Sensori-motor spatial training of number magnitude representation

Ursula Fischer Korbinian Moeller Martina Bientzle Ulrike Cress Hans-Christoph Nuerk An adequately developed spatial representation of number magnitude is associated with children's general arithmetic achievement. Therefore, a new spatial-numerical training program for kindergarten children was developed in which presentation and response were associated with a congruent spatial numerical representation. In particular, children responded by a full-body spatial movement on a digital dance mat in a magnitude comparison task. This spatial-numerical training was more effective than a non-spatial control training in enhancing children's performance on a number line estimation task and a subtest of a standardized mathematical achievement battery (TEDI-MATH). A mediation analysis suggested that these improvements were driven by an improvement of children's mental number line representation and not only by unspecific factors such as attention or motivation. These results suggest a benefit of spatial numerical associations. Rather than being a merely associated covariate, they work as an independently manipulated variable which is functional for numerical development. - Basic numerical competencies as predictors of future arithmetic achievement The notion that childrens early basic numerical competencies reliably predict their future arithmetic abilities has received growing interest in recent years (e.g., Booth & Siegler, 2008; Holloway & Ansari, 2009). One of these basic numerical skills thought to hold particular importance for mathematical development is the processing of the spatial representation of number magnitude. Dehaene, Bossini, and Giraux (1993) proposed numerical magnitude to be represented in ascending order along a left-to-right oriented mental number line on which numbers are spatially coded and reflected in an analogue format. This number line representation is supposed to be accessed automatically whenever a number is encountered and it is assumed to develop as early as first grade of elementary school (Berch, Foley, Hill, & McDonough, 1999; van Galen & Reitsma, 2008). Throughout development, the accuracy of the positioning of numbers along the mental number line increases with age and experience (Booth & Siegler, 2008). The most direct measure for examining the spatial magnitude representation is the number line estimation task (e.g., Siegler & Opfer, 2003). In this task, participants have to indicate the spatial position of a given number (e.g., 37) on a hypothetical number line (e.g., ranging from 0 to 100). Accuracy of the number line representation is then inferred from the distance between participants estimations and the actual positions of the tobe-marked numbers. It has been shown repeatedly that the accuracy of childrens number line representation influences their arithmetic achievement. For instance, Booth and Siegler (2008) observed that children with a more accurate number line representation performed better in arithmetic tasks and, more importantly, also learned answers to unfamiliar arithmetic problems more easily. These findings suggest a functional association between the quality of the mental number line representation and later arithmetical development. Accordingly, number line tasks have been included in successful intervention approaches for dyscalculia, such as the Number Worlds Curriculum (Griffin, 2003; originally published as Rightstart; Griffin, Case, & Siegler, 1994). Seeing as the mental number line representation constitutes an association between numbers and space (as proposed by A Theory of Magnitude, see Bueti & Walsh, 2009), it has been found to be moderated by bodily experiencessuch as in the case of finger counting (e.g., Fischer, 2008)corroborating the notion of embodied cognition which will be introduced in the next section. According to recent findings in neuroscience (e.g., Andres, Olivier, & Badets, 2008), the motor system not just controls and/or monitors actions, but may also contribute to cognitive representations. For example, Goldin-Meadow, Nusbaum, Kelly, and Wagner (2001) observed that being allowed to gesture while solving mathematical problems reduced childrens cognitive load. Moreover, Gherri and Eimer (2010) found that preparation of a manual response on one side in space severely disrupted the direction of attention to stimuli on the other side, and explained these results by shared brain circuits responsible for the control of spatial attention and action. As a possible explanation of such and other findings, several theories of embodied cognition have been proposed (see Wilson, 2002, for an overview). While these theories differ in their definitions of what exactly the term embodied cognition entails, the most basic interpretation is that human cognition is originally rooted in sensori-motor processes and thus determined by bodily experiences. Such an interaction between the cognitive and physical world has been theoretically elaborated by Hommel, Msseler, Aschersleben, and Prinz (2001) in the Theory of Event Coding (TEC). While TEC is not strictly speaking a theory of embodied cognition, it provides an interpretative framework for many of the respective findings. In contrast to traditional views on cognitive processing, TEC proposes that perceived and action-related events are coded, stored and integrated in a common network of feature codes. These feature codes register input from sensory systems and modulate activities of motor systems based on this input and internalized experiences. When a given stimulus is processed, it first activates all stimulus-related feature codes, both perceptual and action-related. Hommel et al. (2001) give the example of perceiving a cherry. This cherry activates the feature codes representing its attributes such as RED, ROUND, and SMALL. These feature codes are then integrated into the event code CHERRY that represents all features of an event in a shared medium. Activation of one feature code (e.g. RED) now facilitates further activation of other feature codes (ROUND and SMALL) if they are part of the same event code (CHERRY). Subsequently, when the event code CHERRY is activated, this facilitates both the perception of other objects that are red, round, and small as well as actions directed towards events that also hold these features. Inversely, selecting the features of a tobe-planned action will facilitate both the perception and the production of other events this action shares features with. In this vein, a task becomes easier to solve the more features are shared by (sensori-perceptual) stimulus and (bodily) response. While Hommel and colleagues did not examine the connection of numerical magnitude and motor activity, the idea of an embodied representation of numerosity has been considered by other researchers (e.g., Domahs, Moeller, Huber, Willmes, & Nuerk, 2010). For example, finger counting habits (e.g., Fischer, 2008) have been shown to be strongly rel (...truncated)