Allgemeinbildung and digital technologies in mathematics education: a review

Authors

Stine Gerster Johansen

Abstract

The conception of Allgemeinbildung in Danish schools might be influenced by the inclusion of digital technologies in mathematics education. This paper presents the results of a literature review aimed at answering the potential and challenges posed by the inclusion of digital technologies in mathematics education in relation to students’ Allgemeinbildung. The analysis is structured after Heinrich Winter’s basic experiences regarding mathematical Allgemeinbildung. The review reveals both challenges and potentials. In particular, the handling of data, the role of outsourcing, and the lack of empirical research are discussed regarding the aim of Allgemeinbildung in the Danish school.

References

Baumert, J. (2002). Deutschland im internationalen Bildungsvergleich [Germany's education in international comparison]. In N. Killius, J. Kluge & L. Reisch (Eds.), Die Zukunft der Bildung [The future of education] (pp. 100-150). Suhrkamp.

Biehler, R. (2019). Allgemeinbildung, mathematical literacy, and competence orientation. In H. N. Jahnke & L. Hefendehl-Hebeker (Eds.), Traditions in German-speaking mathematics education research (pp. 141-170). Springer. https://doi.org/10.1007/978-3-030-11069-7_6

Blomhøj, M. (2001). Hvorfor matematikundervisning? Matematik og almendannelse i et højteknologisk samfund [Why mathematics education? Mathematics and Allgemeinbildung in a high-tech society]. In M. Niss (Ed.), Matematikken og verden (pp. 219-246). Fremad.

Boell, S. & Cecez-Kecmanovic, D. (2014). A hermeneutic approach for conducting literature reviews and literature searches. Communications of the Association for Information Systems, 32, 257-286. https://doi.org/10.17705/1CAIS.03412

Broström, S. (2022). Didaktik og/eller læreplan [Didactics and/or curriculum]. Dansk Pædagogisk Tidsskrift, (2), 7-21.

Bundsgaard, J., Bindslev, S., Caeli, E. N., Petterson, M. & Rusmann, A. (2019). Danske elevers teknologiforståelse: resultater fra ICILS-undersøgelsen 2018 [Danish students technological understanding: results from the ICILS-study]. Aarhus Universitetsforlag.

Danish Ministry of Education (2019). Matematik faghæfte [Curriculum for mathematics]. https://emu.dk/sites/default/files/2020-09/GSK_Fagh%C3%A6fte_Matematik.pdf

Danish Minstry of Education (2021). Forsøg med teknologiforståelse i Folkeskolens obligatoriske undervisning: slutevaluering [Experiment with technology understanding in Folkeskolen's compulsory education: final evaluation]. https://www.emu.dk/sites/default/files/2021-09/gsk_teknologiforst%C3%A5else_evalueringsrapport.pdf

Geiger, V., Goos, M. & Dole, S. (2015). The role of digital technologies in numeracy teaching and learning. International Journal of Science and Mathematics Education, 13 (5), 1115-1137. https://doi.org/10.1007/s10763-014-9530-4

Geiger, V., Goos, M. & Forgasz, H. (2015). A rich interpretation of numeracy for the 21st century: a survey of the state of the field. ZDM, 47 (4), 531-548. https://doi.org/10.1007/s11858-015-0708-1

Geiger, V., Yasukawa, K., Bennison, A., Wells, J. F. & Sawatzki, C. (2020). Facets of numeracy: teaching, learning and practices. In J. Way, C. Attard, J. Anderson, J. Bobis, H. McMaster & K. Cartwright (Eds.), Research in mathematics education in Australasia 2016-2019 (pp. 59-89). Springer. https://doi.org/10.1007/978-981-15-4269-5_4

Gravemeijer, K., Stephan, M., Julie, C., Lin, F.-L. & Ohtani, M. (2017). What mathematics education may prepare students for the society of the future? International Journal of Science and Mathematics Education, 15 (1), 105-123. https://doi.org/10.1007/s10763-017-9814-6

Hischer, H. (2018). "Digitale Bildung" - ein Bildungskonzept? Mitteilungen der Gesellschaft für Didaktik der Mathematik, 44 (104), 8-17. Horlacher, R. (2016). The educated subject and the German concept of Bildung: a comparative cultural history. Routledge.

Hoyles, C., Noss, R., Kent, P. & Bakker, A. (2010). Improving mathematics at work: the need for techno-mathematical literacies. Routledge. https://doi.org/10.4324/9780203854655

Jablonka, E. (2003). Mathematical literacy. In A. Bishop, M. A. Clements, C. Keitel, J. W. Kilpatrick & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 77-104). Kluwer. https://doi.org/10.1007/978-94-010-0273-8_4

Jankvist, U., Misfeldt, M. & Aguilar, M. S. (2019). What happens when CAS procedures are objectified? The case of "solve" and "desolve". Educational Studies in Mathematics, 101 (1), 67-81. https://doi.org/10.1007/s10649-019-09888-5

Keitel, C., Kotzmann, E. & Skovsmose, O. (1993). Beyond the tunnel vision: analysing the relationship between mathematics, society and technology. In C. Keitel & K. Ruthven (Eds.), Learning from computers: mathematics education and technology (pp. 243-279). Springer. https://doi.org/10.1007/978-3-642-78542-9_11

Løvlie, L. (2003). Teknokulturell danning [Techno-cultural Bildung]. In L. Løvlie, R. Slagstad, O. Korsgaard & O. Korsgaard (Eds.), Dannelsens forvandlinger (pp. 347-371). Pax.

