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Vom Fingergefühl zum Rechnen

Bedeutung der Fingergnosie für die Vorhersage numerisch-arithmetischer Fertigkeiten

Published Online:January 01, 2015https://doi.org/10.1024/2235-0977/a000088

Abstract

Zusammenfassung. Aktuelle Studien belegen eine Verbindung zwischen Fingergnosie, der Fähigkeit einzelne Finger voneinander zu unterscheiden, zu benennen und nach Aufforderung vorzuzeigen (Reeve & Humberstone, 2011), und numerisch-arithmetischen Fertigkeiten. Die Fingergnosie wird zum Teil als wichtiger spezifischer Prädiktor späterer mathematischer Fertigkeiten bezeichnet. Um den tatsächlichen Prädiktionswert fingergnostischer Leistungen zu untersuchen, werden hier neben den Leistungen in der nonverbalen Intelligenz, dem visuell-räumlichen Arbeitsgedächtnis und der selektiven Aufmerksamkeit auch die numerisch-arithmetischen Leistungen zu einem früheren Zeitpunkt kontrolliert.

Im Rahmen der SCHUES-Studie sind die Daten zweier Messzeitpunkte einer 1594 Kinder umfassenden epidemiologischen Längsschnittuntersuchung ausgewertet worden. Die Kindergartenkinder waren zum ersten Messzeitpunkt im Mittel 63 Monate alt. Der zweite Messzeitpunkt fand durchschnittlich neun Monate später statt. Fingergnosie und numerisch-arithmetische Fertigkeiten (getrennt nach Zählfertigkeiten, Ziffernkenntnis und Rechnen/Mengenerfassung) sowie nonverbale Intelligenz, visuell-räumliches Arbeitsgedächtnis und selektive Aufmerksamkeit wurden in Individualtestungen erhoben.

Die Korrelationen zwischen Fingergnosie und den numerisch-arithmetischen Fertigkeiten sind gering. In Pfadanalysen erweisen sich die analogen numerisch-arithmetischen Fertigkeiten zu einem früheren Messzeitpunkt als jeweils beste Prädiktoren. Unter zusätzlicher Berücksichtigung der nonverbalen Intelligenz, des visuell-räumlichen Arbeitsgedächtnisses und der selektiven Aufmerksamkeit hat die Fingergnosie einen eigenen, aber geringen Prädiktionswert für Zählfertigkeiten und Rechnen/Mengenerfassung, nicht jedoch für die Ziffernkenntnis zum zweiten Messzeitpunkt. Nach den numerisch-arithmetischen Leistungen ist die nonverbale Intelligenz der bedeutsamste Prädiktor.

Die Ergebnisse zeigen, dass die Fingergnosie einen von der nonverbalen Intelligenz, dem visuell-räumlichen Arbeitsgedächtnis und der selektiven Aufmerksamkeit unabhängigen Vorhersagebeitrag für Zählfertigkeiten und Rechnen/Mengenerfassung erbringt, aber in ihrer Prädiktionskraft späterer numerisch-arithmetischer Leistungen deutlich hinter jenem der frühen numerischen und intellektuellen Leistungsfähigkeit zurückbleibt.


From Fingers to Calculating: Finger Gnosis as a Predictor of Numerical Achievement in Preschool?

Abstract.Background: A lot of papers showed a relationship between the use of fingers and numbers (e. g. Di Luca, Granà, Semenza, Seron, & Pesenti, 2006; Di Luca & Pesenti, 2008; M. H. Fischer, 2008; M. H. Fischer & Brugger, 2011; Moeller & Nuerk, 2012). In 1924 Gerstmann first described a neuroanatomical closeness of finger and magnitude representation.

A distinction has to be made between counting with fingers and finger gnosis. Finger gnosis is the ability to distinguish among fingers, to name and to show them (Reeve & Humberstone, 2011). Recent studies showed a relationship between finger gnosis and numerical abilities. First Fayol, Barrouillet and Marinthe (1998) showed that a neuropsychological test score including finger gnosis in preschool was a good predictor of mathematical performance approximately one year later in the first grade. Noël (2005) replicated the results. Finger gnosis, quality of hand-writing, and logical reasoning, measured in the first grade, could predict numerical skills in the second grade. However, finger gnosis was not found to predict reading performance. Thus, it seems to be a specific predictor of mathematical abilities. After controlling for gender, receptive language and processing speed Penner-Wilger et al. (2007) found that finger gnosis directly predicted numeration skills and indirectly predicted calculating skills in first grade children. Additionally Penner-Wilger et al. (2009) found that finger gnosis in the first grade predicted children's second grade symbolic distance effects. In a sample of eight to eleven year-old children Costa et al. (2011) found that children suffering from dyscalculia significantly differed from children without dyscalculia in regard to finger gnosis. These differences could not be attributed to general intellectual abilities, verbal and non-verbal working memory and visual-motor skills. The only evidence for a functional link between finger gnosis and numeration skills was found in a study of Gracia-Bafalluy and Noël (2008). In two weekly sessions, over a period of eight weeks, a sample of first-grade children were trained on their finger gnosis skills. The training improved not only finger gnosis but also a few areas of numerical competence. However, there is serious methodical criticism on it (see J.-P. Fischer, 2010; Gaidoschik, 2012).

