Numerical and non-numerical cognitive factors

Number sense has been proposed as a core ability underlying the development of mathematical thinking and skills, with its importance often equated to the phonological processing ability underlying literacy. Numerical magnitude processing is most commonly assessed using comparison tasks (Ansari, 2008; Lyons et al., 2015). In these tasks, participants are asked to determine, as quickly and accurately as possible, which of two visually presented numbers or quantities is numerically larger. The stimuli may be either symbolic (e.g., Arabic numerals) or non-symbolic (e.g., sets of dots). In particular, the speed of symbolic magnitude processing has been shown to be a significant indicator of mathematical learning difficulties (Schwenk et al., 2017).

However, mathematical learning difficulties do not always stem from identifiable problems with number sense. The difficulties may be more evident in areas such as number sequencing (Koponen et al., 2025) and reading or writing numbers – particularly when learning the syntax of number words and converting them into written form using Arabic numerals. At the cognitive level, difficulties may be especially evident in linguistic skills, such as phonological processing, vocabulary, rapid recall of verbal labels for visual stimuli, understanding language structures, and linguistic working memory. Among language-related skills, rapid automatized naming (RAN) has consistently been linked to mathematical learning difficulties, particularly to difficulties in developing arithmetic fluency (e.g., Donker et al., 2016; Koponen et al., 2024). In these cases, there are often also difficulties with reading. 

Similarly, deficits in visuospatial processing, i.e., the processing of information related to visual and spatial perception, hamper the development of the number concept and knowledge of the number system in addition to geometric skills. Processing the structure of a number and its place-value information can thus be difficult, as can processing the relationships between number units (tens, hundreds, thousands), making it difficult to calculate using multi-digit numbers. Further, in everyday maths, learning to tell the time and understand monetary units can be particularly problematic. 

Mathematics often requires memorising quantities and numbers while performing operations. It is therefore not surprising that working memory is associated with the development of mathematical skills and learning difficulties in mathematics (David, 2012). Problems in memorising sequential information seem to be more strongly associated with difficulties in learning mathematics than problems in memorising individual stimuli (Attout & Majerus, 2015). This observation is consistent with the fact that sequence often plays a central role in mathematics. As described above, number-sequence skills begin to develop in early childhood, and one of the most important requirements in their development is remembering counting words in the correct order. At a later stage, when calculating with multi-digit numbers, it is necessary to remember the place of each digit in the number; even small errors in the order will change the result. In order to understand a number, it is not enough to remember the individual digits; it is equally important to remember the order in which they appear. 

Motivational and emotional factors

Motivational and emotional factors are not the sole causing factors of mathematical learning difficulties (MD), as neuro-cognitive deficits lie at the core of learning difficulties. However, they definitely should be taken into account because they affect learning and response to support (Koponen et al., 2024) and might lead to math avoidance. In the context of learning difficulties, it is important to remember that a human being is not a machine but a thinking, interpreting, and feeling creature. Therefore, competence, learning, and learning difficulties cannot be simplified or understood solely through cognitive functions. A child’s beliefs and emotions about themselves and learning, as well as their motivation, shape how these difficulties manifest. These factors, together with individual temperament traits, influence, for example, how persistently a child continues to practice even when tasks feel challenging.

In mathematical situations, children may experience wide range of emotions. For some, math tests are positive opportunities to try out and demonstrate their skills. Slight nervousness helps them concentrate and do their best. For others, situations involving mathematics, calculations, and numbers cause fear and anxiety, unpleasant tension in the body, and worry about failure. At worst, the mind feels emptied of everything they learned. These unpleasant emotions and experiences related to mathematics are referred to as math anxiety (Richardson & Suinn, 1972). Anyone can experience temporary anxiety in certain math-related situations but, for some people, mathematics causes anxiety to such an extent that a tendency toward math anxiety can be considered a defining trait.

Although math anxiety is more common among children with math learning difficulties, it can affect children at all skill levels (Sorvo et al., 2017). Anxiety is believed to impact performance through working memory. In situations where worry and negative thoughts related to anxiety burden memory, retaining numbers and intermediate steps needed to solve math problems becomes difficult (Ashcraft & Moore, 2009). A familiar example is being at a store checkout when the total amount or change does not match what they had mentally calculated. Identifying the source of the error can suddenly become surprisingly difficult, even if the calculation is simple and would normally be solved instantly. The situation is not helped by the feeling that the line behind is growing and the calculation needs to be resolved quickly.

