id: 06367060
dt: a
an: 2014f.00507
au: Klep, Joost
ti: Transformation as a fundamental concept in arithmetical competence
modelling: an example of informatical educational science.
so: Rezat, Sebastian (ed.) et al., Transformation ‒ a fundamental idea of
mathematics education. New York, NY: Springer (ISBN
978-1-4614-3488-7/hbk; 978-1-4614-3489-4/ebook). 349-386 (2014).
py: 2014
pu: New York, NY: Springer
la: EN
cc: F30 U70 M50 P50
ut: algorithm; arithmetic; arithmetical skills; arithmetical strategy;
artificial intelligence; calculation; informatical cognitive model;
cognitive psychology; competence; competence modelling; educational
software; generative models; informatical educational science;
informatical model; informatics; intelligent tutors; mathematical
activity; modelling calculations; student modelling; transformation
ci:
li: doi:10.1007/978-1-4614-3489-4_17
ab: Summary: Interpreting calculations as sequences of transformations on
arithmetical expressions, like $3\times 12$, opens new opportunities
for understanding and modelling arithmetical competence. Arithmeticus
is a computer program that produces sequences of transformations, which
can be applied to arithmetical expressions. It can analyse the sequence
of transformations used in a student’s calculation, store them and
try to apply them on other expressions. In this paper it will be
explained how these features are a basis of a dynamic model of
arithmetical competence. Additionally, informatical educational science
will be proposed as a special approach of investigating learning and
teaching processes by informatical methods: in the case of
Arithmeticus, by the dynamical modelling of arithmetical competence and
learning and teaching processes.
rv: