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SEN in Numeracy and mathematical cognition - Coggle Diagram
SEN in Numeracy and mathematical cognition
Factors related to mathematical cognition
Language skills
Executive function skills - inhibitory control
Home maths environment
Spatial reasoning
Pattern recognition
Number knowledge
Maths anxiety
Understanding mathematical cognition - multi-level framework (Gilmore., 2023)
-> General cognitive skills <-> basic mathematical processes - (independently related to maths and impacting the components of maths, and interact with learning)
-> Leads to proficiency with specific components of mathematics (mediation between these factors)
-> Loads onto overall maths achievement, along with the first two factors
-> Loads onto overall maths achievement, along with the first two factors
-> Influenced by learning experiences throughout
Children’s Arithmetic Development: It is Number Knowledge, not the approximate number sense, that counts (Gobel et al., 2014):
ANS efficacy is a strong longitudinal correlation of arithmetic skills
Path models show that knowledge of numerals at 6 was a powerful predictor of growth in arithmetic skills, whereas variations in magnitude-comparison ability played no additional role in predicting variations in arithmetic skills
Verbal processes in labelling numbers and ability to translate between numerals and verbal codes constrains arithmetic development
Number cognition
Numerical cognition relates to the acquisition and development of quantitative skills
Von Aster & Shalev’s (2007) typology of numerical cognition
-> Non-symbolic number system (magnitude and how many) -> symbolic number system -> more complex mathematics skills
The non-symbolic number system provides a foundation for the symbolic number
These two systems combined, provide a platform for more complex mathematics abilities are established
However, the relationship between the two systems remain debated
Non symbolic number understanding - develops in infancy and precedes language
Object tracking system (OTS) - supports exact magnitude identification in small quantities (up to 4)
Approximate number system - ANS stores approximate representations of numerical magnitude in the brain without symbols (Cordes et al., 2001; Dehane., 2011; Feigenson et al., 2004) - asking which set is bigger without counting
-> ANS ratio effect - participants respond more accurately and faster when the ratio between the amounts that they are comparing is larger (Barth et al., 2003) - Szjudlarek & Brannon (2017) review research
-> Chu et al (2015) - 191 3-4 children, ANS accuracy was a significant predictor of maths achievement
-> However, more recent research highlights methodological issues with ANS measures (Gilmore et al., 2011; Krejcsi et al., 2024) - could be measuring inhibitory control instead
The dual mechanism view suggests these systems work together to support our number knowledge (VanMarle et al., 2018)
Symbolic number system -
The symbolic number system is the way in which symbolic numerals are represented in the brain (Mussolin et al., 2014)
There is convincing evidence that early symbolic skills predict later mathematical outcomes (Amland et al., 2025)
-> ANS did not predict symbolic skills - they could be developing alongside each other rather than in a linear way
Gobel et al (2014) - 173 6 year olds (measured from year 1 to year 2)
-> Vocab, arithmetic, magnitude comprehension and number ID skills at T1 loaded onto arithmetic skills at T2
-> Verbal coding of numbers is important - backs up Gilmore's research
Spatial cognition
Spatial cognition - (Farran et al., 2024):
Support the understanding of the properties of objects (location and orientation)
The relationships between objects
Help us visualise, mentally represent and manipulate objects
Spatial abilities are critical for mathematics:
Children with strong spatial abilities have strong mathematics performance (evidence from 45 studies; Atit et al., 2022)
The connection between space and math may be one of the most robust and well-established findings in cognitive psychology (Mix & Cheng., 2012)
-> higher transfer gains in maths areas closer to spatial cognition, such as geometry
Spatial abilities can be trained (evidence from 29 studies; Hawes et al., 2022)
Children from low-income backgrounds show larger gains in maths than children from high income backgrounds (Bower et al., 2020; Schmitt et al., 2018)
-> 30% maths disadvantage gap - spatial training could close this gap
The role of language:
Language skills are associated with success in mathematics
Le Fevre et al., 2010 - show that linguistic measures are reliable early predictors of achievement in maths
Moll et al., 2015 - reported that individuals with language difficulties or reading problems also have poor performance in maths
Specific mathematics language and spatial language is important (Pruden et al., 2011; Purpura et al., 2017)
-> Explicit teaching of maths language can increase knowledge
Other factors in maths cognition
Maths anxiety -
Feelings of tension, worry or fear when engaging with mathematical tasks (Ashcraft., 2002)
-> Anxiety of children and practitioners - practitioner anxiety can increase children’s anxiety, interventions can focus on this
Can occur even in children who have the cognitive ability to succeed in mathematics (Ramirez et al., 2013)
-> Parental anxiety about maths can transfer, young children have maths anxiety and thus it does not develop with more experience
Maths anxiety can emerge in primary school (Ramirez et al., 2013; Sorvo et al., 2017)
Children who experience greater anxiety often perform less well in mathematics negative association between maths anxiety and achievement (r = -.28; Barroso et al., 2021)
