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Differences in counting skills between Chinese and German children are accompanied by differences […] Lonnemann, Jan; Li, Su; Zhao, Pei; Linkersdörfer, Janosch; Lindberg, Sven; Hasselhorn, Marcus; […] Zeitschriftenbeitrag | In: Frontiers in Psychology | 2019 38974 Endnote: Autor*innen: Lonnemann, Jan; Li, Su; Zhao, Pei; Linkersdörfer, Janosch; Lindberg, Sven; Hasselhorn, Marcus; Yan, Song
Titel: Differences in counting skills between Chinese and German children are accompanied by differences in processing of approximate numerical magnitude information
In: Frontiers in Psychology, 9 (2019) , S. 2656
DOI: 10.3389/fpsyg.2018.02656
URL: https://www.frontiersin.org/articles/10.3389/fpsyg.2018.02656/full
Dokumenttyp: 3a. Beiträge in begutachteten Zeitschriften; Aufsatz (keine besondere Kategorie)
Sprache: Englisch
Schlagwörter: Kind; Vorschulalter; Zahlensystem; Fertigkeit; Kognitive Prozesse; Denkfähigkeit; Leistung; Test; Computerunterstütztes Verfahren; Vergleichsuntersuchung; Internationaler Vergleich; Frankfurt a.M.; Deutschland; Beijing; China
Abstract (english): Human beings are supposed to possess an approximate number system (ANS) dedicated to extracting and representing approximate numerical magnitude information as well as an object tracking system (OTS) for the rapid and accurate enumeration of small sets. It is assumed that the OTS and the ANS independently contribute to the acquisition of more elaborate numerical concepts. Chinese children have been shown to exhibit more elaborate numerical concepts than their non-Chinese peers, but it is still an open question whether similar cross-national differences exist with regard to the underlying systems, namely the ANS and the OTS. In the present study, we investigated this question by comparing Chinese and German preschool children with regard to their performance in a non-symbolic numerical magnitude comparison task (assessing the ANS) and in an enumeration task (assessing the OTS). In addition, we compared children's counting skills. To ensure that possible between-group differences could not be explained by differences in more general performance factors, we also assessed children's reasoning ability and processing speed. Chinese children showed a better counting performance and a more accurate performance in the non-symbolic numerical magnitude comparison task. These differences in performance could not be ascribed to differences in reasoning abilities and processing speed. In contrast, Chinese and German children did not differ signi cantly in the enumeration of small sets. The superior counting performance of Chinese children was thus found to be re ected in the ANS but not in the OTS. (DIPF/Orig.)
DIPF-Abteilung: Bildung und Entwicklung

The influence of visual-spatial skills on the association between processing of nonsymbolic […] Lonnemann, Jan; Müller, Christian; Büttner, Gerhard; Hasselhorn, Marcus Zeitschriftenbeitrag | In: Journal of Experimental Child Psychology | 2019 38745 Endnote: Autor*innen: Lonnemann, Jan; Müller, Christian; Büttner, Gerhard; Hasselhorn, Marcus
Titel: The influence of visual-spatial skills on the association between processing of nonsymbolic numerical magnitude and number word sequence skills
In: Journal of Experimental Child Psychology, 178 (2019) , S. 184-197
DOI: 10.25656/01:17467
URN: urn:nbn:de:0111-pedocs-174677
URL: http://nbn-resolving.org/urn:nbn:de:0111-pedocs-174677
Dokumenttyp: 3a. Beiträge in begutachteten Zeitschriften; Aufsatz (keine besondere Kategorie)
Sprache: Englisch
Schlagwörter: Deutschland; Einflussfaktor; Raumvorstellung; Mathematische Kompetenz; Mathematisches Denken; Kind; Vorschulalter; Grundschulalter; Visuelle Wahrnehmung; Zahlensystem; Wort; Assoziation; Größe; Vergleich; Arithmetik; Test
Abstract (english): Nonsymbolic numerical magnitude processing skills are assumed to be fundamental to mathematical learning. Recent findings suggest that visual-spatial skills account for associations between children's performance in visually presented nonsymbolic numerical magnitude comparison tasks and their performance in visually presented arithmetic tasks. The aim of the current study was to examine whether associations between children's performance in visually presented tasks assessing nonsymbolic numerical magnitude processing skills and their performance in tasks assessing early mathematical skills, which do not involve visual stimulation, may also be mediated by visual-spatial skills. This line of reasoning is based on the assumption that children make use of mental visualization processes when working on tasks assessing early mathematical skills, such as knowledge of the sequence of number words, even when these tasks do not involve visual stimulation. We assessed 4- to 6-year-old children's performance in a nonsymbolic numerical magnitude comparison task, in tasks concerning knowledge of the sequence of number words, and in a developmental test to assess visual-spatial skills. Children's nonsymbolic numerical magnitude processing skills were found to be associated with their number word sequence skills. This association was fully mediated by interindividual differences in visual-spatial skills. The effect size of this mediation effect was small. We assume that the ability to construct mental visualizations constitutes the key factor under- lying this mediation effect. (DIPF/Orig.)
DIPF-Abteilung: Bildung und Entwicklung

