Skip to main content
SpringerLink
Log in

The Street Lamp Problem: Technologies and Meaningful Situations in Class

  • Chapter
  • First Online:
Book cover Mathematics and Technology

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

The chapter describes a problem solving activity posed with the use of a Dynamic Geometry Software to middle school students. The problem leads students to face a meaningful situation to be explored, and forces them to make conjectures, to discuss and to formulate an argument. The activity starts with the manipulation of materials (paper and pencil, pictures and flashlights) and continues with the transposition of this exploration through technology. We discuss the use of problem solving activities to improve the argumentation skills and the added value of technology in exploration activities.

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 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
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.

    Confindustria is the main association representing manufacturing and service industries in Italy.

  2. 2.

    We are using the word “basic” without a negative meaning but, on the contrary, with the meaning of simple and easy to find in every house or classroom. Nevertheless, the Italian word used for defining these materials (UMI 2003) can be translated with the word “poor”.

  3. 3.

    For further information , see UMI (2003, p. 28).

References

  • Aldon, G., Arzarello, F., Cusi, A., Garuti, R., Martignone, F., Robutti, O., Sabena, C., & Soury-Lavergne, S. (2013). The meta-didactical transposition: A model for analysing teacher education programs. In A. M. Lindmeier & A. Heinze (Eds.), Proceedings of PME 37 (Vol. 1, pp. 97–124). Kiel: PME.

    Google Scholar 

  • Artigue, M., Drijvers, P., Lagrange, J.-B., Mariotti, M. A., & Ruthven, K. (2009). Technologies numériques dans l’enseignement des mathématiques, où en est-on dans les recherches et dans leur intégration? In C. Ouvrier-Buffet & M.-J. Perrin-Glorian (Eds.), Approches plurielles en didactique des mathématiques: Apprendre à faire des mathématiques du primaire au supérieur: Quoi de neuf? (pp. 185–207). Paris: Université Paris Diderot Paris 7.

    Google Scholar 

  • Arzarello, F., & Bartolini Bussi, M. G. (1998). Italian trends in research in mathematics education: A national case study in the international perspective. In J. Kilpatrick & A. Sierpinska (Eds.), Mathematics education as a research domain: A search of identity (pp. 243–262). Dordrecht: Kluwer.

    Google Scholar 

  • Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (1999). Dalle congetture alle dimostrazioni. Una possibile continuità cognitiva. L’Insegnamento della Matematica e delle Scienze integrate, 22(3), 209–233.

    Google Scholar 

  • Arzarello, F., Cusi, A., Garuti, R., Malara, N., Martignone, F., Robutti, O., & Sabena, C. (2012). Vent’anni dopo: Pisa 1991 – Rimini 2012. Dalla ricerca in didattica della matematica alla ricerca sulla formazione degli insegnanti. Paper presented at the 21st Seminario Nazionale di Ricerca in Didattica della Matematica, Rimini, 26–28 Jan 2012.

    Google Scholar 

  • Arzarello, F., Robutti, O., Sabena, C., Cusi, A., Garuti, R., Malara, N., & Martignone, F. (2014). Meta-didactical transposition: A theoretical model for teacher education programs. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital era (pp. 347–372). Berlin: Springer.

    Chapter  Google Scholar 

  • Bardelle, C., Beltramino, S., Berra, A., Dalè, M., Ferrando, E., Gentile, E., Idrofano, C., Mattei, M., Panero, M., Poli, L., Robutti, O., & Trinchero, G. (2014). How a street lamp, paper folding and GeoGebra can contribute to teachers’ professional development. Quaderni di Ricerca in Didattica, 24(Supplemento 1), 354–358.

    Google Scholar 

  • Bartolini Bussi, M. G. (1996). Mathematical discussion and perspective drawing in primary school. Educational Studies in Mathematics, 31(1), 11–41.

    Article  Google Scholar 

  • Bartolini Bussi, M. G., Chiappini, G., Paola, D., Reggiani, M., & Robutti, O. (2004). Teaching and learning mathematics with tools. In L. Cannizzaro, A. Pesci, & O. Robutti (Eds.), Research and teacher training in mathematics education in Italy: 2000–2003 (pp. 138–169). Bologna: UMI.

