Mathematical learning difficulties are a heterogeneous phenomenon characterised by persistent difficulties in learning and applying mathematical skills.
Mathematical learning difficulties often manifest as impaired recall of arithmetic facts and challenges in applying them to solve other arithmetic problems.
Not all difficulties appear initially, as some can become apparent at different stages.
Children who have difficulties with number structure and the base-ten system may only experience mathematical difficulties when this knowledge needs to be applied, i.e., when an understanding of the structure of numbers is required.
Mathematical learning difficulties refer to persistent difficulties in learning and applying mathematical skills, such as number understanding, calculation, and mathematical reasoning, which significantly interfere with academic performance and are not explained by intellectual disability, sensory impairments, or inadequate instruction (Geary, 2004).
Mathematical learning difficulties do not constitute a single, uniform condition. Rather, they represent a heterogeneous phenomenon characterised by individual variability in the manifestation and severity of difficulties, as well as the underlying cognitive factors. For this reason, the term mathematical learning difficulties is used in the plural to acknowledge the diversity of profiles and pathways through which such difficulties may emerge. No single biological or cognitive factor has been found to account for learning difficulties. However, there is consensus that learning difficulties in mathematics involve functional abnormalities in the brain, which are reflected in the inability to process information related to quantities and numbers (De Smedt et al., 2013; Price & Ansari, 2013).
Although mathematical learning difficulties still lack a coherent conceptualisation and definition, there is relative consensus on the key characteristics of these difficulties. One of the most typical problems with learning difficulties in mathematics is the difficulty in recalling arithmetic facts, such as the answers to small addition and subtraction problems (e.g., 4 + 5 = 9 or 8 – 5 = 3) or multiplication tables (e.g., 6 x 5 = 30) (Mazzocco et al., 2008). In such cases, children typically continue to rely primarily on counting by reciting rather that from memory, even after several years of practice (Geary, 2004; Koponen et al., 2018). When counting, these children often use a strategy involving a lot of reciting. They are unable to use the principle of commutativity in their calculations, instead adding numbers in the order in which they are presented. For example, when calculating 2 + 9, a child may start with the number 2 and add nine to it one by one, instead of taking 9 as the first number. Because learning difficulties often involve limited conceptual knowledge, the child may lack access to effective strategies that could compensate for difficulties in retrieving arithmetic facts from memory or facilitate their memorisation. This may manifest as an inability to develop or select appropriate strategies.
Sometimes, identification of numeracy difficulties and provision of early support are hindered because children who struggle to remember frequently repeated number combinations may nevertheless be able to learn calculation steps and sequences in the same way as their peers. For example, they may be able to perform calculations using the column method, albeit slowly. Conversely, mathematical difficulties may be more specifically associated with mastering calculation procedures and rules, while recalling arithmetic facts, such as multiplication table answers, may be relatively easier
Difficulties in mathematics may not become apparent in the early stages of learning numeracy for all children. If the basic problem is a poor understanding of the structure of numbers and the base-ten system, the difficulties may only appear when application of the numerical system is required. For example, the child may have difficulty understanding the structure of numbers (Geary, 2000). This makes it difficult to compare the sizes of numbers (which is bigger, 301 or 299) and to calculate using large numbers, because the child does not understand that 301 has three hundreds and 299 has two hundreds. The child may thus find it difficult to use their knowledge of the numbers’ order of magnitude when calculating: 299 is one less than 300, so 299 + 56 can be thought of as 300 + 56 – 1 or 300 + 55. Understanding the decimal system can also be difficult for children; if the relationships between units are not clear, multiplying and dividing by tens, hundreds, and thousands will therefore prove difficult.
De Smedt, B., Noël, M., Gilmore, C., & Ansari, D. (2013). How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children’s mathematical skills? A review of evidence from brain and behavior. Trends in neuroscience and education, 2(2), 48-55. https://doi.org/10.1016/j.tine.2013.06.001
Geary, D. C. (2000). From infancy to adulthood: The development of numerical abilities. European child & adolescent psychiatry, 9(S2), S11-S16. https://doi.org/10.1007/s007870070004
Koponen, T. K., Sorvo, R., Dowker, A., Räikkönen, E., Viholainen, H., Aro, M., & Aro, T. (2018). Does Multi-Component Strategy Training Improve Calculation Fluency Among Poor Performing Elementary School Children? Frontiers in psychology, 9, 1187. https://doi.org/10.3389/fpsyg.2018.01187
Mazzocco, M. M. M., Devlin, K. T., & McKenney, S. J. (2008). Is it a Fact? Timed Arithmetic Performance of Children With Mathematical Learning Disabilities (MLD) Varies as a Function of How MLD is Defined. Developmental neuropsychology, 33(3), 318-344. https://doi.org/10.1080/87565640801982403
Schneider, M., Beeres, K., Coban, L., Merz, S., Susan Schmidt, S., Stricker, J., & De Smedt, B. (2017). Associations of non‐symbolic and symbolic numerical magnitude processing with mathematical competence: A meta‐analysis. Developmental science, 20(3), np-n/a. https://doi.org/10.1111/desc.12372
