The Intersection of Language and Maths
In my work with children who face significant and persistent challenges with numbers, I have also encountered many with equally notable struggles in understanding and using language. Some of these children have language disorders that make it difficult for them to comprehend maths symbols and the language in the questions. Others struggle to find the right words to express what they know. I found that their vocabularies tend to be smaller and more restricted than what is typical for their age, and they often have trouble constructing grammatically correct sentences.
I am particularly intrigued by the connection between speech and language development and dyscalculia, a significant learning difficulty related to arithmetic. Could there be an overlap between these developmental challenges? By better understanding these overlap in difficulties we may be able to develop effective intervention strategies to support children struggling in both areas, leading to improved outcomes. While most children acquire these abilities naturally, some struggle in these areas, hindering their academic and social success.
Language is the central bridge that serves to connect non-symbolic primitive number approximate quantity system believed to be present in babies with symbolic number systems that begins to develop between 18-24 months.
Interestingly, this very foundation plays a pivotal role in mathematical reasoning that is further reliant on the child’s vocabulary and comprehension.
Understanding Speech and Language Development
Speech and language development comprises of a wide range of skills. These include:
- understanding spoken language (receptive language)
- producing speech sounds correctly (articulation)
- using language to express thoughts and ideas (expressive language)
- adhering to grammatical and social communication rules
This wide range of language struggles may be linked to Developmental Language Disorder (DLD).
DLD significantly affects a child’s ability to communicate, impacting key areas such as speaking, listening, reading, and writing. Previously known as specific language impairment, language delay, or developmental dysphasia, DLD is one of the most common developmental disorders, affecting about 1 in 14 kindergarten-aged children (NIDCD, 2023). Crucially, its effects can persist into adulthood, highlighting the importance of understanding how DLD fits into the broader landscape of speech and language development. Maths is highly language based and therefore children with DLD are at a greater risk of significant maths difficulties.
Understanding developmental dyscalculia and its linguistic and symbolic integration
Dyscalculia is also a developmental disorder and is a specific and persistent learning difficulty that impacts a child’s ability to understand and work with numbers. It may present as challenges in grasping numerical concepts, performing arithmetic operations, and applying number knowledge to solve word problems. Children with dyscalculia often struggle to develop “number sense,” an intuitive understanding of how numbers relate to each other and the ability to use numbers meaningfully and fluently.
Just as letters are embedded within a network of relationships (shape and sound) and when blended form words that convey meaning. Similarly, numbers are unique symbols with specific shapes, assigned with a declarative form, written and quantitative information that is sequenced along a mental number line.
In maths, we additionally use signs (e.g., +, =, %) that hold a symbolic meanings, and these operations are also described using specific words, such as “+” being referred to as “plus”, sum, “add.” This consistent use of terms, or collocation, helps reduce cognitive effort when learning or explaining mathematical concepts. Given the structured way both numbers and letters are embedded within networks of meaning, it raises the possibility of shared cognitive pathways that underlie the learning of both numerical and linguistic systems.
The Cognitive Link Between Language and Maths
Speech and language development and dyscalculia may seem like separate challenges—one involving verbal skills and the other numerical abilities—but they may rely on shared cognitive processes.
Key areas where these overlaps may include:
- Working Memory: Working memory is essential for temporarily holding and manipulating information. In language development, working memory helps children process and organise spoken words. In mathematics, working memory is needed to hold numbers in mind while performing word-problems, mental maths and calculations.
- Phonological Processing: Phonological processing refers to the brain’s ability to recognise and manipulate sound structures in language. This skill is crucial for learning to read, write and speak but it also plays a role in numeracy. For example, understanding number words and linking them to numerical values also requires phonological skills. Children who experience delays in phonological processing—whether in comprehension, expression, or both—may find it harder to connect number words to the corresponding numerical concepts, which makes solving arithmetic problems more difficult.
- Executive Function: Executive function includes cognitive skills needed for planning, organising, and problem-solving. These skills are important for both language development and mathematical reasoning. In language, executive function helps children organise their thoughts and form coherent sentences. In mathematics, it supports problem-solving by helping children break down tasks into manageable steps.
This co-occurrence could be attributed to some of the shared cognitive processes involved in both language and numeracy development.
There are domain specific and domain general areas in the brain that processes language; Broca’s area for speech production and grammatical structuring, located in the left frontal lobe. Wernicke’s area, in the left temporal lobe; understanding spoken and written language. Additionally, the angular gyrus, located in the posteroinferior region of the parietal lobe, helps interpret written words and symbols, facilitating reading comprehension and connecting visual inputs; auditory, visual or sensory with language.
“While he knows his numbers and manipulates these with fluency, he struggles with understanding simple words such as ‘share’, ‘divide’, ‘more than’. How can he grasp these words?”
The connection between language and mathematics becomes particularly evident when considering how mathematical ideas are processed, communicated and understood. Mathematical terms, symbols and expressions communicate specific meaning that we refer to as vocabulary.