(What came first?) Difficulties with mathematics can contribute to anxiety, while anxiety may further interfere with mathematical learning and performance (Carey et al., 2016)
-> Maths anxiety (worry, avoidance, cognitive interference) -> debilitating anxiety -> mathematical difficulties (errors and negative experiences) -> deficit theory -> maths anxiety
Executive functions
Help us to regulate our thoughts and behaviour to achieve goals (Diamond., 2013)
Three core executive functions are particularly relevant to mathematics
-> Working memory
-> Inhibitory control
-> Cognitive flexibility - use of tasks that challenge this can create pedagogical issues as the task becomes more difficult for children that struggle with this
Associated with mathematical achievement, even after accounting for other cognitive abilities (Cragg & Gilmore., 2014)
Executive function difficulties may contribute to mathematical learning difficulties, particularly when tasks involve multiple steps, complex instructions or competing information
34% of variance in mathematics achievement is explained by executive function skills (Cragg et al., 2017)
-> Direct effect - predict maths achievement, independent of numerical skills
-> Indirect effect - EF predict mathematics achievement through their effect on numerical skills
--> Domain-specific numerical skills - number magnitude representation, numerical knowledge and simple arithmetic skills -> maths achievement
Cognitive factors underlying maths skills
Longitudinal predictors - Amland et al., 2025
-> Symbolic number skills
-> Spatial ability
-> Nonverbal intelligence
-> Language comprehension
-> Non-symbolic number skills
Links between behavioural regulation and preschoolers’ literacy, vocabulary and maths skills (McClelland et al., 2007):
Behavioural regulation (measured with Head-to-Toes task) significantly and positively predicts literacy, vocabulary and maths skills on Woodcock Johnson tests of achievement
Growth in behavioural regulation also positively related to growth in these factors
Numeracy for life:
Numeracy = the ability of people to use mathematical and data skills and knowledge to solve everyday problems
Reading with young children happens five to seven times a week on average - number related play happens around once a week
Numeracy = recognise when tools are needed
Mathematical knowledge = understanding and practising these skills
Developmental dyscalculia
Terminology - Dyscalculia, Mathematical Learning Disabilities (MLD), Mathematics Disorder (MD)
Prevalence - 5-7% (Shalev., 2007) - debate remains
Smaller or less active parietal regions (Kucian et al., 2011)
Persistent - not developmental delay
Frequently comorbid with dyslexia (Gross-Tsur et al., 1996)
Some debate about characterising DD (Dowker., 2024)
Signs - Roulstone et al., 2026 - teacher awareness is low for dyscalculia
Measures - struggles to understand mathematical concepts - speed, time etc and problem handling money - working out change etc
Spatial / temporal - Difficulties with telling time, left/right confusion and map reading difficulties
Memory - cannot accurately recall number facts, constantly re-learning and recapping skills and organisational issues
Counting - difficulty navigating back and forth along a number line or sequence, can lose place easily, finds counting in twos and threes etc problematic
Calculations - lack confidence in their answers and problems transferring information
Numbers - struggles with place value and struggles to understand chronology
Foundational numerical capacities and the origins of dyscalculia (Butterworth., 2010):
Deficit in numerosity coding which arithmetic builds on causes dyscalculia - need longitudinal and intervention studies to see this through fully
Competing theories of ANS deficit and numerical capacity deficit
Dyscalculia: From Brain to Education (Butterworth et al., 2011):
Adaptive software interventions can act as effective evidence-based education for dyscalculic learners due to their impairment in numerosity coding - difficulty mapping symbols to magnitudes
Diagnostic criteria should encapsulate the possible range of dyscalculia deficits
Personalised learning applications help to evaluate theory-based intervention
What it looks like in the classroom -
Number magnitude -> Difficulty deciding if 47 or 74 is larger
Number relationships -> Difficulty understanding that 8 can be partitioned into 5 and 3
Arithmetic fact retrieval -> Continuing to count to solve simple additions
Place value -> Confusing tens and units
Calculation -> Difficulty selecting or maintaining appropriate calculation strategies
Research interventions -
Mental number line training in children with developmental dyscalculia (Kohn et al., 2020; Kucian et al., 2011)
67 children with DD (34 training, 33 control, 7-11 years)
12 weeks of computer-based training targeting number representations and arithmetic
Moderate improvements in arithmetic (g = .49), number line processing (g = .55) and quantity comparison (g = .44)
Improvements largely maintained at three-month follow-up
Children with lower maths anxiety and without co-occurring literacy difficulties benefitted more
Mathematics and learning disabilities (Geary., 2004):
MLD children - average number processing skills, but show persistent deficit in some areas of arithmetic and counting knowledge - use problem-solving skills seen in younger children
Commit procedural errors - semantic memory deficit, working memory, EF
Poor attentional control and poor inhibition
How to support children with maths difficulties: Targeted, structured and responsive to individual
Explicit, systematic instruction -> model strategies, provide guided practice and give immediate feedback (Gersten et al., 2009; Fuchs et al., 2021)
