Abstract
From a socio-cultural perspective it is argued that the modality of artefacts has, structuring effects on the activities in which the artefact is involved. The mathematics textbook is an artefact that has a major influence on the activity of learning mathematics. Against this setting, the structures of the units in German mathematics textbooks for different grades and ability levels have been analysed. Firstly, the different structural elements have been examined with regard to: characteristics in terms of content; linguistic characteristics; visual characteristics; their pedagogical functions within the learning process; and situative conditions. Secondly, the orders of the structural elements within the units of the different textbooks have been compared. The findings reveal that the structure of the units is very similar in different mathematics textbooks. The units are not only composed of analogous structural elements, but these elements are also arranged in almost the same sequence. In order to develop a deeper understanding of these findings the structure of the units has been compared to the influential learning theories of J. F. Herbart and H. Roth. On this basis it is argued that the structure of the units seems to reflect the phases of idealised learning processes in general. The issue is raised if this is an appropriate structure in order to provide opportunities to learn mathematics.
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References
Becherer, J. (2001):Einblicke Mathematik S. Hauptschule, Rheinland-Pfalz—Stuttgart. Ernst Klett
Bromme, R., Hömberg, E. (1981):Die andere Hälfte des Arbeitstages—Interviews unit Mathematiklehrern über alltägliche Unterrichtsvorbereitung.—Bielefeld Institut für Didaktik der Mathematik der Universität Bielefeld (Materialien und Studien; 25).
Buck, H., Dürr, R., Freudigmann, H., Reinelt, G., Zinser, M. (2000)Lambacher Schweizer Analysis. Grundkurs, Gynmasium, Hessen, Niedersachsen, Bremen. Hamburg. Schleswig-Holstein, Rheinland-Pfalz und Saarland.— Stuttgart Ernst Klett
Buck, H., Dürr, R., Freudigmann, H., Reinelt, G., Zinser, M. (2002):Lambacher Schweizer Analysis. Leistungskurs, Gymnasium, Nordrhein-Westfalen. Stuttgart: Ernst Klett
Dormolen, J. v. (1986): Textual Analysis.— In: Christiansen, B., Howson, A. G. and Otte, M. (Eds.),Perspectives on Mathematics Education, Dordrecht: Reidel (Mathematics Education Library), p. 141–171
Dowling, P. (1998)The Sociology of Mathematics Education. Mathematical Myths/Pedagogic Texts.— London: The Falmer Press, (Studies in Mathematics Education Series, 7)
Griesel, H., Postel, H., Hofe, R. v. (Eds.) (2002),Mathematik heute S. Realschule, Hessen— Hannover: Schroedel
Griesel, H., Postel, H., Suhr, F. (Eds.) (2004):Elemente der Mathematik S.— Hannover: Schroedel
Hacker, H. (1980)Didaktische Funktionen des Mediums Schulbuch— In: Hacker, H. (Ed.), Das Schulbuch Funktion und Verwendung im Unterricht. Bad Heilbrunn Klinkhardt (Studientexte zur Grundschuldidaktik), p. 7–30.
Hopf, D. (1980):Mathematikunterricht. Eine empirische Untersuchung zur Didaktik und Unterrichtsmethode in der 7 Klasse des Gymnasiums.— Stuttgat Klett-Cotta (Veröffentlichungen aus dem Projekt Schulleistung, 4).
Howson, G. (1995):Mathematics Textbooks: A Comparative Study of Grade 8 Texts— Vancouver, Pacific Educational Press (TIMSS Monograph, 3).
Jahnke, T., Wuttke, H. (Eds.) (2001):Mathematik Analysis.— Berlin: Cornelsen
Klingberg, L. (1972):Einführung in die Allgemeine Didaktik.— Berlin: Volk und Wissen
Koullen, R. (Ed.) (2004)Mathematik Real 8, Realschule, Nordrhein-Westfalen.— Berlin: Cornelsen
Leppig, M. (Ed.) (2001):Lernstufen Mathematik, 8 Hauptschule, Nordrhein-Westfalen.— Berlin, Cornelsen.
Lergenmüller, A., Schmidt, G. (Eds.) (2002):Mathematik-Neue Wege 8. Gymnasium.— Hannover: Schroedel
Lerman, S. (2006):Socio-Cultural Research in PME.—In:Gutiérrez, A. andBoero, P. (Eds.),Handbook of Research on the Psychology of Mathematics Education.—Rotterdam: Sense Publishers, p. 347–366.
Love, E., Pimm, D. (1996): This is so: a text on texts.—In: Bishop, A. J., Clements, K., Keitel, C., Kilpatrick, J. and Laborde, C. (Eds.)International Handbook of Mathematics Education Vol. 1 Dordrecht: Kluwer, p. 371–409.
Maroska, R., Olpp, A., Stöckle, C., Wellstein, H. (2004):Schmittpunkt 8—Stuttgart: Ernst Klett
Mayring, P. (2000): Qualitative Content Analysis.—In:Forum Qualitative Sozialforschung/Forum: Qualitative Social Research [On-line Journal] 1(2), http://www.qualitative-research.net/fqs-texte/2-00/2-00mayring-e.htm (Date of access: 19.09.2006).
Mayring, P. (2003):Qualitative Inhaltsanalyse.—Weinheim, Basel Beltz
Meyer, H. (1987)Unterrichtsmethoden Bd. 1.—Frankfurt a. M.: Cornelsen Scriptor
Pohlmann, D., Stoye, W. (Eds.) (2001):Mathematik plus & Gynmasium. Nordrhein-Westfalen.—Berlin: Volk und Wissen
Rabardel, P. (2002):People and Technology: a cognitive approach to contemporary instruments. http://ergoserv.psy.univ-paris8.fr/Site/ShowArticle.asp?NumArt=99&Act_Group=1 http://ergoserv.psy.univ-paris8.fr/Site/ShowArticle.asp?NumArt=100&Act_Group=1 (Date of access: 28.07.2005)
Rein, W., Pickel, A., Scheller, E. (1903):Theorie und Praxis des Volksschulunterrichts nach Herbartischen Grundsätzen. Das erste Schuljahr—Leipzig: Verlag von Heinrich Bredt
Roth, H. (1983):Pädagogische Psychologie des Lehrens und Lernens.—Hannover: Schroedel
Schmid, A., Weidig, I. (Eds.) (2002):Lambacher Schweizer 8. Gymnasium, Nordrhein-Westfalen.—Stuttgart Ernst Klett
Schröder, M., Wurl, B., Wynands, A. (Eds.) (2003).Maßstab 8.—Hannover: Schroedel
Stodolsky, S. S. (1989) Is Teaching Really by the Book?—In: Jackson, P. W. and Haroutunian-Gordon (Eds.),From Socrates to Software: The Teacher as Text and the Text as Teacher: Chicago: University of Chicago Press (Yearbook of the National Society for the Study of Education; 1). p. 159–184.
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: Kluwer
Woodward, A., Elliott, D. L. (1990): Textbook Use and Teacher Professionalism.—In: Elliott, D. L. and Woodward, A. (Eds.)Textbooks an Schooling in the United States. Chicago: The University of Chicago Press (Yearbook of the National Society for the Study of Education; 1), p. 178–193.
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Rezat, S. The structures of German mathematics textbooks. Zentralblatt für Didaktik der Mathematik 38, 482–487 (2006). https://doi.org/10.1007/BF02652785
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DOI: https://doi.org/10.1007/BF02652785