In almost every classroom, there are pupils who try hard in mathematics and still feel lost. They listen carefully, follow instructions, and yet numbers never quite stick. Quantities feel slippery, procedures break down halfway, and even familiar tasks require enormous effort. For learners with dyscalculia, this experience goes far beyond a dislike of math.
Dyscalculia is a specific learning difficulty that affects number sense, quantity processing, and the ability to manipulate numerical information, even when instruction is clear and well-structured (Butterworth, Varma, & Laurillard, 2011).
Recognising dyscalculia means changing how we interpret pupils’ struggles. These learners are not careless, unmotivated, or inattentive. Research shows that their difficulties are rooted in how numerical information is represented and accessed cognitively, not in intelligence or effort (Price & Ansari, 2013). Once this perspective is adopted, the pedagogical question shifts. The issue is no longer how to make pupils adapt to mathematics, but how to adapt mathematics to pupils with different ways of thinking.This change in perspective has practical implications for how mathematics activities, materials, and classroom experiences are designed.
One of the strongest insights from research is that pupils with dyscalculia need more time and more experiences to build meaning before abstraction. Mathematical symbols only become useful when they refer to something the learner already understands. Educational psychology consistently supports the use of a concrete–representational–abstract progression, especially for learners with persistent difficulties (Fyfe et al., 2014). What is often overlooked, however, is that this progression is rarely linear. Many learners need to move back and forth between manipulation, visualisation, and symbols over a long period of time.
For this reason, approaches that deliberately slow down the introduction of formal notation are particularly powerful. When learners are first invited to explore a concept through action, discussion, and everyday examples, they can begin to form mental structures that later support symbolic thinking. Learning designs structured around stories, riddles, manipulation, and collaboration naturally reflect this pedagogical approach. This is the direction adopted in the Enigmathico project, where mathematical concepts are introduced through structured sequences built around stories, riddles, manipulation, and collaboration, rather than in isolation. This extended phase of exploration is especially supportive for pupils with dyscalculia, who rely heavily on concrete reference points to stabilise understanding.
Manipulation plays a crucial role here, but it becomes even more effective when combined with play. Place value, for example, is easier to grasp when pupils regularly take part in simple exchange games, trading ten single objects for one “ten” token while playing a board game or managing points in a shared challenge. Through repeated action, “ten ones make one ten” becomes something they do, not just something they hear.
Fractions benefit greatly from visual and playful tools at this age. Using fraction circles, strips, or paper “pizzas,” pupils can build, compare, and share parts of a whole in concrete situations such as a classroom shop or a cooking game. Games like fraction dominoes or matching activities help stabilise recognition and comparison without pressure. Research shows that pupils who develop these strong visual models of fractions achieve deeper and more lasting understanding than those who work mainly with symbols (Siegler et al., 2013). For learners with dyscalculia, these concrete experiences are not optional supports; they are the essential pathway through which abstraction later becomes meaningful.
Emotional experience matters just as much as cognitive structure. Many pupils with dyscalculia associate mathematics with repeated failure, anxiety, and loss of confidence. Math anxiety has been shown to interfere directly with working memory and performance, creating a vicious cycle that disproportionately affects vulnerable learners (Ashcraft, 2002; Maloney & Beilock, 2012). In this context, playful and game-based approaches can offer a powerful counterbalance, but only when they are designed with learning in mind.
Games that focus on a single mathematical idea, provide immediate feedback, and allow mistakes without public exposure can genuinely transform practice into participation. A simple example is a number-line board game in which pupils roll a die and move a token forward or backward. The result of each move is instantly visible: if a pupil lands on the wrong number, the board itself invites discussion and adjustment without singling anyone out. The feedback comes from the material, not from the teacher’s judgement. Rather than being evaluated, pupils are invited to try, adjust, and try again, and thus offered emotional safety. In learning designs that use riddles or challenges as entry points, errors become part of the investigation rather than evidence of failure. This shift is particularly important for learners with dyscalculia, who often disengage when they feel constantly judged by speed or accuracy.
