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In how many ways is the approximate number system associated with exact calculation? Pinheiro-Chagas, Pedro; Wood, Guilherme; Knops, André; Krinzinger, Helga; Lonnemann, Jan; […] Zeitschriftenbeitrag | In: PLoSOne | 2014 34983 Endnote: Autor*innen: Pinheiro-Chagas, Pedro; Wood, Guilherme; Knops, André; Krinzinger, Helga; Lonnemann, Jan; Starling-Alves, Isabella; Willmes, Klaus; Haase, Vitor Geraldi
Titel: In how many ways is the approximate number system associated with exact calculation?
In: PLoSOne, 9 (2014) 11, S. e111155
DOI: 10.1371/journal.pone.0111155
Dokumenttyp: 3a. Beiträge in begutachteten Zeitschriften; Aufsatz (keine besondere Kategorie)
Sprache: Englisch
Schlagwörter: Arithmetik; Brasilien; Empirische Untersuchung; Forschungsstand; Grundrechenart; Grundschule; Leistungsmessung; Mathematische Kompetenz; Mathematisches Denken; Rechnen; Schüler; Schülerleistung; Schülerleistungstest; Symbol; Vergleich; Zahlbegriff; Zahlensystem
Abstract: The approximate number system (ANS) has been consistently found to be associated with math achievement. However, little is known about the interactions between the different instantiations of the ANS and in how many ways they are related to exact calculation. In a cross-sectional design, we investigated the relationship between three measures of ANS acuity (non-symbolic comparison, non-symbolic estimation and non-symbolic addition), their cross-sectional trajectories and specific contributions to exact calculation. Children with mathematical difficulties (MD) and typically achieving (TA) controls attending the first six years of formal schooling participated in the study. The MD group exhibited impairments in multiple instantiations of the ANS compared to their TA peers. The ANS acuity measured by all three tasks positively correlated with age in TA children, while no correlation was found between non-symbolic comparison and age in the MD group. The measures of ANS acuity significantly correlated with each other, reflecting at least in part a common numerosity code. Crucially, we found that non-symbolic estimation partially and non-symbolic addition fully mediated the effects of non-symbolic comparison in exact calculation.(DIPF/Org.)
DIPF-Abteilung: Bildung und Entwicklung

Developmental changes in the association between approximate number representations and addition […] Lonnemann, Jan; Linkersdörfer, Janosch; Hasselhorn, Marcus; Lindberg, Sven Zeitschriftenbeitrag | In: Frontiers in Psychology | 2013 33942 Endnote: Autor*innen: Lonnemann, Jan; Linkersdörfer, Janosch; Hasselhorn, Marcus; Lindberg, Sven
Titel: Developmental changes in the association between approximate number representations and addition skills in elementary school children
In: Frontiers in Psychology, 4 (2013) , S. 783
DOI: 10.3389/fpsyg.2013.00783
URL: http://www.frontiersin.org/Developmental_Psychology/10.3389/fpsyg.2013.00783/abstract
Dokumenttyp: 3a. Beiträge in begutachteten Zeitschriften; Beitrag in Sonderheft
Sprache: Englisch
Schlagwörter: Arithmetik; Größe; Grundrechenart; Grundschüler; Kognitive Entwicklung; Mathematische Kompetenz; Mathematisches Denken; Rechnen; Schulanfänger; Schuljahr 01; Schuljahr 02; Symbol; Test; Urteilsfähigkeit; Zahlensystem
Abstract: The approximate number system (ANS) is assumingly related to mathematical learning but evidence supporting this assumption is mixed. The inconsistent findings might be attributed to the fact that different measures have been used to assess the ANS and mathematical skills. Moreover, associations between the performance on a measure of the ANS and mathematical skills may be discontinuous, i.e., stronger for children with lower math scores than for children with higher math scores, and may change with age. The aim of the present study was to examine the development of the ANS and arithmetic skills in elementary school children and to investigate how the relationship between the ANS and arithmetic skills develops. Individual markers of children's ANS (internal Weber fractions and mean reaction times in a non-symbolic numerical comparison task) and addition skills were assessed in their first year of school and 1 year later. Children showed improvements in addition performance and in the internal Weber fractions, whereas mean reaction times in the non-symbolic numerical comparison task did not change significantly. While children's addition performance was associated with the internal Weber fractions in the first year, it was associated with mean reaction times in the non-symbolic numerical comparison task in the second year. These associations were not found to be discontinuous and could not be explained by individual differences in reasoning, processing speed, or inhibitory control. The present study extends previous findings by demonstrating that addition performance is associated with different markers of the ANS in the course of development.
DIPF-Abteilung: Bildung und Entwicklung

Mathematik plus - Zahlentreppen. Lehrmittel für das 1. Schuljahr Krajewski, Kristin Monographie | Berlin: Cornelsen | 2008 7828 Endnote: Autor*innen: Krajewski, Kristin
Titel: Mathematik plus - Zahlentreppen. Lehrmittel für das 1. Schuljahr
Erscheinungsvermerk: Berlin: Cornelsen, 2008
Dokumenttyp: 1. Monographien (Autorenschaft; Monographie (keine besondere Kategorie)
Sprache: Deutsch
Schlagwörter: Zahlensystem; Arithmetik; Rechnen; Schuljahr 01; Schulanfänger; Mathematikunterricht; Rechenunterricht; Grundrechenarten; Grundschüler; Grundschule; Unterrichtsmittel; Arbeitsmaterial; Deutschland
Abstract: Die Zahlentreppe demonstriert verschiedene Mengendarstellungen von Zahlen. Die sechs Seiten der Holzquader sind mit sechs verschiedenen Darstellungsformen bedruckt: Zahl, Zahlenstrahl, Fingerbild, Würfelbild, Punktbild und Uhr. (DIPF/Orig.)
DIPF-Abteilung: Bildung und Entwicklung