    Google Scholar 

  • CIEAEM. (2000). 50 years of CIEAEM: where we are and where we go: Manifesto 2000 for the Year of Mathematics. Berlin: Freie Universitðt Berlin. http://www.cieaem.org/?q=system/files/cieaem-manifest2000-e.pdf. Accessed on July 2015.

  • Chevallard, Y. (1999). L’analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en Didactique des Mathématiques, 19(2), 221–266.

    Google Scholar 

  • Churchhouse, R. F., Cornu, B., Howson, A. G., Kahane, J.-P., van Lint, J. H., Pluvinage, F., Ralston, A., & Yamaguti, M. (Eds.). (1986). The influence of computers and informatics on mathematics and its teaching. Cambridge: Cambridge University Press.

    Google Scholar 

  • Clark-Wilson, A., Aldon, G., Cusi, A., Goos, M., Haspekian, M., Robutti, O., & Thomas, M. (2014). The challenges of teaching mathematics with digital technologies. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of PME 38 and PME-NA 36 (Vol. 1, pp. 87–116). Vancouver: PME.

    Google Scholar 

  • Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: Instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213–234.

    Article  Google Scholar 

  • Marrades, R., & Gutierrez, A. (2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics, 44(1), 87–125.

    Article  Google Scholar 

  • NCTM. (2011). Technology in teaching and learning mathematics: A position of the NCTM. http://www.nctm.org/about/content.aspx?id=31734. Accessed 30 July 2015.

  • OECD. (2003). The PISA (2003) assessment framework: Mathematics, reading, science and problem solving knowledge and skills. Paris: OECD.

    Google Scholar 

  • Paola, D., & Robutti, O. (2001). La dimostrazione alla prova: Itinerari per un insegnamento integrato di algebra, logica, informatica, geometria. Quaderni del MPI, 45, 97–202.

    Google Scholar 

  • Rabardel, P. (1995). Les hommes et les technologies: Approche cognitive des instruments contemporains. Paris: Colin.

    Google Scholar 

  • Sinclair, N., & Robutti, O. (2013). Technology and the role of proof: The case of dynamic geometry. In M. A. K. Clements, A. J. Bishop, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Third international handbook of mathematics education (pp. 571–596). New York: Springer.

    Google Scholar 

  • UMI. (2001). La Matematica per il cittadino: Attività didattiche e prove di verifica per un nuovo curricolo di matematica. Scuola Primaria e Scuola Secondaria di primo grado. Lucca: Liceo Vallisneri.

    Google Scholar 

  • UMI. (2003). La Matematica per il cittadino: Attività didattiche e prove di verifica per un nuovo curricolo di matematica. Ciclo Secondario. Lucca: Liceo Vallisneri.

    Google Scholar 

  • Van den Heuvel-Panhuizen, M., & Drijvers, P. (2014). Realistic mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 521–525). Dordrecht: Springer.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S.S. I grado “Holden”, Chieri, Italy

    Elisa Gentile

  2. S.S. I grado “Don Bosco”, S. Benigno Canavese, Italy

    Monica Mattei

Authors
  1. Elisa Gentile
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Monica Mattei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Elisa Gentile .

Editor information

Editors and Affiliations

  1. Laboratoire de recherche : S2HEP, EducTice - InstitutFrançais de l’Éducation - École Normale Supérieure de Lyon, Lyon, France

    Gilles Aldon

  2. Département de mathématiques (GROUTEAM), Université du Québec à Montréal, Montréal, Québec, Canada

    Fernando Hitt

  3. Dipartimento di Matematica, Università degli Studi di Torino, Torino, Italy

    Luciana Bazzini

  4. Fachbereich Erziehungswissenschaft und Psychologie, Freie Universität Berlin, Berlin, Germany

    Uwe Gellert

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Gentile, E., Mattei, M. (2017). The Street Lamp Problem: Technologies and Meaningful Situations in Class. In: Aldon, G., Hitt, F., Bazzini, L., Gellert, U. (eds) Mathematics and Technology. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-51380-5_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-51380-5_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-51378-2

  • Online ISBN: 978-3-319-51380-5

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics

Search

Navigation