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      Rechenschwäche im Grundschulalter: Reduzierte Verfügbarkeit basalen arithmetischen Faktenwissens und Belastung des Arbeitsgedächtnisses bei Drittklässlern

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          Abstract

          Nachteile im Aufbau und Abruf basalen arithmetischen Faktenwissens (zum Beispiel der Summe zweier Ziffern) bilden ein zentrales Merkmal bei Kindern mit Rechenschwäche. Die vorliegende Studie verfolgt das Ziel, die reduzierte Verfügbarkeit basalen arithmetischen Wissens und dadurch bedingte besondere Belastungen des Arbeitsgedächtnisses bei Kindern mit Rechenschwäche genauer zu untersuchen. Drittklässler mit und ohne Rechenschwäche bearbeiteten Verifikationsaufgaben zur Addition im Zahlenraum bis 20 mit und ohne Zehnerübergang, einerseits unter Standardbedingungen, andererseits unter kontinuierlicher Ausführung einfacher Zweitaufgaben (verbal und motorisch). In getrennten Varianzanalysen (VA) zur Lösungsgüte und zur Lösungszeit erwiesen sich alle drei Haupteffekte zu den Faktoren Rechenleistung, Zehnerübergang und Durchführungsbedingung (in beiden VA) und alle Zweifachinteraktionen (in der VA zur Lösungsgüte) als signifikant. Kinder mit Rechenschwäche haben demnach grundlegende Nachteile beim Abruf basaler arithmetischer Fakten und besonders ausgeprägte Nachteile bei Aufgaben mit Zehnerübergang und unter Belastung des Arbeitsgedächtnisses durch Zweitaufgaben. Die Befunde untermauern die Annahme, dass die Rechenschwäche eng mit Defiziten im basalen arithmetischen Faktenwissen assoziiert ist. Darüber hinaus legen sie nahe, dass sich diese Defizite umso gravierender auswirken, je größer die aktuelle Belastung des Arbeitsgedächtnisses ausfällt. Die Relevanz des frühen Aufbaus von arithmetischem Faktenwissen und die Notwendigkeit des Einsatzes geeigneter diagnostischer Maßnahmen zur frühzeitigen Erkennung von entsprechenden Defiziten werden hervorgehoben.

          Arithmetical Disabilities in Elementary School Years: Difficulties in Retrieving Basic Arithmetic Facts and Working Memory Load in Third Graders

          Background: The acquisition of arithmetic skills is one of the major goals pursued during elementary school years. Struggling at school in this area may cause academic failure and difficulties in social adjustment in the long run. While a lot of students do not have any problems in learning arithmetic, others show serious difficulties.

          The importance of basic arithmetic facts and their causal role in the acquisition of arithmetic skills is widely discussed in the research field ( Ashcraft, 1982; Siegler & Shrager, 1984). Children create or refer to basic arithmetic facts within their knowledge base while solving simple arithmetic problems, such as single digit addition tasks (5 + 4). During elementary school years, the use of counting strategies is continuously replaced by retrieval of arithmetic facts. However, children who have an issue with storing arithmetic facts are further bound to intricate backup strategies (e. g. counting). Such intricate strategies require a large capacity of (phonological) working memory as information has to be temporarily stored and processed. This may lead to memory overload and can cause inaccurate calculation. Therefore, former studies discussed fragile arithmetic facts as a determinant of arithmetical disabilities (cf. Butterworth, 2005a, 2005b; Dowker, 2005). Further, stable arithmetic facts are important when children have to work on more complex tasks: The retrieval of basic arithmetic facts requires less capacity of working memory than counting strategies do. Working memory capacity released by fact retrieval may be used to solve these complex tasks (e. g. addition up to 1000).

          Aims: In this study, specific characteristics of arithmetic facts and their role for arithmetic disabilities are further explored. To this end, children with and without arithmetical disabilities dealt with simple addition verification problems (addition up to ten and up to 20). It is expected that children with arithmetical disabilities perform worse in these tasks. In order to examine working memory load, children had to perform secondary tasks (articulation or tapping) while working on verification tasks (cf. Hitch et al., 1987). These dual-task conditions are expected to have a more adverse effect on performance in children with fragile arithmetic facts, because they need more working memory capacity (as a result of activated intricate back up strategies) than children of the control group (cf. Kaye, 1986). Furthermore, it shall be explored whether performance is more affected by the articulation secondary task than by the tapping task. This pattern of results would point to the use of verbal counting strategies. Finally, it will be analyzed whether the dual-task effect is more considerable in the higher number range (up to 20) than in number range up to ten.

