id: 06618323
dt: j
an: 2016e.00600
au: Weber, Christof
ti: Making logarithms accessible ‒ operational and structural basic models
for logarithms.
so: J. Math.-Didakt. 37, Suppl. 1, S69-S98 (2016).
py: 2016
pu: Springer, Berlin/Heidelberg; Gesellschaft für Didaktik der Mathematik
(GDM), Berlin
la: EN
cc: F50 H30 C30
ut: logarithms; concept formation; subject-matter didactics; basic models;
mental representation; operational-structural conceptions; content
knowledge for teaching; upper secondary school
ci:
li: doi:10.1007/s13138-016-0104-6
ab: Summary: 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.
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