Concrete and visual representations -> Use counters, ten frames, base-ten blocks and number lines, linking these to numerical symbols (Gersten et al., 2009)
Teaching number relationships -> Practise comparing, ordering, partitioning, and combining numbers (Dowker., 2005; Kroesbergen & Van Luit., 2003)
Targeted arithmetic instruction -> Explicitly teach addition and subtraction strategies, number bonds and arithmetic fact retrieval (Fuchs et al., 2013)
Individualised intervention -> assess specific difficulties and target teaching to the child’s needs (Dowker., 2005)
Regular progress monitoring -> use short assessments to identify errors, track progress and adapt instruction (Gersten et al., 2009)
Early identification and interventions for students with mathematics difficulties (Gersten et al., 2005):
Mathematics difficulties are not stable over time
Presence of reading difficulties seems related to slower progress in many aspects of mathematics
Almost all students with MD demonstrate problems with accurate and automatic retrieval of basic arithmetic combinations, such as 6+3 - reliable measures include magnitude comparison, sophistication of counting strategies and fluent identification of numbers, as well as working memory
Translating research
Communication is essential for translating research into practice i.e. evidence based practice
This includes communication with teachers, special educational needs coordinators (SENCO’s) or other educational professionals
What are the barriers to effective communication with educators -
-> Teachers are extremely busy, and need clear, easy to implement guidance
-> You must pay for many journal articles
-> Journal articles can be very theory-based and technical
-> How should teachers judge which studies are good quality
Why do teachers engage with research evidence - it needs to be relevant and accessible to increase its use in educational practice
Finding -> implication for researchers (Dagenais et al., 2012 - 24 study review)
-> Research is used infrequently - publishing findings is not enough
-> Relevance to practice matters - provide clear, practical recommendations
-> Research literacy influences engagement - use accessible language and formats
-> Collaboration supports research use - build relationships with educators
-> Time and school culture matter - support implementation within school contexts
This paper is outdated - more research evidence is being implemented in the UK
Barriers - time, training and resources available as well as culture within schools
Translation - it is about intervention not about jargon and about relevance to practice
Using social media to communicate with educators -
LinkedIn - educators use for professional networking, CPD, research updates and educational discussions
-> Opportunities for researchers - share research findings, connect with education professionals and promote resources
Instagram - visual teaching ideas, classroom activities, short videos and practical resources
-> Use infographics, carousels and reels to make research accessible and engaging
Facebook - teacher communities, SEND networks, specialist groups and peer support
-> Share resources, engage in discussions and reach established practitioner communities
Choosing the correct platform and format is important based on the audience, to communicate in an accessible, relevant and engaging way
Microblogging -
-> Be clear and engaging
-> Use hashtags to highlight key words
-> Talk to people not at them
-> Add an image for attention
-> Less than 300 characters
-> Use humour appropriately
-> Use tags
Blogs - the purpose of a blog is to aid marketing to a point where the content you deliver is targeted specifically to the wants and needs of your audience
-> Provide answers to their most commonly asked questions or provide advice to areas within your niche that your business is an expert on
Dyspraxia and developmental coordination disorder (Dusnmuir et a., 2024)
Marked impairment in motor coordination and Shown from early age and observed as clumsiness, and slowness and inaccuracy in performance of motor skills learning of everyday motor skills
Used when difficulty is not better explained by specific congenital or acquired neurological conditions affecting movement or an ID
Shown from early age and observed as clumsiness, and slowness and inaccuracy in performance of motor skills
Theory - difficulty with automatisation of motor skills, or difficulty with sequencing and predicting the consequences of a motor (Zwicker et al., 2012)
-> Also theorised to be due to ineffective communication between the sensorimotor network in the brain and other key functional networks (Rinat et al., 2020), such as spatial memory
Children with DCD have difficulty with motor tasks in the classroom, particularly with handwriting - if it is not fluent and automatic, there is a greater working memory load and on the cognitive resources that could be used for planning and drawing on language
Longer pauses between each letter rather than longer drawing - longer when task was more complex
This could be due to motor learning and sequencing letters taking longer, cognitive development of planning and other EF and having less hand strength (Prunty et al., 2013)
DCD can impact educational outcomes longterm, but identifying early and providing targeted support is helpful
However, barriers can be unfamiliarity and associated SES features
Many young people show areas of difficulty in visuospatial organisation, psychomotor skills and abstract thinking in perceptual concepts (Portwood., 2005)
Tasks such as driving a car also become hard in adulthood, leading to a new set of challenges as an adult (Kirby et al., 2011)
Can lead to mental health risk (Kirby et al., 2013)