Skip to main content
SpringerLink
Log in

Freudenthal’s Work Continues

  • Chapter
  • First Online:
Selected Regular Lectures from the 12th International Congress on Mathematical Education

  • 3385 Accesses

Abstract

In this paper I address a number of projects on elementary mathematics education carried out at the Freudenthal Institute. The focus is on (i) using picture books to support kindergartners’ development of mathematical understanding, (ii) revealing mathematical potential of special needs students, and (iii) conducting textbook analyses to disclose the learning opportunities that textbooks offer. I discuss how these projects are grounded in the foundational work of Freudenthal and his collaborators in the past and how our work will be continued.

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
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

Similar content being viewed by others

References

  • Anderson, A., Anderson, J., & Shapiro, J. (2005). Supporting multiple literacies: Parents’ and children’s mathematical talk within storybook reading. Mathematics Education Research Journal, 16(3), 5–26.

    Article  Google Scholar 

  • Bakker, M., Van den Heuvel-Panhuizen, M., Van Borkulo, S., & Robitzsch, A. (2011). Effects of mini-games for enhancing multiplicative abilities: A first exploration. Poster presented at Serious Games: The challenge, Ghent, Belgium, pp. Oct 19–21 2011.

    Google Scholar 

  • Bokhove, J., Borghouts, C., Kuipers, K., & Veltman, A. (2009). Rekenrijk. Groningen/Houten: Noordhoff Uitgevers.

    Google Scholar 

  • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates Inc.

    Google Scholar 

  • De Jong, R. (1986). Wiskobas in methoden (Wiskobas in textbooks). Utrecht The Netherlands: OW&OC, Utrecht University.

    Google Scholar 

  • De Lange, J. (1987). Mathematics, insight and meaning. Utrecht, The Netherlands: OW&OC, Utrecht University.

    Google Scholar 

  • De Lange, J. (2007). Large-scale assessment and mathematics education. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1111–1142). Greenwich, CT: Information Age Publishing.

    Google Scholar 

  • De Moor, E., & De Jong, R. (1980). Kunnen de boeken ‘tegen een stootje’? Over het beoordelen en kiezen van leermiddelen (Can textbooks stand rough handling? About judging and choosing educational tools). In S. Pieters (Ed.), De achterkant van de Möbiusband (pp. 96–101). Utrecht, The Netherlands: IOWO.

    Google Scholar 

  • Dekker, T., & Feijs, E. (2005). Scaling up strategies for change. Assessment in Education: Principles, Policy and Practice, 12(3), 237–254.

    Article  Google Scholar 

  • Elia, I., Van den Heuvel-Panhuizen, M., & Georgiou, A. (2010). The role of pictures in picture books on children’s cognitive engagement with mathematics. European Early Childhood Education Research Journal, 18(3), 125–147.

    Article  Google Scholar 

  • Freudenthal, H. (1968). Why to teach mathematics as to be useful? Educational Studies in Mathematics, 1(1), 3–8.

    Article  Google Scholar 

  • Freudenthal, H. (1973a). Mathematics as an educational task. Dordrecht, The Netherlands: D. Reidel Publishing Company.

    Google Scholar 

  • Freudenthal, H. (1973b). Rekenen, dat moeilijke vak (Arithmetic, that difficult subject). Wiskobasbulletin, 2(6), 971–972.

    Google Scholar 

  • Freudenthal, H. (1975). Wandelingen met Bastiaan (Having walks with Bastiaan). Pedomorfose, 25, 51–64.

    Google Scholar 

  • Freudenthal, H. (1976). Bastiaan’s lab (Bastiaan’s lab). Pedomorfose, 30, 35–54.

    Google Scholar 

  • Freudenthal, H. (1977). Bastiaan’s experiment on Archimedes’ principle. Educational Studies in Mathematics, 8, 3–16.

    Article  Google Scholar 

  • Freudenthal, H. (1978a). Weeding and sowing. Preface to a science of mathematical education. Dordrecht, The Netherlands: D. Reidel Publishing Company.

    Google Scholar 

  • Freudenthal, H. (1978b). Bastiaan meet zijn wereld (Bastiaan is measuring his world). Pedomorfose, 37, 62–68.

    Google Scholar 

  • Freudenthal, H. (1981). Major problems of mathematics education. Educational Studies in Mathematics, 12, 133–150.

    Article  Google Scholar 

  • Freudenthal, H. (1982). Wat is er met het aftrekken aan de hand? (What is going on with subtraction?). Willem Bartjens, 1(2), 1–4.

    Google Scholar 

  • Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht, The Netherlands: D. Reidel Publishing Company.