Løvlie, L. (2011). Dannelse og professionel tenkning: utfordringen for lærerutdanningen de neste tiårene [Bilding and professionel thinking: challenges for teacher training in the next decade]. In B. Hagtvet & G. Ognjenovic (Eds.), Dannelse: tenkning, modning, refleksjon. Nordiske perspektiver på allmenndannelsens nødvendighet i høyere utdanning og forskning (pp. 735-753). Dreyer.

Michelsen, C. (2016). Den matematiske og naturvidenskabelige dannelse. In A. von Oettingen (Ed.), Almen dannelse - dannelsesstandarder og fag (pp. 37-80). Hans Reitzel.

Neubrand, M. (2000). Reflecing as a didaktik construction: speaking about mathematics in the mathematics classroom. In I. Westbury, S. Hopmann & K. Riquarts (Eds.), Teaching as a reflective practice (pp. 251-266). Lawrence Erlbaum.

Neubrand, M. (2015). Bildungstheoretische Grundlagen des Mathematikunterrichts [Education-theoretical foundation of mathematics teaching]. In R. Bruder, L. Hefendehl-Hebeker, B. Schmidt-Thieme & H.-G. Weigand (Eds.), Handbuch der mathematikdidaktik (pp. 51-73). Springer. https://doi.org/10.1007/978-3-642-35119-8_3

Niss, M. (2021). Matematisk dannelse i det 21. århundrede [Mathematical Bildung in the 21st century]. In P. Weng, M. A. Wahl & L. Østerlind (Eds.), Håndbog om matematik i grundskolen : læring, undervisning og vejledning (pp. 71-85). Dansk Psykologisk Forlag.

Niss, M. & Jablonka, E. (2020). Mathematical literacy. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 548-553). Springer. https://doi.org/10.1007/978-3-030-15789-0_100

Nocar, D., Dofkova, R., Bartek, K. & Zdrahal, T. (2019). Development of pupils' digital literacy in teaching mathematics. In L. G. Chova, A. L. Martinez & I. C. Torres (Eds.), Edulearn19: 11th International Conference on Education and New Learning Technologies (pp. 7585-7588). IATED. https://doi.org/10.21125/edulearn.2019.1833

Noss, R. (1998). New numeracies for a technological culture. For the Learning of Mathematics, 18 (2), 2-12.

OECD (2019). PISA 2018 Assessment and analytical framework. OECD Publishing. https://doi.org/10.1787/b25efab8-en

Oettingen, A. von (2016). Almen dannelse og fag [Allgemeinbildung and school subjects]. In A. von Oettingen (Ed.), Almen dannelse: dannelsesstandarder og fag (pp. 7-10). Hans Reitzel.

Peschek, W. & Schneider, E. (2002). CAS in general mathematics education. ZDM, 34 (5), 189-195. https://doi.org/10.1007/BF02655821

Skovsmose, O. & Nielsen, L. (1996). Critical mathematics education. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick & C. Labord (Eds.), International handbook of mathematics education (pp. 1257-1288). Kluwer.

Stacey, K. & Turner, R. (2015). The evolution and key concepts of the PISA mathematics frameworks. In K. Stacey & R. Turner (Eds.), Assessing mathematical literacy: the PISA experience (pp. 5-33). Springer. https://doi.org/10.1007/978-3-319-10121-7_1

Steen, L. (1999). Numeracy: the new literacy for a data-drenched society. Educational Leadership, 57, 8-13.

Straehler-Pohl, H. (2017). De/mathematisation and ideology in times of capitalism: recovering critical distance. In H. Straehler-Pohl, N. Bohlmann & A. Pais (Eds.), The disorder of mathematics education: challenging the sociopolitical dimensions of research (pp. 35-52). Springer. https://doi.org/10.1007/978-3-319-34006-7_3

Vohns, A. (2017). Bildung, mathematical literacy and civic education: the (strange?) case of contemporary Austria and Germany. In A. Chronaki (Ed.), Mathematics education and life at times of crisis. Proceedings of the ninth international mathematics education and society conference (pp. 968-978). University of Thessaly Press.

Vohns, A. (2018). Mathematische Bildung am Ausgang ihrer Epoche? Eine nicht bloß rhetorisch gemeinte Frage [Mathematical Bildung at the end of its epoch? Not just a rhetorical question]. Mitteilungen der Gesellschaft für Didaktik der Mathematik, 105, 8-21.

Vohns, A. (2021). Das Digitale als Bildungsherausforderung für den Mathematikunterricht? (Un-)Zeitgemäße Betrachtungen [The digital as an educational challenge for mathematics teaching? (Un)contemporary considerations]. Mitteilungen der Gesellschaft für Didaktik der Mathematik, 110, 47-55.

Vollmer, H. J. (2021). Bildung as the central category of education? Didactics, subject didactics, and general subject didactics in Germany. In E. Krogh, A. Qvorttrup & S. T. Graf (Eds.), Didaktik and curriculum in ongoing dialogue (pp. 137-163). Routledge. https://doi.org/10.4324/9781003099390-10

Winter, H. (1995). Mathematikunterricht und Allgemeinbildung. Mitteilungen der Gesellschaft für Didaktik der Mathematik, 61, 37-46.

Zevenbergen, R. (2004). Technologizing numeracy: intergenerational differences in working mathematically in new times. Educational Studies in Mathematics, 56 (1), 97-117. https://doi.org/10.1023/B:EDUC.0000028399.76056.91

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Published

2023-12-01

How to Cite

Johansen, S. G. (2023). Allgemeinbildung and digital technologies in mathematics education: a review. NOMAD Nordic Studies in Mathematics Education, 28(3-4), 35–54. Retrieved from https://tidsskrift.dk/NOMAD/article/view/149031