TY - JOUR

T1 - Arithmetische Konzepte aus kognitiv-entwicklungspsychologischer Sicht

AU - Fritz, Annemarie

AU - Ehlert, Antje

AU - Leutner, Detlev

PY - 2018/4/1

Y1 - 2018/4/1

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.

AB - 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 - Acquisition of arithmetical concepts

KW - Arithmetic

KW - Development of concepts

KW - Developmental model

KW - Mathematic in the primary school

KW - Psychologie

UR - http://www.scopus.com/inward/record.url?scp=85044506411&partnerID=8YFLogxK

U2 - 10.1007/s13138-018-0131-6

DO - 10.1007/s13138-018-0131-6

M3 - Zeitschriftenaufsätze

AN - SCOPUS:85044506411

VL - 39

SP - 7

EP - 41

JO - Zeitschrift für Mathematikdidaktik (JMD)

JF - Zeitschrift für Mathematikdidaktik (JMD)

SN - 0173-5322

IS - 1

ER -