (2000). The use of original sources in the mathematics classroom. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: The ICMI study. New ICMI Study Series (Vol. 6, pp. 291–328). Dordrecht: Kluwer.

    Chapter  Google Scholar 

  • Jahnke, H. N., Richter, K., Bertalan, D., Glaubitz, M. R., Banse, R., Schöneburg, S., et al. (2008). Geschichte der Mathematik. Mathematik lehren, 151, 1–69.

    Google Scholar 

  • Jankvist, U. T. (2009). Using history as a “goal” in mathematics education (Doctoral dissertation). IMFUFA, Roskilde University, Denmark.

    Google Scholar 

  • Klein, F. (1933). Elementarmathematik vom höheren Standpunkt aus I: Arithmetik—Algebra—Analysis. Berlin: Springer.

    Google Scholar 

  • Kliemann, S., Puscher, R., Segelken, S., Schmidt, W., & Vernay, R. (2006). Mathe live 5: Mathematik für Sekundarstufe I. Stuttgart: Ernst Klett.

    Google Scholar 

  • Köbel, J. (1536). Geometrei vonn künstlichem Messen unnd absehen allerhand höhe, fleche, ebene, weite und breyte als Thürn, Kirchen, baew, baum, velder unnd äcker ec. mit künstlich zuebereiteten Jacob stab, Philosophischen Spiegel, Schatten unnd Mesruten. Oppenheim: Köbel. http://www.mdz-nbn-resolving.de/urn/resolver.pl?urn=urn:nbn:de:bvb:12-bsb10806709-6. Accessed August 27, 2017.

  • Lakoma, E. (2000). History of mathematics in curricula and school: A case study of Poland. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: The ICMI study. New ICMI Study Series (Vol. 6, pp. 19–29). Dordrecht: Kluwer.

    Google Scholar 

  • Lindner, F. W. (1808). Über die historisch-genetische Methode: Ein Beytrag zur Verbesserung und Vereinfachung des Unterrichts sowohl in höhern, als niedern Schulen, als Einladungsschrift zu den von Ostern 1808 an zu haltenden sowohl theoretischen, als auch praktischen, pädagogischen Vorlesungen. Leipzig: Gräff.

    Google Scholar 

  • Matthews, M. R. (2014). International handbook of research in history, philosophy and science teaching. Dordrecht: Springer.

    Book  Google Scholar 

  • Mayring, P. (2008). Qualitative Inhaltsanalyse: Grundlagen und Techniken. Weinheim/Bergstr. & Basel: Beltz.

    Google Scholar 

  • Nickel, G. (2013). Vom Nutzen und Nachteil der Mathematikgeschichte für das Lehramtsstudium. In H. Allmendinger, K. Lengnink, A. Vohns & G. Wickel (Eds.), Mathematik verständlich unterrichten: Perspektiven für Unterricht und Lehrerbildung (pp. 253–266). Wiesbaden: Springer.

    Google Scholar 

  • Nietzsche, F. (1874/2009). Vom Nutzen und Nachtheil der Historie für das Leben. (G. Figal, Ed.). Stuttgart: Reclam.

    Google Scholar 

  • Ott, B. (2016). Textaufgaben grafisch darstellen: Entwicklung eines Analyseinstruments und Evaluation einer Interventionsmaßnahme. Münster: Waxmann.

    Google Scholar 

  • Radbruch, K. (1997). Der philosophische Wille zur allgemeinen Mathematik. Unpublished lecture manuscript. University Kaiserslautern.

    Google Scholar 

  • Rezat, S. (2009). Das Mathematikbuch als Instrument des Schülers: Eine Studie zur Schulbuchnutzung in den Sekundarstufen. Wiesbaden: Vieweg & Teubner.

    Book  Google Scholar 

  • Rezat, S. (2013). The textbook-in-use: students’ utilization schemes of Mathematics textbooks related to self-regulated practicing. ZDM—The International Journal of Mathematics Education, 45(5), 659–670.

    Article  Google Scholar 

  • Rüsen, J. (2001). Zerbrechende Zeit: Über den Sinn der Geschichte. Cologne: Böhlau.

    Google Scholar 

  • Sauer, M. (2009). Geschichte unterrichten: Eine Einführung in die Didaktik und Methodik. Stuttgart: Kallmeyersche Verlag.

    Google Scholar 

  • Sächsisches Staatsministerium für Kultus. (2004). Lehrplan Mittelschule. Dresden: Saxoprint GmbH. https://www.schule.sachsen.de/lpdb/web/downloads/lp_ms_mathematik_2009.pdf?v2. Accessed April 17, 2017.

