Dr Francesco Sella is a Senior Lecturer at the Centre for Mathematical Cognition in the Department of Mathematics Education at Loughborough University. His research examines the cognitive foundations of numerical development and how these processes relate to learning difficulties, such as dyscalculia. Edited by Dr Bethany Woollacott.

In this blog post, Francesco Sella explores new insights from his research on severe developmental dyscalculia (full paper linked at the end of this blogpost). This research shows that children with this learning disability struggle when processing symbolic (e.g., 9) and non-symbolic (e.g., collections of dots) numerosities. Children with developmental dyscalculia might also exhibit deficits in domain-general cognitive skills – i.e., issues with processing information in general, not just in mathematics. However, our findings suggest the presence of impairments in numerical processing. These findings are useful because they could help inform early diagnosis efforts in educational and clinical settings.

Introduction

Developmental dyscalculia affects approximately 5-6% of the population and presents as a specific difficulty with numbers. It is often observed in conjunction with other disorders, such as dyslexia². One of the major challenges is that children with developmental dyscalculia often experience a variety of challenges whilst learning. In many studies, children show difficulties in numerical tasks and broader domain-general cognitive functions (i.e., processing information in general), particularly visuospatial working memory³ – where we temporarily store and manipulate visual and spatial information. The variation in the challenges that children with developmental dyscalculia face makes it difficult to pinpoint whether dyscalculia is primarily about number processing or more general cognitive impairments.

Our study

To understand the nature of numerical difficulties in developmental dyscalculia, we tested two groups of children: one group with severe dyscalculia and a control group. Both were referred to the same neuropsychiatric unit for learning assessment, ensuring similar backgrounds. Importantly, all children had average general cognitive skills and visuospatial memory. What set them apart was their mathematical ability.

Each child completed a range of short, computer-based tasks designed to tap into both symbolic (number-based) and non-symbolic (quantity-based) numerical processing. Here is a quick overview of what those tasks looked like:

Symbolic Tasks

• Digit Comparison. Children saw two digits on the screen (e.g., 4 and 7) and had to quickly choose which one was the numerically larger. This task measures how easily children can access the numerical magnitude of numerical symbols.
• Number Order. Children viewed a sequence of three digits (e.g., 2-3-4) and judged whether the numbers were in ascending order. This taps into their understanding of number sequences and ordinality.
• Number Line. A horizontal line labelled 0 at one end and 1,000 at the other was displayed on the screen. Children were shown a number (like 450) and asked to click where they thought it belonged on the line⁴. This assesses how well children map numbers onto the visual line, reflecting their symbolic knowledge of numerical intervals.

Non-symbolic Tasks

• Match-to-Sample. In this task, children were briefly shown a set of dots, followed by a second set, and asked whether the two sets contained the same number of dots⁵. Because the arrays were shown one after the other, children had to mentally hold the first set in memory and compare it to the second.
  The match-to-sample task included both small and large numerosities. Comparing small numerosities (like 1, 2, or 3 dots) is thought to rely on what’s called the object tracking system—our brain’s ability to represent and keep track of a few individual items at once. This is closely linked to a process known as subitising, where we instantly “see” how many items there are without counting. In contrast, comparing larger numerosities (like 5, 6, or 7 dots) engages a different system—the approximate number system, which helps us estimate and compare quantities without needing precise counting.
  By including both small and large quantities, this task allowed us to explore whether children with dyscalculia show specific weaknesses in one or both of these fundamental number processing systems.
• Panamath. Here, two sets of coloured dots appeared on the screen at the same time, and children had to choose which set contained more dots⁶. This task is designed to test the approximate number system—our brain’s intuitive sense of quantity—while also controlling for non-numerical visual factors like dot size.

So, what did we find?

Children with dyscalculia were significantly slower in performing symbolic tasks, such as digit comparison and number order judgment, and made more errors in number-line estimation.

In the match-to-sample task, children with dyscalculia showed less accuracy, especially with larger quantities, and were slower even for small sets. Conversely, no differences were observed in the Panamath task.

Just two simple tasks—comparing digits and matching dot sets—were sufficient to reliably distinguish between children with and without dyscalculia.

What does this mean?

Children with severe developmental dyscalculia showed clear difficulties in both symbolic and non-symbolic numerical processing. They were slower and made more errors in tasks involving digits, number sequences, and dot comparisons—suggesting challenges in the basic processing of numerical information.

Notably, two tasks stood out as particularly effective in distinguishing children with and without dyscalculia: digit comparison and match-to-sample. These are simple, quick tasks that could potentially be used in schools or clinics to help spot numerical difficulties early.

Crucially, we observed these differences despite the fact that both groups of children had similar levels of general cognitive ability and visuospatial memory. This is important. It suggests that the difficulties seen in dyscalculia are not simply due to broader learning or memory problems, but rather reflect specific weaknesses in how numerical information is processed.

Disclaimer: A ChatGPT model was used to support the writing of this blogpost. For more information, contact b.woollacott@lboro.ac.uk

References

1.         Decarli, G., Sella, F., Lanfranchi, S., Gerotto, G., Gerola, S., Cossu, G. & Zorzi, M. (2023) Severe Developmental Dyscalculia Is Characterized by Core Deficits in Both Symbolic and Non-symbolic Number Sense. Psychological Science, 34, 8–21. https://doi.org/10.1177/09567976221097947

2.         Morsanyi, K., van Bers, B. M. C. W., McCormack, T. & McGourty, J. (2018). The prevalence of specific learning disorder in mathematics and comorbidity with other developmental disorders in primary school-age children. British Journal of Psychology, 109, 917–940. https://doi.org/10.1111/bjop.12322

3.         Szűcs, D., Devine, A., Soltesz, F., Nobes, A. & Gabriel, F. (2013) Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment. Cortex , 49, 2674–2688. https://doi.org/10.1016/j.cortex.2013.06.007

4.         Siegler, R. S. & Opfer, J. E. (2003). The development of numerical estimation: evidence for multiple representations of numerical quantity. Psychological Science, 14, 237–243. https://doi.org/10.1111/1467-9280.02438

5.         Sella, F., Lanfranchi, S. & Zorzi, M. (2013). Enumeration skills in Down syndrome. Research in Developmental Disabilities, 34, 3798–3806. https://doi.org/10.1016/j.ridd.2013.07.038

6.         Halberda, J., Ly, R., Wilmer, J. B., Naiman, D. Q. & Germine, L. (2012). Number sense across the lifespan as revealed by a massive Internet-based sample. Proceedings of the National Academy of Sciences of the United States of America, 109, 11116–11120. https://doi.org/10.1073/pnas.1200196109