Children in early primary education can also experience math anxiety; at that stage, anxiety already appears to be linked to weaker performance (Sorvo et al., 2017). Research findings on the relationship between math anxiety and math performance have been contradictory regarding which influences the other: does poor skill lead to anxiety or does anxiety impair performance in evaluative situations? Recent studies (e.g., Szczygieł et al., 2024) suggest that the relationship is reciprocal. Among students who experience math anxiety, underperformance seems to be particularly caused by time pressure and the feeling of urgency, such as in test situations (Ashcraft & Moore, 2009). It is possible that some students’ true skill level never becomes apparent in assessment situations due to the impact of math anxiety on their performance. In addition to test situations, especially anxiety-inducing moments may include those involving social pressure, such as answering a teacher’s question during a math lesson or solving a problem on the board. In the worst cases, math anxiety can become so generalized that a person may find any math-related situation distressing.

Environmental factors

Parents’ mathematical skills are associated with their children’s mathematical development, both through genetic and environmental pathways. First, mathematical abilities are partly heritable, meaning that parents can pass on genetic predispositions that support or hinder the development of numerical and mathematical skills. Second, parents influence their children’s learning through the home math environment by providing math-related activities, helping with homework, and communicating positive attitudes and expectations about mathematics. Parents’ mathematical skill levels may also interact with these learning activities and related attitudes, indirectly influencing children’s mathematical development through the home learning environment. Parents with stronger mathematical skills are more likely to engage their children in numeracy-related activities and to foster positive attitudes toward mathematics, which in turn can support the development of children’s mathematical skills. As a result, children’s mathematical achievement is shaped by both inherited factors and the learning experiences and attitudes they encounter at home.

The home math environment (HME) refers to the ways parents support their children’s mathematical learning at home. Research has traditionally focused on math-related activities such as counting, number games, and helping with homework. More recently, the concept has been expanded to include parents’ attitudes, beliefs, expectations, and everyday communication about mathematics. Thus, children’s mathematical development is influenced not only by the learning opportunities parents provide but also by how parents think and feel about mathematics (Daucourt et al., 2021).

References

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Ashcraft, M. H., & Moore, A. M. (2009). Mathematics Anxiety and the Affective Drop in Performance. Journal of psychoeducational assessment, 27(3), 197-205. https://doi.org/10.1177/0734282908330580

Attout, L., & Majerus, S. (2015). Working memory deficits in developmental dyscalculia: The importance of serial order. Child neuropsychology, 21(4), 432-450. https://doi.org/10.1080/09297049.2014.922170

Daucourt, M. C., Napoli, A. R., Quinn, J. M., Wood, S. G., & Hart, S. A. (2021). The home math environment and math achievement: A meta-analysis. Psychological Bulletin, 147(6), 565–596. https://doi.org/10.1037/bul0000330

Donker, M., Kroesbergen, E., Slot, E., Van Viersen, S., & De Bree, E. (2016). Alphanumeric and non-alphanumeric Rapid Automatized Naming in children with reading and/or spelling difficulties and mathematical difficulties. Learning and individual differences, 47, 80-87.

Koponen, T., Aro, T., Leskinen, M., Peura, P., Viholainen, H., & Aro, M. (2024). Cognitive Skills, Math-Related Emotions, and Beliefs Explaining Response to Arithmetic Fluency Intervention. The Journal of Experimental Education, 92(3), 411–430.

Koponen, T., Eklund, K., Aunola, K., Poikkeus, A., Lerkkanen, M., & Torppa, M. (2025). Predicting Adolescent Arithmetic and Reading Dysfluency. Journal of learning disabilities, 58(3), 163-178. https://doi.org/10.1177/00222194241275644

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Lyons, I. M., Nuerk, H.-C., & Ansari, D. (2015). Rethinking the implications of numerical ratio effects for understanding the development of representational precision and numerical processing across formats. Journal of Experimental Psychology: General, 144, 1021–1035. http://dx.doi.org/10.1162/jocn.2009.21124

Richardson, F. C., & Suinn, R. M. (1972). The Mathematics Anxiety Rating Scale: Psychometric data. Journal of counseling psychology, 19(6), 551-554. https://doi.org/10.1037/h0033456

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Szczygieł, M., & Sarı, M. H. (2024). The relationship between numerical magnitude processing and math anxiety, and their joint effect on adult math performance, varied by indicators of numerical tasks. Cognitive Processing, 25(3), 421–442. https://doi.org/10.1007/s10339-024-01186-0

Sorvo, R., Koponen, T., Viholainen, H., Aro, T., Räikkönen, E., Peura, P., Dowker, A., Aro, M. (2017). Math anxiety and its relationship with basic arithmetic skills among primary school children. British journal of educational psychology, 87(3), 309-327. https://doi.org/10.1111/bjep.12151