  • Schieder, T. (1974). Geschichtsinteresse und Geschichtsbewusstsein heute. In C. J. Burckhardt (Ed.), Geschichte zwischen Gestern und Morgen (pp. 63–90). Munich: Paul List Verlag.

    Google Scholar 

  • Schubring, G. (1978). Das genetische Prinzip in der Mathematik-Didaktik. Stuttgart: Klett-Cotta.

    Google Scholar 

  • Shen, C.-H., Liu, D., & Wang, X.-Q. (2013). “Simple solid figures” of high school mathematics textbooks in China, Singapore, America and France from the culture perspective. Journal of Mathematics Education, 4(30–33), 102.

    Google Scholar 

  • Smestad, B. (2000a). History of mathematics in Norwegian textbooks. Presentation by distribution at WGA 13 (History and culture in mathematics education), ICME 9, Makuhari, Japan. https://www.researchgate.net/publication/263733919_History_of_Mathematics_in_Norwegian_textbooks. Accessed January 8, 2017.

  • Smestad, B. (2000b). The introduction of history of mathematics in Norwegian schools. In W.-S. Horng & F.-L. Lin (Eds.), Proceedings of the HPM conference on history in mathematics education: Challenges for a new millennium—A satellite meeting of ICME-9. Taipei: National Taiwan Normal University. http://www.clab.edc.uoc.gr/HPM/HPM_2000_-_Vol_1_2000.pdf. Accessed January 8, 2017.

  • Smestad, B. (2002). Matematikkhistorie i grunnskolens lærebøker: En kritisk vurdering. https://www.researchgate.net/publication/268362807_Matematikkhistorie_i_grunnskolens_laereboker_en_kritisk_vurdering. Accessed January 8, 2017.

  • Sriraman, B. (2012). Crossroads in the history of mathematics and mathematics education, MME Monographs (Vol. 12). Charlotte, NC: Information Age.

    Google Scholar 

  • Stein, M. K., Grover, B. W., & Henningsen, M. A. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33, 455–488.

    Article  Google Scholar 

  • Thomaidis, Y., & Tzanakis, C. (2010). The implementation of the history of mathematics in the new curriculum and textbooks in Greek secondary education. In V. Durand-Guerrier, F. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of CERME 6 (pp. 2801–2810). Lyon: Institut National de Recherche Pédagogique.

    Google Scholar 

  • Toeplitz, O. (1927). Das Problem der Universitätsvorlesung über Infinitisimalrechnung und ihrer Abgrenzung gegenüber der Infinitisimalrechnung an den höheren Schulen. Jahresbericht der Deutschen Mathematikervereinigung, 36, 90–100.

    Google Scholar 

  • Tzanakis, C., Arcavi, A., Correia de Sa, C., Isoda, M., Lit, C.-K., Niss, M., et al. (2000). Integrating history of mathematics in the classroom: An analytic survey. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: The ICMI study. New ICMI Study Series (Vol. 6, pp. 201–240). Dordrecht: Kluwer.

    Chapter  Google Scholar 

  • Valverde, G., Bianchi, L. J., Wolfe, R., Schmidt, W. H., & Houang, R. T. (2002). According to the book: Using TIMSS to investigate the translation of policy into practice through the world of textbooks. Dordrecht: Springer.

    Book  Google Scholar 

  • Wille, R. (2001). Allgemeine Mathematik – Mathematik für die Allgemeinheit. In K. Lengnink, S. Prediger, & F. Siebel (Eds.), Mathematik und Mensch: Sichtweisen der Allgemeinen Mathematik (pp. 3–20). Mühltal: Verlag Allgemeine Wissenschaft.

    Google Scholar 

  • Winter, H., Zerger, H., Barthel, H., Heinz, G., Vogt, J., Windmann, B., et al. (1986). Geschichte—Geschichten. Mathematik lehren, 19, 1–58.

    Google Scholar 

  • Wittmann, E. C., & Müller, G. N. (2011). Das Zahlenbuch 3. Stuttgart: Ernst Klett.

    Google Scholar 

  • Xenofontos, C., & Papadopoulos, C. E. (2015). Opportunities of learning through the history of mathematics: The example of national textbooks in Cyprus and Greece. International Journal for Mathematics Teaching and Learning, 1–18. http://www.cimt.org.uk/journal/xenofontos.pdf. Accessed April 14, 2017.

Download references

Author information

Authors and Affiliations

  1. Justus-Liebig-Universität Giessen, Karl-Glöckner-Str. 21c, 35394, Giessen, Germany

    Sebastian Schorcht

Authors
  1. Sebastian Schorcht
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sebastian Schorcht .

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

Schorcht, S. (2018). History of Mathematics in German Mathematics Textbooks. 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_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-73924-3_8

  • 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