No abstract

Number line estimation (i.e., indicating the position of a given number on a physical line) is a standard assessment of children's spatial representation of number magnitude. Importantly, there is an ongoing debate on the question in how far the bounded task version with start and endpoint given (e.g., 0 and 100) might induce specific estimation strategies and thus may not allow for unbiased inferences on the underlying representation. Recently, a new unbounded version of the task was suggested with only the start point and a unit fixed (e.g., the distance from 0 to 1). In adults this task provided a less biased index of the spatial representation of number magnitude. Yet, so far there are no children data available for the unbounded number line estimation task. Therefore, we conducted a cross-sectional study on primary school children performing both, the bounded and the unbounded version of the task. We observed clear evidence for systematic strategic influences (i.e., the consideration of reference points) in the bounded number line estimation task for children older than grade two whereas there were no such indications for the unbounded version for any one of the age groups. In summary, the current data corroborate the unbounded number line estimation task to be a valuable tool for assessing children's spatial representation of number magnitude in a systematic and unbiased manner. Yet, similar results for the bounded and the unbounded version of the task for first- and second-graders may indicate that both versions of the task might assess the same underlying representation for relatively younger children—at least in number ranges familiar to the children assessed. This is of particular importance for inferences about the nature and development of children's magnitude representation.

In this study, we aimed at investigating whether it is indeed the spatial magnitude representation that links number line estimation performance to other basic numerical and arithmetic competencies. Therefore, estimations of 45 fourth-graders in both a bounded and a new unbounded number line estimation task (with only a start-point and a unit given) were correlated with their performance in a variety of tasks including addition, subtraction, and number magnitude comparison. Assuming that both number line tasks assess the same underlying mental number line representation, unbounded number line estimation should also be associated with other basic numerical and arithmetic competencies. However, results indicated that children's estimation performance in the bounded but not the unbounded number line estimation task was correlated significantly with numerical and arithmetic competencies. We conclude that unbounded and bounded number line estimation tasks do not assess the same underlying spatial-numerical representation. Rather, the observed association between bounded number line estimation and numerical/arithmetic competencies may be driven by additional numerical processes (e.g., proportion judgement, addition/subtraction) recruited to solve the task.

No abstract

Recent empirical evidence indicates that seemingly abstract numerical cognitions are rooted in sensory and bodily experiences. In particular in finger counting finger-based representations reflect a specific case of embodied cognition, we termed embodied numerosity. Furthermore, we suggest that finger-based representations should be considered a distinct representation of number (magnitude) and argue that this representation is activated automatically whenever we encounter a number. We discuss in what way such a theoretical framework can account for the associations of fingers and numbers observed so far. In the final part, we evaluate whether the concept of embodied numerosity should be generalized beyond finger-based representations with particular focus on whether bodily-sensory experiences (such as moving the whole body along the mental number line) may corroborate numerical capabilities. In a series of intervention studies, we consistently observed more pronounced training effects for our embodied numerosity trainings for different age groups, different digital media, different number ranges, and different control conditions. Taken together, we conclude that embodied representations of number (magnitude) exist, are not limited to finger-based representations, and influence number processing in a systematic and functional way that can be used to foster the efficiency of numerical trainings.