TY  - JOUR
A1  - Fritz, Annemarie
A1  - Ehlert, Antje
A1  - Leutner, Detlev
T1  - Arithmetische Konzepte aus kognitiv-entwicklungspsychologischer Sicht
T1  - Artihmetic Concepts From a Cognitive Developmental-psychology Perspective
JF  - Journal für Mathematik-Didaktik
N2  - The acquisition of basic arithmetic concepts of children at pre-school and primary-school age (about 4 to 8 years of age) can be described by a cognitive developmental model with 6 levels: (1) count number, (2) mental number line, (3) cardinality and decomposability, (4) class inclusion and embeddedness, (5) relationality, and (6) units in numbers (bundling and unbundling). In this paper, 3 studies for longitudinally testing the model are presented. In Studies 1 (N = 26; heterogeneous age) and 2 (N = 62; homogeneous age) it shows that the individual development of arithmetic concepts across 18 months (Study 1:4 points of measurement) respectively 17 months (Study 2:3 points of measurement before, at, and after entering primary school) follows the levels of the model. In Study 3 (N = 243) it shows that the acquisition of curricular mathematical competencies at the end of Grade 2 is better predicted by conceptual arithmetic understanding at the end of Grade 1 than by intelligence. The results substantiate the validity of the model und confirm the relevance of basic arithmetic concepts for mathematical learning at school with respective consequences for the remedial training of children with math learning difficulties and dyscalculia.
KW  - Arithmetic
KW  - Development of concepts
KW  - Developmental model
KW  - Acquisition of arithmetical concepts
KW  - Mathematic in the primary school
Y1  - 2018
U6  - https://doi.org/10.1007/s13138-018-0131-6
SN  - 0173-5322
SN  - 1869-2699
VL  - 39
IS  - 1
SP  - 7
EP  - 41
PB  - Springer
CY  - Heidelberg
ER  -