Sensori-motor spatial training of number magnitude representation

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.     

Magnitude representation in sequential comparison of two-digit numbers is not holistic either

There is accumulating evidence suggesting that two-digit number magnitude is represented in a decomposed fashion into tens and units rather than holistically as one integrated entity. However, recently, it has been claimed that this property does not hold for the case when two to-be-compared numbers are presented sequentially. In the present study, we pursued this issue in two experiments by evaluating perceptual as well as strategic aspects arising for sequential stimulus presentation in a magnitude comparison task. We observed reliable unit-decade compatibility effects indicating decomposed processing of tens and units in a magnitude comparison task with sequential presentation of the to-be-compared numbers. In particular, we found that both confounding low-level perceptual features and stimulus set characteristics determining cue validity of the units influenced the compatibility effect. Taken together, our results clearly indicate that decomposed representations of tens and units seem to be a general characteristic of multi-digit number magnitude processing, rather than an exception occurring under very specific conditions only. Implications of these results for the understanding of number magnitude representations are discussed.     

Negative Numbers are not yet Automatically Associated with Space in 6th Graders

ABSTRACT

The metaphor of the mental number line accounts for numerous empirical effects of spatial-numerical associations. In the present study, we aimed at investigating directional spatial-numerical associations reflected by SNARC-like digit-direction and sign-direction congruency effects as well as the sign-digit compatibility effect when 6^th graders performed magnitude comparisons of multi-symbol numbers (i.e., positive and negative numbers). As spatial-numerical associations were associated with sensorimotor experiences, we used whole-body and finger tapping responses to manipulate the extent of motor responses. We only observed a SNARC-like digit-direction congruency effect, but neither a sign-direction congruency nor a sign-digit compatibility effect. This indicates that 6^th graders may already have developed spatial-numerical associations for absolute number magnitude, but not yet for polarity signs. Furthermore, not observing a sign-digit compatibility effect seemed to suggest that 6^th graders may not yet process multi-symbol numbers in the same parallel componential way as adults do. We argue that while 6^th graders are able to process negative numbers, they are not yet automatically associated with space or integrated in the place-value structure of the Arabic number system like multi-digit numbers are at this age.     

Chronically ill and handicapped children and adolescents: Personality studies in relation to disease

Personality was studied in three groups of chronically ill and handicapped children and adolescents and compared to that of healthy control groups. Among physically handicapped children a pattern emerged indicating lack of emotional integration into environment without conflict. Hemophiliacs and diabetics did not differ from controls. However, there were important correlations between personality variables and clinical parameters for all three groups.     

Behavioural evidence for sex differences in the overlap between subtraction and multiplication

The present study aims to identify factors that may influence the dissociability of number magnitude processing and arithmetic fact retrieval at the behavioural level. To that end, we assessed both subtraction and multiplication performance in a within-subject approach and evaluated the interdependence of unit-decade integration measures on the one hand as well as sex differences in the interdependence of performance measures on the other hand. We found that subtraction items requiring borrowing (e.g. 53–29 = 24, 3 < 9) are more error prone than subtraction items not requiring borrowing (e.g. 59–23 = 34, 9 > 3), thereby demonstrating a borrowing effect, which has been suggested as a measure of unit-decade integration in subtraction. Furthermore, we observed that multiplication items with decade-consistent distractors (e.g. 6 × 4 = 28 instead of 24) are more error prone that multiplication items with decade-inconsistent distractors (e.g. 6 × 4 = 30 instead of 24), thereby demonstrating a decade-consistency effect, which has been suggested as a measure of unit-decade integration in simple multiplication. However, the borrowing effect in subtraction was not correlated with the effect of decade consistency in simple multiplication in either men or women. This indicates that unit-decade integration arises from different systems in subtraction and multiplication. Nevertheless, men outperformed women not only in subtraction, but also in multiplication. Furthermore, subtraction and multiplication performance on correct solution probes were correlated in women, but unrelated in men. Thus, the view of differential systems for number magnitude processing and arithmetic fact retrieval may not be universal across sexes.     

Training the equidistant principle of number line spacing

The characteristics of effective numerical trainings are still under scientific debate. Given the importance of number line estimation due to the strong relation between task performance and arithmetic abilities, the current study aimed at training one important number line characteristic: the equidistant spacing of adjacent numbers. Following an embodied training approach, second-graders were trained using a randomized crossover design to divide a presented line into different numbers of equal segments by walking the line with equally spaced steps. Performance was recorded, and feedback as to the correct equidistant spacing was provided using the Kinect sensor system. Training effects were compared to a control training with no involvement of task-specific whole-body movements. Results indicated more pronounced specific training effects after the embodied training. Moreover, transfer effects to number line estimation and arithmetic performance were partially observed. In particular, differential training effects for bounded versus unbounded number line estimation corroborate the assumption that not only bodily experiences but also the need for a flexible adaption of the perspective on the training material might influence training success. Hence, more pronounced training effects of the embodied training might stem from different cognitive processes involved.     

Basic number processing deficits in developmental dyscalculia: Evidence from eye tracking

Recent research suggests that developmental dyscalculia is associated with a subitizing deficit (i.e., the inability to quickly enumerate small sets of up to 3 objects). However, the nature of this deficit has not previously been investigated. In the present study the eye-tracking methodology was employed to clarify whether (a) the subitizing deficit of two boys with dyscalculia resulted from a general slowing in the access to magnitude representation, or (b) children with dyscalculia resort to a back-up counting strategy even for small object sets. In a dot-counting task, a standard problem size effect for the number of fixations required to encode the presented numerosity within the subitizing range was observed. Together with the finding that problem size had no impact on the average fixation duration, this result suggested that children with dyscalculia may indeed have to count, while typically developing controls are able to enumerate the number of dots in parallel, i.e., subitize. Implications for the understanding of developmental dyscalculia are considered.     

The exact vs. approximate distinction in numerical cognition may not be exact, but only approximate: How different processes work together in multi-digit addition

Two types of calculation processes have been distinguished in the literature: approximate processes are supposed to rely heavily on the non-verbal quantity system, whereas exact processes are assumed to crucially involve the verbal system. These two calculation processes were commonly distinguished by manipulation of two factors in addition problems: the identity of the target and the distance of the distractor. However, in all previous studies, these two factors were not manipulated independently. In this fMRI study, we could disentangle the two factors by using a different (two-digit) number stimulus set. Both behavioral and neurofunctional data suggest that the cognitive processes involved could be best explained by the (independent) factors target and distractor distance. Based on these data we suggest that the exact/approximate distinction does not seem to be as generally valid as previously assumed. We conclude that this study may be a starting point for a closer examination of the experimental, procedural and strategic conditions of when the exact/approximate distinction is valid and when it is not.     

The initial capitalization superiority effect in German: evidence for a perceptual frequency variant of the orthographic cue hypothesis of visual word recognition

A perceptual frequency variant of the orthographic cue (OC) hypothesis (Peressotti, Cubelli, & Job, 2003) was tested in two perceptual identification experiments using the variable viewing position technique: German nouns and non-nouns that are most frequently perceived with or without initial letter capitalization, respectively, were tachistoscopically presented in upper-case, lower-case, or with initial capitalization. The results indicated that words were best recognized in the form they are most frequently perceived in, which suggests that during reading acquisition abstract as well as case- and item-specific OCs may be learned and used for recognition.