On the Relation between the Mental Number Line and Arithmetic Competencies

Number line estimation strategies in children with mathematical learning difficulties measured by eye tracking

Introduction

Number line estimation is one of the skills related to mathematical performance. Previous research has shown that eye tracking can be used to identify differences in the estimation strategies children with dyscalculia and children with typical mathematical development use on number line estimation tasks. The current study extends these findings to a larger group of children with mathematical learning disabilities (MLD).

Method

A group of 9–11-year-old children with MLD (N = 14) was compared to a control group of children without math difficulties (N = 14). Number line estimation was measured using a 0–100 and a 0–1000 number-to-position task. A Tobii T60 eye tracker was used to measure the children’s eye movements during task performance.

Results

The behavioral data showed that the children with MLD had higher error scores on both number lines than the children in the control group. The eye tracking data showed that the groups also differed in their estimation strategies. The children with MLD showed less adaptation of their estimation strategies to the number to be estimated.

Conclusion

This study shows that children with MLD attend to different features of the number line than children without math difficulties. Children with math difficulties are less capable of adapting their estimation strategies to the numbers to be estimated and of effectively using reference points on the number line.

Electronic supplementary material

The online version of this article (doi:10.1007/s00426-015-0736-z) contains supplementary material, which is available to authorized users.

An integration of competing accounts on children's number line estimation

Children’s estimation patterns in bounded number line estimation (NLE) reveal marked developmental changes. Three different theoretical accounts were proposed to explain these changes: a log-to-linear shift account, a proportion-judgment account and a two-linear account considering familiarity with numbers or the understanding of the place-value structure of the Arabic number system. However, only the first two accounts are considered prominently in the ongoing scientific debate. Therefore, we first present a reanalysis of NLE data of Austrian first-graders contrasting all three accounts. Results indicate that the two-linear account is a reliable alternative to the log-to-linear shift as well as the proportion-judgment account. However, we do not claim the two-liner account to provide an exhaustive explanation for the observed developmental changes. We rather introduce the idea that aspects of all three accounts may complement – instead of exclude – each other. Jointly considering conceptual (i.e., familiarity, place-value) and procedural (i.e., proportion-judgments) aspects will allow for a more comprehensive understanding of children’s development in NLE.

How number line estimation skills relate to neural activations in single digit subtraction problems

The Number Line (NL) task requires judging the relative numerical magnitude of a number and estimating its value spatially on a continuous line. Children's skill on this task has been shown to correlate with and predict future mathematical competence. Neurofunctionally, this task has been shown to rely on brain regions involved in numerical processing. However, there is no direct evidence that performance on the NL task is related to brain areas recruited during arithmetical processing and that these areas are domain-specific to numerical processing. In this study, we test whether 8- to 14-year-old's behavioral performance on the NL task is related to fMRI activation during small and large single-digit subtraction problems. Domain-specific areas for numerical processing were independently localized through a numerosity judgment task. Results show a direct relation between NL estimation performance and the amount of the activation in key areas for arithmetical processing. Better NL estimators showed a larger problem size effect than poorer NL estimators in numerical magnitude (i.e., intraparietal sulcus) and visuospatial areas (i.e., posterior superior parietal lobules), marked by less activation for small problems. In addition, the direction of the activation with problem size within the IPS was associated with differences in accuracies for small subtraction problems. This study is the first to show that performance in the NL task, i.e. estimating the spatial position of a number on an interval, correlates with brain activity observed during single-digit subtraction problem in regions thought to be involved in numerical magnitude and spatial processes.

Spatial Associations in Numerical Cognition—From Single Digits to Arithmetic

The literature on spatial associations during number processing is dominated by the SNARC (spatial–numerical association of response codes) effect. We describe spatial biases found for single digits and pairs of numbers, first in the “original” speeded parity task and then extending the scope to encompass different tasks, a range of measures, and various populations. Then we review theoretical accounts before surveying the emerging evidence for similar spatial associations during mental arithmetic. We conclude that the mental number line hypothesis and an embodied approach are useful frameworks for further studies.