Another key support lies in storytelling and meaningful context. Bare numbers can feel arbitrary, especially for pupils who struggle to retain them. Stories give numbers a role and a reason to exist. Bruner (1991) argued that narrative is one of the primary ways humans make sense of the world, and this insight has important implications for mathematics education. When problems are embedded in situations that resemble real or imaginable experiences, learners can anchor reasoning in meaning rather than memorisation. The narrative context also acts as a memory anchor, helping pupils recall the mathematical situation more easily than abstract numbers alone.
Contextualised mathematics also helps reduce cognitive load. When learners recognise the structure of a situation, they can devote more attention to the mathematical relationships involved. Research on realistic and narrative-based mathematics shows that stories act as a bridge between language and logical reasoning, supporting learners who struggle with purely symbolic representations (Van den Heuvel-Panhuizen, 2012). For pupils with dyscalculia, this bridge is essential.
Narrative approaches are particularly helpful for multi-step problems, which place heavy demands on working memory. When each step corresponds to an event in a story, learners can externalise their thinking through drawings, objects, or discussion. The final equation then appears not as an abstract demand, but as a concise record of something that has already been understood. In pedagogical methods that rely on story-driven challenges, learners often revisit the same narrative framework across sessions, allowing familiarity to reduce cognitive effort while mathematical complexity gradually increases.
Beyond individual strategies, inclusion depends on classroom culture. Pupils with dyscalculia benefit from environments where tools such as number lines, manipulatives, and visual supports are normalised and available to everyone. When these tools are presented as “smart strategies” rather than special accommodations, they lose their stigma. Removing unnecessary time pressure and valuing explanation over speed further supports learners whose understanding develops more slowly but just as meaningfully.
Progress for pupils with dyscalculia is often uneven and non-linear. Yet, through concrete experiences, emotionally safe practice, and meaningful stories, many develop a functional and, at times, confident relationship with mathematics. Approaches that combine manipulation, collaboration, and narrative show that inclusion does not mean simplifying mathematics. It means recognising that understanding grows over time, through experience, and through human connection.
When learning feels like unravelling an enigma worth exploring, rather than passing a test, mathematics opens up to everyone. This perspective guides the pedagogical approach adopted in Enigmathico.
References:
Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science, 11(5), 181-185. https://doi.org/10.1111/1467-8721.00196
Bruner, J. S. (1991). The narrative construction of reality. Critical Inquiry, 18(1), 1-21. https://doi.org/10.1086/448619
Butterworth, B., Varma, S., and Laurillard, D. (2011). Dyscalculia: From brain to education. Science, 332(6033), 1049-1053. https://doi.org/10.1126/science.1201536
Fyfe, E. R., McNeil, N. M., Son, J. Y., and Goldstone, R. L. (2014). Concreteness fading in mathematics and science instruction: A systematic review. Educational Psychology Review, 26(1), 9-25. https://doi.org/10.1007/s10648-014-9249-3
Maloney, E. A., and Beilock, S. L. (2012). Math anxiety: Who has it, why it develops, and how to guard against it. Trends in Cognitive Sciences, 16(8), 404-406. https://doi.org/10.1016/j.tics.2012.06.008
Price, G. R., and Ansari, D. (2013). Dyscalculia. In D. Reisberg (Ed.), The Oxford handbook of cognitive psychology (pp. 781-794). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780195376746.013.0050
Siegler, R. S., Thompson, C. A., and Schneider, M. (2013). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273-296. https://doi.org/10.1016/j.cogpsych.2011.03.001 Van den Heuvel-Panhuizen, M. (2012). The role of contexts in assessment problems in mathematics. ZDM – The International Journal on Mathematics Education, 44(4), 571-582. https://doi.org/10.1007/s11858-012-0408-6