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

Transcoding abilities in typical and atypical mathematics achievers. The role of working memory and […] Moura, Ricardo; Wood, Guilherme; Pinheiro-Chagas, Pedro; Lonnemann, Jan; Krinzinger, Helga; […] Zeitschriftenbeitrag | In: Journal of Experimental Child Psychology | 2013 33776 Endnote: Autor*innen: Moura, Ricardo; Wood, Guilherme; Pinheiro-Chagas, Pedro; Lonnemann, Jan; Krinzinger, Helga; Willmes, Klaus; Geraldi Haase, Vitor
Titel: Transcoding abilities in typical and atypical mathematics achievers. The role of working memory and procedural and lexical competencies
In: Journal of Experimental Child Psychology, 116 (2013) 3, S. 707-727
DOI: http://dx.doi.org/10.1016/j.jecp.2013.07.008
URL: http://www.sciencedirect.com/science/article/pii/S0022096513001434
Dokumenttyp: 3a. Beiträge in begutachteten Zeitschriften; Aufsatz (keine besondere Kategorie)
Sprache: Englisch
Schlagwörter: Arbeitsgedächtnis; Brasilien; Gesprochene Sprache; Grundschüler; Kognitive Entwicklung; Lernschwierigkeit; Mathematische Kompetenz; Schülerleistung; Zahlensystem
Abstract: Transcoding between numerical systems is one of the most basic abilities acquired by children during their early school years. One important topic that requires further exploration is how mathematics proficiency can affect number transcoding. The aim of the current study was to investigate transcoding abilities (i.e., reading Arabic numerals and writing dictation) in Brazilian children with and without mathematics difficulties, focusing on different school grades. We observed that children with learning difficulties in mathematics demonstrated lower achievement in number transcoding in both early and middle elementary school. In early elementary school, difficulties were observed in both the basic numerical lexicon and the management of numerical syntax. In middle elementary school, difficulties appeared mainly in the transcoding of more complex numbers. An error analysis revealed that the children with mathematics difficulties struggled mainly with the acquisition of transcoding rules. Although we confirmed the previous evidence on the impact of working memory capacity on number transcoding, we found that it did not fully account for the observed group differences. The results are discussed in the context of a maturational lag in number transcoding ability in chil- dren with mathematics difficulties.
DIPF-Abteilung: Bildung und Entwicklung

Home and preschool learning environments and their relations to the development of early numeracy […] Anders, Yvonne; Roßbach, Günter; Weinert, Sabine; Ebert, Susanne; Kuger, Susanne; Schmidt, Simone; […] Zeitschriftenbeitrag | In: Early Childhood Research Quarterly | 2012 32608 Endnote: Autor*innen: Anders, Yvonne; Roßbach, Günter; Weinert, Sabine; Ebert, Susanne; Kuger, Susanne; Schmidt, Simone; von Maurice, Jutta
Titel: Home and preschool learning environments and their relations to the development of early numeracy skills
In: Early Childhood Research Quarterly, 27 (2012) 2, S. 231-244
Dokumenttyp: 3a. Beiträge in begutachteten Zeitschriften; Aufsatz (keine besondere Kategorie)
Sprache: Englisch
Schlagwörter: Bayern; Einflussfaktor; Elementarbereich; Empirische Untersuchung; Familie; Frühkindheit; Frühkindliche Bildung; Hessen; Kind; Kognitive Entwicklung; Lernumgebung; MIgrationshintergrund; Qualität; Rechnen; Sozioökonomische Lage; Vorschulalter; Zahlensystem
Abstract (english): This study examined the influence of the quality of home and preschool learning environments on the development of early numeracy skills in Germany, drawing on a sample of 532 children in 97 preschools. Latent growth curve models were used to investigate early numeracy skills and their development from the first (average age: 3 years) to the third year (average age: 5 years) of preschool. Several child and family background factors (e.g., gender, maternal education, socioeconomic status), measures of the home learning environment (e.g., literacy- and numeracy-related activities), and measures of preschool structural and process quality (e.g., ECERS-E, ECERS-R) were tested as predictors of numeracy skills and their development. The analyses identified child and family background factors that predicted numeracy skills in the first year of preschool and their development over the three points of measurement - particularly gender, parental native language status (German/other), socioeconomic status, and mother's educational level. The quality of the home learning environment was strongly associated with numeracy skills in the first year of preschool, and this advantage was maintained at later ages. In contrast, the process quality of the preschool was not related to numeracy skills at the first measurement, but was significantly related to development over the period observed. The results underline the differential impact of the two learning environments on the development of numeracy skills. Interaction effects are explored and discussed.
DIPF-Abteilung: Bildungsqualität und Evaluation