Numbers, although manipulated through abstract symbols, are tied to language. For example, vocabulary such as “add”, “difference” or “double” are linguistically rooted, and introduced in classrooms through verbal instructions, or word problems. Nation (2001) argues that vocabulary should be tested in context because real-world language comprehension requires understanding words as part of a larger discourse, not in isolation.
Teaching isolated word lists does not provide the depth of understanding of a learner’s vocabulary.
Schmitt (2014) makes an important point that while the learner may know a word’s meaning, they may not fully understand its nuance, meaning, collocations, or pragmatic uses.
Dynamo Maths intervention addresses meaning of words through active participation and encouraging critical reasoning, beyond just numerical working-out.
Challenges in Language Development and Maths Learning
McGregor, K. K. (2020) states “As a population, people with DLD face significant risks. Compared to other students, those with DLD are 6 times more likely to have reading disabilities, 6 times more likely to have significant spelling problems, 4 times more likely to struggle with maths, and 12 times more likely to face all three of these difficulties combined (Young et al., 2002). People who have DLD are 6 times more likely than others to experience clinical levels of anxiety and 3 times more likely to have clinical depression (Conti-Ramsden & Botting, 2008).”
Addressing these challenges early on could be key to improving communication and learning outcomes.
Delays in speech and language can also influence the cognitive processes necessary for other learning areas and for some an overlap in processing numbers, a significant and persistent difficulty that affects 5-6% of the population known as dyscalculia (Shalev and Gross-Tsur, 2001) .
The Role of Early Intervention and Integrated Support
Children who experience challenges in both language and numeracy require purposeful and intentional assessments to identify areas of struggle. Early intervention is crucial, as language and maths skills are foundational for academic achievement. Incorporating language-rich maths instruction—where complex terms are broken down into accessible language—can improve comprehension. Activities that strengthen meaningful understanding of words are an additional step towards boosting both literacy and numeracy skills. Dynamo Maths takes a developmental approach and built within the intervention are ready-made Lesson Plans to engage the children in fun games where they take the lead and use language, vocabulary and critical reasoning. All this helps the interventionist to listen and observe if the child has comprehended the leaning. This shift towards active child participation gives children who are not meeting developmental milestones to independent, enquiry-based learning opportunities.
Conclusion
Evidence from Dynamo Maths shows that where opportunities are provided for children to participate actively, using critical thinking and reasoning, mathematics can provide a platform to develop language skills. Ros Fisher & Shirley Larkin (2008) explain that the opportunity for children to hold their space and exert their rules of participation rather than be managed by expectations or responses, the struggles for children with language difficulties will enhance.
The strong intersection between speech and language development and dyscalculia highlights the importance of early identification and targeted support. Both language and maths skills are crucial life skills.
References
Conti-Ramsden, G., & Botting, N. (2008). Emotional health inadolescents with and without a history of specific languageimpairment (SLI). The Journal of Child Psychology and Psy-chiatry, 49(5), 516–525. https://doi.org/10.1111/j.1469-7610.2007.01858.x
Fisher, R., & Larkin, S. (2008). Pedagogy or ideological struggle? An examination of pupils’ and teachers’ expectations for talk in the classroom. Language and Education, 22(1), 1-16. https://doi.org/10.2167/le722.0
McGregor, K. K. (2020). How We Fail Children with Developmental Language Disorder. Language, Speech & Hearing Services in Schools, 51(4), 981–992. https://doi.org/10.1044/2020_LSHSS-20-00003
Nation, I. S. P. (2001). Learning vocabulary in another language. Cambridge University Press.
National Institute on Deafness and Other Communication Disorders (NIDCD). (2023, May 8). Developmental language disorder. National Institutes of Health. https://www.nidcd.nih.gov/health/developmental-language-disorder
Schmitt, N.(2014). Size and Depth of Vocabulary Knowledge: What the Research Shows. Language Learning
Shalev, R. S., & Gross-Tsur, V. (2001). Developmental dyscalculia. Pediatric neurology, 24(5), 337-342.
Young, A. R., Beitchman, J. H., Johnson, C., Douglas, L., Atkinson,L., Escobar, M., & Wilson, B. (2002). Young adult academicoutcomes in a longitudinal sample of early identified and control children. The Journal of Child Psychologyand Psychiatry, 43(5), 635–645. https://doi.org/10.1111/1469-7610.00052
Karima Esmail
Co-founder of Dynamo Maths, an award-winning, research and evidence-based inclusive programme proven to support students with dyscalculia and those not meeting age-related expectations.
I have 15 years of experience as a senior lecturer at the University of Hertfordshire. More recently, I undertook research at University College London, which inspired the creation of Puffin Maths for the deaf and hard of hearing, which now provides access to the National Curriculum using British Sign Language (BSL). Puffin Maths was ‘Highly Commended’ at BETT 2022.
I have also co-authored Dynamo Post 16 Number Sense Profiler and Dyscalculia Self Perception Indicators Questionnaire.