    Google Scholar 

  • Freudenthal, H. (1984a). Onderwijsontwikkeling voor de kleuterschool—Cognitief, wiskundig (Educational development for kindergarten—Cognitive, mathematical). In H. Freudenthal, Appels en peren/wiskunde en psychologie (Apples and pears/mathematics and psychology) (pp. 7–24). Apeldoorn, The Netherlands: Van Walraven.

    Google Scholar 

  • Freudenthal, H. (1984b). Verhoudingen als verschijnsel (Ratio as phenomenon). In H. Freudenthal, Appels en peren/wiskunde en psychologie (Apples and pears/mathematics and psychology) (pp. 68–89). Apeldoorn, The Netherlands: Van Walraven.

    Google Scholar 

  • Freudenthal, H. (1991). Revisiting mathematics education. China lectures. Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  • Jandl, E., & Junge, N. (2000). Vijfde zijn (Being fifth). Amsterdam, The Netherlands: Ploegsma.

    Google Scholar 

  • Jupri, A., Drijvers, P., & Van den Heuvel-Panhuizen, M. (2014). Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Journal, 26(4), 683–710.

    Article  Google Scholar 

  • Kolovou, A. (2011). Mathematical problem solving in primary school. Utrecht, The Netherlands: Utrecht University (doctoral thesis).

    Google Scholar 

  • Kolovou, A., Van den Heuvel-Panhuizen, M., & Bakker, A. (2009). Non-routine problem solving tasks in primary school mathematics textbooks—A needle in a haystack. Mediterranean Journal for Research in Mathematics Education, 8(2), 31–68.

    Google Scholar 

  • Kraemer, J., Van der Schoot, F., & Van Rijn, P. (2009). Balans van het reken- en wiskundeonderwijs in het speciaal basisonderwijs 3 (Assessment of mathematics education at special education schools 3). Arnhem, The Netherlands: CITO.

    Google Scholar 

  • La Bastide-Van Gemert, S. (2006). Elke positieve actie begint met critiek. Hans Freudenthal en de didactiek van de wiskunde (Each positive action starts with criticism. Hans Freudenthal and the didactics of mathematics). Hilversum, The Netherlands: Uitgeverij Verloren.

    Google Scholar 

  • Many of the publications in which I am involved can be downloaded at http://www.staff.science.uu.nl/~heuve108/download/ICME 12 Regular Lecture

  • Mathematisch Instituut., & IOWO. (1975). Feestboek. Prof. Dr. Hans Freudenthal—70 jaar (Celebration book. Prof. Dr. Hans Freudenthal—70 year). Utrecht, The Netherlands: Author.

    Google Scholar 

  • Peltenburg, M., Van den Heuvel-Panhuizen, M., & Robitzsch, A. (2012). Special education students’ use of indirect addition in solving subtraction problems up to 100—A proof of the didactical potential of an ignored procedure. Educational Studies in Mathematics, 79(3), 351–369.

    Article  Google Scholar 

  • Strain, L. B. (1969). Children’s literature: An aid in mathematics instruction. Arithmetic Teacher, 16, 451–455.

    Google Scholar 

  • Ter Heege, H. (1980). Vermenigvuldigen met een afhaker (Doing multiplication with a drop out). In S. Pieters (Ed.), De achterkant van de Möbiusband (pp. 77–83). Utrecht: IOWO.

    Google Scholar 

  • Ter Heege, H. (1981–1982). Het rekenen van Gijsbert (Gijsbert’s arithmetic). Willem Bartjens, 1(1), 25–26; (2), 67–68; (3), 109–111; (4), 172–177.

    Google Scholar 

  • Terpstra, P., & De Vries, A. (2010). Reken zeker. Groningen/Houten: Noordhoff Uitgevers.

    Google Scholar 

  • Treffers, A. (1978). Wiskobas doelgericht (Wiskobas goal-directed). Utrecht: IOWO.

    Google Scholar 

  • Treffers, A. (1987). Three dimensions. A model of goal and theory description in mathematics instruction—The Wiskobas project. Dordrecht, The Netherlands: Reidel Publishing Company.

    Google Scholar 

  • Valverde, G. A., Bianchi, L. J., Wolfe, R. G., 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/Boston/London: Kluwer Academic Publishers.

    Google Scholar 

  • Van Borkulo, S. P., Van den Heuvel-Panhuizen, M., & Bakker, M. (2011). One mini-game is not like the other: Different opportunities to learn multiplication tables. Poster presented at Serious Games: The challenge, Ghent, Belgium, Oct 19–21, 2011.

    Google Scholar 

  • Van den Heuvel-Panhuizen, M. (1996). Assessment and realistic mathematics education. Utrecht, The Netherlands: CD-β Press, Utrecht University.