Explaining school mathematics performance from symbolic and nonsymbolic magnitude processing: […] Oliveira Ferreira, Fernanda de; Wood, Guilherme; Pinheiro-Chagas, Pedro; Lonnemann, Jan; […] Zeitschriftenbeitrag | In: Psychology & Neuroscience | 2012 32798 Endnote: Autor*innen: Oliveira Ferreira, Fernanda de; Wood, Guilherme; Pinheiro-Chagas, Pedro; Lonnemann, Jan; Krinzinger, Helga; Willmes, Klaus; Haase, Vitor Geraldi
Titel: Explaining school mathematics performance from symbolic and nonsymbolic magnitude processing: similarities and differences between typical and low-achieving children
In: Psychology & Neuroscience, 5 (2012) 1, S. 37-46
DOI: 10.3922/j.psns.2012.1.06
URL: http://dx.doi.org/10.3922/j.psns.2012.1.06
Dokumenttyp: 3a. Beiträge in begutachteten Zeitschriften; Aufsatz (keine besondere Kategorie)
Sprache: Englisch
Schlagwörter: Brasilien; Experimentelle Untersuchung; Grundschulalter; Kind; Kognitive Prozesse; Lernschwierigkeit; Mathematikunterricht; Rechenschwäche; Rechentest; Schülerleistung; Symbol; Unterdurchschnittliche Leistung; Zahlensystem
Abstract (english): Magnitude processing is one of the most central cognitive mechanisms that underlie persistent mathematics difficulties. No consensus has yet been reached about whether these difficulties can be predominantly attributed to deficits in symbolic or nonsymbolic magnitude processing. To investigate this issue, we assessed symbolic and nonsymbolic magnitude representations in children with low or typical achievement in school mathematics. Response latencies and the distance effect were comparable between groups in both symbolic and nonsymbolic tasks. The results indicated that both typical and low achievers were able to access magnitude representation via symbolic and nonsymbolic processing. However, low achievers presented higher error rates than typical achievers, especially in the nonsymbolic task. Furthermore, measures of nonsymbolic magnitude explained individual differences in school mathematics better than measures of symbolic magnitude when considering all of the children together. When examining the groups separately, symbolic magnitude representation explained differences in school mathematics in low achievers but not in typical achievers. These results suggest that symbolic magnitude is more relevant to solving arithmetic problems when mathematics achievement is particularly low. In contrast, individual differences in nonsymbolic processing appear to be related to mathematics achievement in a more general manner.
DIPF-Abteilung: Bildung und Entwicklung

Micro and macro pattern analyses of FMRI data support both early and late interaction of numerical […] Koten, Jan Willem; Lonnemann, Jan; Willmes, Klaus; Knops, André Zeitschriftenbeitrag | In: Frontiers in Human Neuroscience | 2011 32096 Endnote: Autor*innen: Koten, Jan Willem; Lonnemann, Jan; Willmes, Klaus; Knops, André
Titel: Micro and macro pattern analyses of FMRI data support both early and late interaction of numerical and spatial information
In: Frontiers in Human Neuroscience, (2011) , S. 5:115
DOI: 10.3389/fnhum.2011.00115/full
URL: https://www.frontiersin.org/articles/10.3389/fnhum.2011.00115/full
Dokumenttyp: 3a. Beiträge in begutachteten Zeitschriften; Aufsatz (keine besondere Kategorie)
Sprache: Englisch
Schlagwörter: Clusteranalyse; Experimentelle Untersuchung; Hirnforschung; Kognitive Prozesse; Neuropsychologie; Raumvorstellung; Visuelle Wahrnehmung; Zahlensystem
Abstract (english): Numbers and space are two semantic primitives that interact with each other. Both recruit brain regions along the dorsal pathway, notably parietal cortex. This makes parietal cor- tex a candidate for the origin of numerical spatial interaction. The underlying cognitive architecture of the interaction is still under scrutiny. Two classes of explanations can be dis- tinguished. The early interaction approach assumes that numerical and spatial information are integrated into a single representation at a semantic level. A second approach pos- tulates independent semantic representations. Only at the stage of response selection and preparation these two streams interact. In this study we used a numerical landmark task to identify the locus of the interaction between numbers and space. While lying in an MR scanner participants decided on the smaller of two numerical intervals in a visually presented number triplet. The spatial position of the middle number was varied; hence spatial intervals were congruent or incongruent with the numerical intervals. Responses in incongruent trials were slower and less accurate than in congruent trials. By combining across-vertex correlations (micro pattern) with a cluster analysis (macro pattern) we identi- fied large-scale networks that were devoted to number processing, eye movements, and sensory motor functions. Using support vector classification in different regions of inter- est along the intraparietal sulcus, the frontal eye fields, and supplementary motor area we were able to distinguish between congruent and incongruent trials in each of the networks. We suggest that the identified networks participate in the integration of numerical and spa- tial information and that the exclusive assumption of either an early or a late interaction between numerical and spatial information does not do justice to the complex interaction between both dimensions.
DIPF-Abteilung: Bildung und Entwicklung

