Abstract
Mathematical literacy implies the capacity to apply mathematical knowledge to various and context-related problems in a functional, flexible and practical way. Improving mathematical literacy requires a learning environment that stimulates students cognitively as well as allowing them to collect practical experiences through connections with the real world. In order to achieve this, students should be confronted with many different facets of reality. They should be given the opportunity to participate in carrying out experiments, to be exposed to verbal argumentative discussions and to be involved in model-building activities. This leads to the idea of integrating science into maths education. Two sequences of lessons were developed and tried out at the University of Education Schwäbisch Gmünd integrating scientific topics and methods into maths lessons at German secondary schools. The results show that the scientific activities and their connection with reality led to well-based discussions. The connection between the phenomenon and the model remained remarkably close during the entire series of lessons. At present the sequences of lessons are integrated in the European ScienceMath project, a joint project between universities and schools in Denmark, Finland, Slovenia and Germany (see www.sciencemath.ph-gmuend.de).
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Notes
A detailed description of the teaching units, including some examples from the worksheets mentioned in this article, is given as a download under www.sciencemath.ph-gmuend.de (link: Teaching Material).
A more detailed description of worksheets and pupil’s ideas given as a download under www.sciencemath.ph-gmuend.de (link: Teaching Material).
Complete worksheets: see Beckmann (2006).
All utterances produced by the students represent example cases supporting the results of the qualtitative analysis of the lessons.
A graph matching the test results is intended here.
References
Baumert, et al. (2002) PISA 2000 im Überblick: Grundlagen, Methoden, Ergebnisse. Berlin: Max-Planck Institut.
Beckmann, A. (2006). Experimente zum Funktionsbegriffserwerb. Köln: Aulis.
Beckmann, A. (2007a). ScienceMath–ein fächerübergreifendes europäisches Projekt. In GDM, Beiträge zum Mathematikunterricht 2007. Berlin: Franzbecker.
Beckmann, A. (2007b). Non-linear functions in secondary school of lower qualification level (German Hauptschule). The Montana Mathematics Enthuisiast, 4(2), 251–257.
Cunningham, R. F. (2005). Algebra teachers’ utilization of problems requiring transfer between algebraic, numeric, and graphic representations. School Science and Mathematics, 105(2), 73–79.
DeMarois, P., & Tall, D. (1996). Facets and Layers of the Function Concept. In Proceedings of PME 20 (Valencia), 2 (pp. 297–304).
Doorman, L. M., & Gravemeijer, K. P. E. (2007). Learning mathematics through applications by emergent modeling: The case of slope and velocity. In C. Michelsen, A. Beckmann & B. Sriraman (Eds.), Proceedings of the second international symposium of mathematics and its connections to the arts and sciences. Odense: Syddansk universitet press.
Dubinsky, E., & Harel, G. (1992). The concept of function, aspects of epistemology and pedagogy. Mathematical Ass. of America/USA.
Golez, T. (2005). Calculus between mathematics and physics: Real-time measurements- A great opportunity for high-school teachers. In A. Beckmann, C. Michelsen & B. Sriraman (Eds.), Proceedings of the first international symposium of mathematics and its connections to the arts and sciences (pp. 190–200). Berlin: Franzbecker.
Gravemeijer, K. (1997). Mediating between concrete and abstract. In B. Nunes (Ed.), Learning and teaching mathematics: An international perspective (pp. 315–345). Hove: Psychology Press.
Gravemeijer, K. (2002). Emergent modelling as the basis for an instructional sequence on data analysis. http://icots6.haifa.ac.il/PAPERS/2D5_GRAV.PDF. Accessed on 30 March 2008.
Gray, E. M., & Tall, D. O. (2001). Relationships between embodied objects and symbolic precepts: An explanatory theory of success and failure in mathematics. In Heuvel-Panhuizen, M. (Ed.), Proceedings of the 25th conference of the international group for the psychology of mathematics education 3 (pp. 65–72).
