Making logarithms accessible - operational and structural basic models for logarithms.

Autor/in	Weber, Christof
Titel	Making logarithms accessible - operational and structural basic models for logarithms.
Quelle	In: Journal für Mathematik-Didaktik, 37 (2016) Suppl. 1, S.69-98 PDF als Volltext Link als defekt meldenVerfügbarkeit
Sprache	englisch; deutsche Zusammenfassung
Dokumenttyp	online; gedruckt; Zeitschriftenaufsatz
ISSN	0173-5322; 1869-2699
DOI	10.1007/s13138-016-0104-6
Schlagwörter	Wissen; Sekundarstufe II; Lehren; Fachdidaktik; Logarithmus; Konzeption; Modell
Abstract	Logarithms have a reputation for being difficult and inaccessible. As an analysis of their historical, mathematical and educational background suggests, this problem might be due to the way in which logarithms are interpreted and explained in textbooks: as the inverse of exponents. If this conclusion is right, additional interpretations of logarithms are required. By combining the theoretical construct of `Grundvorstellungen' (translated as `basic models') and the distinction between operational and structural conceptions, I identify and elaborate four interpretations of logarithms: (i) the basic model of `multiplicative measuring', (ii) the basic model of `counting the number of digits', (iii) the basic model of `decreasing the hierarchy level', and (iv) the basic model of `inverse exponent'. Three models (i-iii) reflect operational conceptions and interpret logarithms in contexts familiar to students. In combination with (iv), a structural basic model, this paper argues on a theoretical level that they could help to make logarithms accessible and understandable to students. Following the tradition of `Stoffdidaktik' (`subject-matter didactics'), the study thus aims to unpack some of the content knowledge required for the teaching of logarithms.
Erfasst von	FIZ Karlsruhe - Leibniz-Institut für Informationsinfrastruktur
Update	2017/1