    Google Scholar 

  • Van den Heuvel-Panhuizen, M. (2001). Realistic mathematics education in the Netherlands. In J. Anghileri (Ed.), Principles and practices in arithmetic teaching: Innovative approaches for the primary classroom (pp. 49–63). Buckingham/Philadelphia: Open University Press.

    Google Scholar 

  • Van den Heuvel-Panhuizen, M. (2008a). Learning from “Didactikids”: An impetus for revisiting the empty number line. Mathematics Education research Journal, 20(3), 6–31.

    Article  Google Scholar 

  • Van den Heuvel-Panhuizen M., (Ed.) (2008b). Children learn mathematics. A learning-teaching trajectory with intermediate attainment targets for calculation with whole numbers in primary school. Rotterdam/Taipei: Sense Publishers. (previously published in 2001 by the Freudenthal Institute).

    Google Scholar 

  • Van den Heuvel-Panhuizen, M. (2010). Reform under attack—Forty years of working on better mathematics education thrown on the Scrapheap? No way! In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education: Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia (pp. 1–25). Fremantle: MERGA.

    Google Scholar 

  • Van den Heuvel-Panhuizen, M. (2012). Mathematics education research should come more often with breaking news. Lecture on the occasion of receiving the Svend Pedersen Lecture Award 2011. http://www.mnd.su.se/polopoly_fs/1.76181.1329229188!/menu/standard/file/svendPedersenLecture_120205.pdf

  • Van den Heuvel-Panhuizen, M., & Becker, J. (2003). Towards a didactic model for assessment design in mathematics education. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 689–716). Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Chapter  Google Scholar 

  • Van den Heuvel-Panhuizen, M., & Elia, I. (2012). Developing a framework for the evaluation of picturebooks that support kindergartners’ learning of mathematics. Research in Mathematics Education, 14(1), 17–47.

    Article  Google Scholar 

  • Van den Heuvel-Panhuizen, M., & Elia, I. (2013). The role of picture books in young children’s mathematics learning. In L. English & J. Mulligan (Eds.), Reconceptualizing early mathematics learning (pp. 227–251). Heidelberg, Germany: Springer.

    Google Scholar 

  • Van den Heuvel-Panhuizen, M., Elia, I., & Robitzsch, A. (2014). Effects of reading picture books on kindergartners’ mathematics performance. Educational Psychology: An International Journal of Experimental Educational Psychology. http://dx.doi.org/10.1080/01443410.2014.963029

  • Van den Heuvel-Panhuizen, M., Kühne, C., & Lombard, A.-P. (2012). The learning pathway for number in the early primary grades. Johannesburg, South Africa: Macmillan.

    Google Scholar 

  • Van den Heuvel-Panhuizen, M., & Van den Boogaard, S. (2008). Picture books as an impetus for kindergartners’ mathematical thinking. Mathematical Thinking and Learning, 10(4), 341–373.

    Article  Google Scholar 

  • Van den Heuvel-Panhuizen, M., Van den Boogaard, S., & Doig, B. (2009). Picture books stimulate the learning of mathematics. Australian Journal of Early Childhood, 34(3), 30–39.

    Google Scholar 

  • Van Zanten, M., & Van den Heuvel-Panhuizen, M. (2014). Freedom of design: The multiple faces of subtraction in Dutch primary school textbooks. In Y. Li & G. Lappan (Eds.), Mathematics curriculum in school education (pp. 231–259). Heidelberg, Germany: Springer.

    Google Scholar 

  • Whitehurst, G. J., Falco, F. L., Lonigan, C., Fischel, J. E., DeBaryshe, B. D., Valdez-Menchaca, M. C., & Caulneld, M. (1988). Accelerating language development through picture book reading. Developmental Psychology, 24, 552–558.

    Article  Google Scholar 

  • Wijaya, A., Van den Heuvel-Panhuizen, M., Doorman, M., & Robitzsch, A. (2014). Difficulties in solving context-based PISA mathematics tasks: An analysis of students’ errors. The Mathematics Enthousiast, 11(3), 555–584.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Freudenthal Institute and Department of Education & Pedagogy, Utrecht University, Utrecht, The Netherlands

    Marja Van den Heuvel-Panhuizen

Authors
  1. Marja Van den Heuvel-Panhuizen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marja Van den Heuvel-Panhuizen .

Editor information

Editors and Affiliations

  1. Seoul National University, Seoul, Korea, Republic of (South Korea)

    Sung Je Cho

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Van den Heuvel-Panhuizen, M. (2015). Freudenthal’s Work Continues. In: Cho, S. (eds) Selected Regular Lectures from the 12th International Congress on Mathematical Education. Springer, Cham. https://doi.org/10.1007/978-3-319-17187-6_18

Download citation

Publish with us

Policies and ethics

Search

Navigation