Höfer, T. (2007). Fermat meets pythagoras. In B. Sriraman (Ed.), Proceedings of the second international symposium of mathematics and its connections to the arts and sciences. Odense: Syddansk universitet press.
Höfer, T. (2008). Das Haus des funktionalen Denkens–Entwicklung und Erprobung eines Modells für die Planung und Analyse methodischer und didaktischer Konzepte zur Förderung des funktionalen Denkens. Berlin: Franzbecker-Verlag.
Hoogland, K. (2003). Mathematical literacy and numeracy. http://www.gecijferdheid.nl/pdf/HooglandJablonka_UK.PDF. Accessed on 30 March 2008.
Jablonka, E. (2003). Mathematical literacy. In Bishop et al. (Eds.), Second international handbook of mathematics education (pp. 75–102). Dordrecht: Kluwer.
Kadunz, G., Kautschitsch, H., Ossimitz, G., & Schneder, E. (1996). Trends and perspectives. Wien: Hölder-Pichler-Tempsky.
Kaput, J. (1994). The representational roles of technology in connecting mathematics with authentic experience. In R. Biehler (Ed.), Didactics of mathematics as a scientific discipline (pp. 379–397). Dordrecht: Kluwer.
Michelsen, C. (2001). Begrebsdannelse ved Domaeneudvidelse. Odense: Syddansk Universitet.
Michelsen, C. (2006). Functions: a modelling tool in mathematics and science. ZDM, 38(3), 269–280. doi:10.1007/BF02652810.
Michelsen, C., & Beckmann, A. (2007). Förderung des Begriffsverständnisses durch Bereichserweiterung–Funktionsbegriffserwerb und Modellbildungsprozesse durch Integration von Mathematik, Physik und Biologie. Der Mathematikunterricht, 53(1/2), 45–57.
Neubrand, J., Neubrand, M., & Sibberns, H. (1998). Die TIMSS-Aufgaben aus mathematikdidaktischer Sicht: Stärken und Defizite deutscher Schülerinnen und Schüler. In E. Blum & M. Neubrand (Eds.), TIMSS und der Mathematikunterricht (pp. 17–27). Hannover: Schroedel.
Niss, M., Blum, W., & Huntley, I. (Eds.) (1991). Teaching of mathematical modelling and applications. New York: Horwood.
OECD Deutsches PISA- Konsortium, Deutschland (2000a). Internationales und nationales Rahmenkonzept für die Erfassung von mathematischer Grundbildung in PISA. Paris: OECD.
OECD Deutsches PISA- Konsortium, Deutschland (2000b). PISA 2000. Opladen: Leske & Budrich.
OECD Deutsches PISA- Konsortium, Deutschland (2003). PISA 2003. Ergebnisse des zweiten internationalen Vergleichs. Berlin: Waxmann.
OECD (2006). Assessing scientific, reading and mathematical literacy: a framework for PISA 2006. http://www.oecd.org/dataoecd/38/51/33707192.pdf. Accessed on 30 March 2008.
Pädagogisches Zentrum Rheinland Pfalz (1990). Funktionen und Graphen. PZInformation Mathematik. Bad Kreuznach: PZ-press.
Sfard, A. (1991). On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same concept. Educational Studies in Mathematics, 22, 1–36. doi:10.1007/BF00302715.
Swan, M. (1982). The teaching of functions and graphs. In Conference on functions, 1–5 (pp. 151–165), Enschede.
Vollrath, H. -J. (1978). Schüler/Schülerinnenversuche zum Funktionsbegriff. Der Mathematikunterricht, 24(4), 90–101.
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Höfer, T., Beckmann, A. Supporting mathematical literacy: examples from a cross-curricular project. ZDM Mathematics Education 41, 223–230 (2009). https://doi.org/10.1007/s11858-008-0117-9
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DOI: https://doi.org/10.1007/s11858-008-0117-9