@inbook {MATHEDUC.06367060,
author = {Klep, Joost},
title = {Transformation as a fundamental concept in arithmetical competence modelling: an example of informatical educational science.},
year = {2014},
booktitle = {Transformation -- a fundamental idea of mathematics education},
isbn = {978-1-4614-3488-7},
pages = {349-386},
publisher = {New York, NY: Springer},
doi = {10.1007/978-1-4614-3489-4_17},
abstract = {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.},
msc2010 = {F30xx (U70xx M50xx P50xx)},
identifier = {2014f.00507},
}