Neurokognitive Korrelate der Dyskalkulie Lonnemann, Jan; Linkersdörfer, Janosch; Hasselhorn, Marcus; Lindberg, Sven Zeitschriftenbeitrag | In: Kindheit und Entwicklung | 2011 31589 Endnote: Autor*innen: Lonnemann, Jan; Linkersdörfer, Janosch; Hasselhorn, Marcus; Lindberg, Sven
Titel: Neurokognitive Korrelate der Dyskalkulie
In: Kindheit und Entwicklung, 20 (2011) 1, S. 13-20
Dokumenttyp: 3a. Beiträge in begutachteten Zeitschriften; Beitrag in Sonderheft
Sprache: Deutsch
Schlagwörter: Arithmetik; Entwicklungsstörung; Kind; Kognition; Neurowissenschaften; Rechenschwäche; Rechnen; Zahlensystem
Abstract: Dargestellt werden potentielle kognitive und neuronale Verursachungsfaktoren der Dyskalkulie. Ergebnisse zu approximativen Mengenrepräsentationen, basalen visuellen Mechanismen der Mengenwahrnehmung (Subitizing), symbolischen Mengenrepräsentationen und arithmetischen Prozessen werden skizziert und diskutiert. Die berichteten Befunde legen nahe, dass verschiedene Ursachen für das Zustandekommen einer Dyskalkulie verantwortlich sein können, denen spezifische Störungen auf neuronaler Ebene zugrunde liegen könnten. Individuelle Störungsprofile sollten daher stärkere Beachtung finden, um in der Zukunft individuelle Förderansätze entwickeln zu können.
Abstract (english): Various potential determinants of dyscalculia on the cognitive as well as on the neural level are presented. Findings concerning approximate quantity representations, basic visual mechanisms for capturing quantities (subitizing), symbolic quantity representations, and arithmetic processes are outlined and discussed. The reported findings suggest that there might be a number of different causes for the occurrence of dyscalculia, which come along with specific impairments at the neural level. Individual profiles of dyscalculia should therefore receive more attention in order to be able to develop approaches to support individuals.
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

Vorschulische Förderung bei beeinträchtigter mathematischer Entwicklung Krajewski, Kristin Sammelbandbeitrag | Aus: Borchert, Johann; Hartke, Bodo; Jogschies, Peter (Hrsg.): Frühe Förderung entwicklungsauffälliger Kinder und Jugendlicher | Stuttgart: Kohlhammer | 2008 8217 Endnote: Autor*innen: Krajewski, Kristin
Titel: Vorschulische Förderung bei beeinträchtigter mathematischer Entwicklung
Aus: Borchert, Johann; Hartke, Bodo; Jogschies, Peter (Hrsg.): Frühe Förderung entwicklungsauffälliger Kinder und Jugendlicher, Stuttgart: Kohlhammer, 2008 (Heil- und Sonderpädagogik), S. 122-135
Dokumenttyp: 4. Beiträge in Sammelwerken; Sammelband (keine besondere Kategorie)
Sprache: Deutsch
Schlagwörter: Kind; Mathematische Kompetenz; Vorschulalter; Entwicklung; Frühförderung; Präventivmaßnahmen; Rechenschwierigkeit; Zahlensystem; Mengenlehre; Schülerleistung; Mathematikunterricht; Grundschule
Abstract: Die Entwicklung mathematischer Kompetenzen eines Kindes beginnt lange vor Schuleintritt und zeigt bereits frühzeitig einen sehr stabilen Verlauf. Rückstände von Kindern mit einer verzögerten mathematischen Entwicklung bleiben nicht selten bestehen, sodass Grundschüler mit Schwierigkeiten im Rechnen im Vergleich zu mathematisch unauffälligen Kindern oft schon im Vorschulalter schwächere Mengen-Zahlen-Kompetenzen aufwiesen. Ziel einer frühen mathematischen Förderung zur Prävention späterer Rechenschwierigkeiten sollte es daher sein, die frühen Mengen-Zahlen- Kompetenzen von Kindern systematisch aufzubauen, sich dabei an der natürlichen Entwicklung mathematischer Kompetenzen zu orientieren und den Kindern unter Rückgriff auf geeignete Darstellungsmittel ein Verständnis für die abstrakte Struktur der Zahlen zu vermitteln.(DIPF/Autor)
DIPF-Abteilung: Bildung und Entwicklung