Developmental Dyscalculia is Characterized by Order Processing Deficits: Evidence from Numerical and Non-Numerical Ordering Tasks

ABSTRACT

This study tested the hypothesis that individuals with dyscalculia have an order processing deficit. The ordering measures included both numerical and non-numerical ordering tasks, and ordering of both familiar and novel sequences was assessed. Magnitude processing/estimation tasks and measures of inhibition skills were also administered. The participants were 20 children with developmental dyscalculia, and 20 children without maths difficulties. The two groups were closely matched on age, gender, socio-economic status, educational experiences, IQ and reading ability. The findings revealed differences between the groups in both ordering and magnitude processing skills. Nevertheless, diagnostic status was best predicted by order processing abilities.

Acknowledgments

We would like to say thank you to John Eakin for his great help with recruiting schools for this study, and facilitating interactions with local educational psychologists and school principals. We also thank Martina Maggio and Francesca Mastrantonio for their help with data collection and data entry.

Declaration of interest

The views expressed are those of the authors and not necessarily those of the Foundation. More information is available at www.nuffieldfoundation.org.

Notes

^1. We note that some studies (e.g., Skagerlund & Träff, 2014; Vicario, Rappo, Pepi, Pavan, & Martino, 2012) have found impaired time estimation abilities in dyscalculia. However, this skill, which is likely to rely on separate specialized timing mechanisms, was not investigated in the current study.

^2. Note that the nature of the involvement of inhibition processes in dot comparison performance is debated (see Keller & Libertus, 2015; various contributions in Henik, 2016).

^3. The DSM-5 diagnostic criteria for dyscalculia/specific learning disorder in mathematics (in contrast with the DSM-IV criteria), do not require a discrepancy between maths scores and IQ. However, for the purposes of this study, we recruited children with a significant maths-IQ discrepancy, as this can help in disentangling the effects of low maths scores vs. low IQ on their performance on the tasks. We also did this so that we could obtain samples with IQs in the normal range. In terms of the individual profiles of the children in the DD group, in the case of 10 children, there was a discrepancy of at least seven standard points between both the children’s IQ and reading scores and their maths scores (i.e., half of the children only had a difficulty in maths). There were four additional children who had a relatively large discrepancy between their IQ and maths scores, but only a small discrepancy between their maths and English scores (i.e., they had difficulties with both maths and English). Nevertheless, these children did not have a diagnosis of dyslexia, and, for this reason, we decided to keep them in our dyscalculia sample. In the case of the remaining 6 children, there was a large discrepancy between their maths and English scores, but only a small discrepancy between their maths and IQ scores. We decided to include these children in our sample on the basis that their sustained difficulties with maths did not extend to other aspects of learning. Although we acknowledge that this results in a DD group with a somewhat heterogeneous cognitive profile, this is quite common in the literature on dyscalculia. Regarding the profile of the control children, they did not represent very well a typical population. However, our aim was to maximize the differences in maths skills, while minimizing the differences in all other relevant factors between the children in the two groups.

^4. This task was modeled on Morsanyi et al. (2017). A list of all trials can be found in the paper.

^5. The group difference was also significant in a non-parametric statistical analysis, using a Mann-Whitney U test (p = .038).

^6. It could be argued that, because performance was close to ceiling on this task, the ANOVA analyses were not appropriate. Nevertheless, the group difference was also present when we used a Mann-Whitney U test (p = .005). We preferred to present the results of the ANOVA analyses in the main text, because this is the typical analysis strategy in the relevant literature (e.g., Gilmore et al., 2014; Price et al., 2007).

^7. Another way to deal with multicollinearity would be to combine the scores from highly correlated variables. However, for interpretative purposes, it is more useful to assess the individual contribution of each task.

^8. The results regarding explained variance and the model’s ability to identify participants as DD/control might seem contradictory. It might be useful to consider that model 4 was particularly successful at identifying participants who were not dyscalculic, whereas model 5 showed the best performance in identifying DD participants (i.e., correct classification is not additive, when a new variable is included in the model). In other words, overall explained variance in diagnostic status increases with each additional relevant predictor variable, however, the ability of the model to correctly identify an individual’s diagnostic status will depend on the fit between each individual’s profile and the profile predicted by the statistical model.

^9. These effects indicate that in the case of correctly ordered trials, participants find it easier to recognize correct trials when the items immediately follow each other (e.g., 1 2 3), but they sometimes incorrectly reject trials where the items do not form a familiar sequence (e.g., 2 5 8). In the case of mixed-order trials, participants experience more difficulty on close trials (e.g., 2 4 3) – i.e., sometimes they incorrectly accept these.

^10. For a comparison, on the basis of the parental questionnaire alone, 70% of the participants could be identified correctly as DD or control. Using the order working memory task or the number line task alone, 67.5% of the participants could be correctly classified.

^11. An example for a transitive reasoning task is: “If bicycles are faster than aeroplanes, and cars are faster than bicycles, then are cars faster than aeroplanes?” This task involves the requirement to order items along a single continuum (in this case, according to how fast they are), and make judgments about the relative position of the items. Some of the tasks also require participants to accept premises that are unbelievable, which might require the inhibition of beliefs.

Additional information

Funding

This project was supported by a Nuffield Foundation Research and Innovation grant to K.M. and T.M. (grant reference number: EDU/42027). The Nuffield Foundation is an endowed charitable trust that aims to improve social well-being in the widest sense. It funds research and innovation in education and social policy and also works to build capacity in education, science and social science research.