Other well-known factors for prediction of numerical abilities are logical reasoning (e. g. De Jong & van der Leij, 1999; Krajewski & Schneider, 2009; Passolunghi, Mammarella, & Altoe, 2008), visual-spatial memory (De Smedt et al., 2009; Krajewski, Schneider, & Nieding, 2008; McKenzie, Bull, & Gray, 2003; Rasmussen & Bisanz, 2005) and selective attention (Aunola et al., 2004; Steele, Karmiloff-Smith, Cornish, & Scerif, 2012).

Aims: The current study explored the relationship between finger gnosis and numerical abilities, particularly knowledge of numerals, counting skills and calculating/quantity, in pre-school children under consideration of non-verbal intelligence, visual-spatial working memory and selective attention as well as the numerical abilities nine months before. This procedure allows the examination of the true predictive value of finger gnosis in a representative sample. A simultaneous control of the mentioned variables wasn't considered in earlier studies.

Method: The current study is based on data of a large epidemiological study (called SCHUES), funded by the Bundesministerium für Bildung und Forschung. 1704 children were tested twice with an interval of approximately nine months starting on average one year before entering school. The mean age of the children at t1 was 63 months (SD = 4.38; min = 54, max = 81), at t2 72 months (SD = 4.22; min = 63, max = 89).

Non-verbal intelligence, visual-spatial working memory and selective attention were assessed individually at t1, finger gnosis and numerical skills were assessed at t1 and t2. The finger gnosis task was based on Noël (2005). The experimenter lightly touched one or two of the child's fingers simultaneously while the child's view was obstructed by a blind placed on its wrist. After removing the blind, the child was asked to show the finger that was touched. The numerical tasks were based on the German neuropsychological test ZAREKI-K (von Aster, Bzufka, & Horn, 2009). Adapted to our previous work (Wyschkon et al., 2014) the items were merged into three factors: counting skills (counting forward, counting backward, counting from 7 to 12, counting objects), knowledge of numerals (reading numbers, quantity-number matching, number-quantity matching) and calculating/quantity (non-verbal subtraction, non-verbal addition, word problems addition and subtraction, non-symbolic comparison, contextual estimation). To asses non-verbal intelligence a subtest of BUEVA-III (Esser & Wyschkon, in prep.) was used. The visual-spatial working memory was assessed using a six block version of Corsi-Block (Roebers & Zoelch, 2005). Selective attention was measured with a visual searching task from BUEVA-III.

Results: The correlations between the three scores of numerical abilities and finger gnosis were low at both times of assessment with the highest correlations to calculating/quantity. The coefficients ranged between r = .15 (finger gnosis t2 and knowledge of numerals t2) and r = .33 (finger gnosis t1 and calculating/quantity t1). As finger gnosis correlated nearly equally high with knowledge of numerals and counting skills as with nonverbal intelligence and visual-spatial working memory, finger gnosis seems to be no specific predictor. Regarding the predictive power of numerical skills the results showed, that the specific numerical skills at t1 (25 % – 45 %) could explain much more variance than finger gnosis at t1 (3 % – 10 %).

To consider the predictive value of finger gnosis under consideration of the stability of numerical skills, non-verbal intelligence, visual-spatial memory and selective attention in predicting children's numerical achievement at t2 path analysis models were conducted. Regarding children's counting skills at t2, the achievement score in counting skills nine months before was the best predictor. Furthermore, finger gnosis, non-verbal intelligence and selective attention at t1 could explain much less variance of the criterion. The model showed a very good data fit (χ 2 (2) = 1.76, p = .414, RMSEA = .001, CFI = 1.00). For the prediction of knowledge of numerals at t2 a model consisting of the stability of knowledge of numerals and non-verbal intelligence at t1 showed a very good data fit (χ 2 (1) = 0.01, p = .699, RMSEA = .001, CFI = 1.00). With regard to children's calculating/quantity skills at t2 the following factors at t1 had predictive value: calculating/quantity, non-verbal intelligence, finger gnosis, selective attention and visual-spatial memory. The final model showed a very good data fit as well (χ 2 (3) = 7.37, p = .061, RMSEA = .03, CFI = 1.00).

Discussion: This study evaluates the relevance of finger gnosis for early numeral development in a large sample of preschoolers. In summary, the link between finger gnosis and numerical skills is relatively weak. Above well-known predictors (non-verbal intelligence, visual-spatial skills and selective attention) and the stability of numerical skills, finger gnosis has its own but less predictive value for the factors counting skills and calculating/quantity, but not for knowledge of numerals. Under consideration of the stability of numerical abilities the best independent predictor in all three path models was the non-verbal intelligence. Thus the results of the present study cannot confirm finger gnosis being a better predictor of later numerical skills. Moreover intellectual ability at least in preschool displays more predictive power than finger gnosis. This is contrary to the results of Gracia-Bafalluy und Noël (2008). Further research will show the variation of the results when testing elementary school children.

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