          Methods: Sixty-eight third-graders (aged from 8 years 8 months to 10 years 5 months) were assigned to two groups: (1) children with arithmetical disabilities ( n = 34), specified by low performance in a standardized test for mathematics (DEMAT 2+, Krajewski et al., 2004; T < 40) and at least average level of reading/spelling and (2) a control group ( n = 34) who showed average mathematical achievement ( T > 43). The groups were matched for age, general intelligence (CFT 1, Cattell et al., 1997) and reading/spelling performance (WRT 2+, Birkel, 2007; ELFE 1 – 6, Lenhard & Schneider, 2006).

          In a computer based verification task, children of both groups solved single digit addition problems in lower and higher number range (addition up to 10 and up to 20) under standard and dual-task conditions (articulation: «deedeedee» and tapping: pushing space-bar on the keypad). Articulation was implemented to prevent the usage of verbal counting strategies while tapping was implemented as a motor control condition to articulation. For each item, correctness and latency (time to solve the problem) were registered.

          Results: Children with and without arithmetical disabilities differed significantly in accuracy for additions of the higher number range (up to 20) in the standard condition (no dual-task). A similar pattern could be revealed in dual-task conditions for additions up to ten and up to 20. No significant differences occurred for accuracy in addition up to ten in the standard condition. Regarding latency, groups differed significantly in every cell of analysis (number range and condition). Two 2 (mathematical achievement) x 2 (number range) x 2 (condition) factorial ANOVAs with repeated measurements were conducted for accuracy on the one hand and for latency on the other hand. For latency all main effects, but none of the interaction effects were significant. For accuracy, all main effects and two-way interaction terms were significant: Children with arithmetical disabilities performed worse especially in dual-task conditions on the one hand and for addition problems up to 20 on the other hand; furthermore the dual-task effect was larger for the higher number range. Finally, articulation and tapping conditions were compared in terms of accuracy and latency: No advantage of tapping condition over articulation condition was found.

          Discussion: Performance in a simple verification task under standard and dual-task conditions was investigated to analyze basic arithmetic facts in children with and without arithmetical disabilities. Results support the assumption that children with arithmetical disabilities have problems retrieving arithmetic facts. Children of the control group outperformed children with arithmetical disabilities in nearly every cell of the experimental design – except for addition problems up to ten under standard condition. Because no differences were found between articulation and tapping conditions were found, children obviously are not bound to counting strategies that are verbal in nature.

          Furthermore, results point to an important role of working memory load resulting from fragile basic arithmetic fact knowledge: Children with arithmetic disabilities show a larger impairment when they have to manage an additional secondary task, and they show lower performance with higher number range problems. Additionally, it was shown that the magnitude of the dual-task effect for higher number range exceeds that for lower number range. The combination of these results is consistent with the assumption that fragile fact knowledge (in children with arithmetic disabilities and/or in the case of higher number range) is associated with larger consumption of working memory resources.

          As a consequence of this, higher levels of consumption of working memory resources resulting from fragile arithmetic fact knowledge may explain the higher error rates that occur when children with arithmetic disabilities have to solve more complex tasks that comprise simple arithmetic. Therefore, it is important to consolidate basic arithmetic fact knowledge as early as possible. Furthermore, appropriate diagnostic procedures focusing on arithmetic facts should be applied in elementary school years.

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          Most cited references35

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                Author and article information

                Journal
                lls
                Lernen und Lernstörungen
                Die interdisziplinäre Zeitschrift für den lebenslangen Prozess des Lernens
                Hogrefe AG, Bern
                2235-0977
                2235-0985
                January 2013
                : 2
                : 4
                : 217-227
                Affiliations
                [ 1 ] Carl von Ossietzky Universität Oldenburg
                Author notes
                Jenny Busch, Carl von Ossietzky Universität Oldenburg, Ammerländer Heerstraße 114 – 118, 26129 Oldenburg, Deutschland Jenny.Busch@ 123456uni-oldenburg.de
                Article
                lls_2_4_217
                10.1024/2235-0977/a000043
                2de6ccc6-543c-4f45-a0b4-f7a1819b621c
                Copyright @ 2013
                History
                Categories
                Empirische Arbeit

                Pediatrics,Psychology,Neurosciences,Family & Child studies,Development studies,Clinical Psychology & Psychiatry
                basales arithmetisches Faktenwissen,Rechnen,Arbeitsgedächtnis,Rechenschwäche,working memory,Lernschwächen,learning disabilities,arithmetic disabilities,basic arithmetic facts

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