OLIVER JOHN VELLA, DEPARTMENT OF MATHEMATICS, KING’S COLLEGE SCHOOL, WIMBLEDON, UK
Introduction
Supporting neurodivergent learners has become an increasingly central part of my classroom practice, particularly in my Year 9 bottom-set maths group, where several pupils present with attention deficit hyperactivity disorder (ADHD), a neurodevelopmental condition involving differences in attention, inhibition and self-regulation. Over time, I realised that many of the traditional expectations on which I had relied – silent working, extended copying, tightly controlled movement – were unintentionally creating barriers. What looked like disengagement was often the environment asking pupils to do internally what they simply couldn’t yet manage.
This sparked a desire to look more closely into the research in this area. Barkley’s early work on behavioural inhibition (1997) offered a clear explanation: students with ADHD struggle not because of motivation, but because inhibition, working memory, self-talk and emotional regulation are harder to internalise. These executive functions – the mental processes that we use to plan, remember, regulate emotions and stay focused – often need to be externalised (Barkley, 2012, 2015), made visible, structured and supported in the environment. That idea became the turning point for me.
Research that informed my practice
Barkley’s model changed the way in which I interpreted what I was seeing. Movement, talk or emotional intensity were not signs of defiance but attempts to regulate and stay engaged. Barkley’s work has shaped how I design tasks, structure lessons and understand the behaviours of the ADHD pupils in my class. Once I understood that these pupils struggle to internalise working memory, self-talk, emotional regulation and motivation, it became obvious that my classroom needed to externalise these processes for them. Other research reinforced this shift. Rapport et al. (2008) and Kofler et al. (2017) show that hyperactivity can support cognitive performance. Gathercole and Packiam Alloway (2008) and Holmes et al. (2014) highlight how vulnerable working memory is in ADHD, especially when tasks involve dense visual information. Morsink et al. (2021) emphasise the importance of autonomy-supportive environments where pupils can externalise thinking through talk and movement. Together, these studies helped me to see that the pupils weren’t the problem – the environment was.
How I adapted my practice
Reducing cognitive load (externalising working memory)
I now provide pre-printed worksheets with one or two carefully chosen examples. This reflects Barkley’s argument (2012) that pupils with ADHD need working memory demands to be externalised. In maths, this has been especially helpful when introducing expanding and factorising expressions or solving linear equations; pupils can focus on the process rather than copying the setup from the board.
Allowing purposeful movement (externalising self-regulation)
I stopped treating movement as something to suppress. Students can walk to the board, stand while working or briefly step away. Barkley (2015) notes that physical movement often acts as an external regulatory mechanism. In practice, allowing movement reduces frustration and helps students to stay with the task for longer.
Encouraging talk as thinking (externalising internal speech)
I now encourage pupils to verbalise their reasoning. Barkley (2012) argues that pupils with ADHD struggle to internalise self-talk. In mathematics, narrating each step – for example, ‘I’m expanding the brackets first… now I’m dividing both sides…’ – has improved accuracy and reduced cognitive strain, especially in algebra and rearranging trigonometric formulas.
Relational warmth (externalising emotional regulation)
High fives, fist bumps and brief, encouraging check-ins have become part of the classroom rhythm. Barkley (2015) highlights that emotional regulation is affected by impaired inhibition, meaning that pupils often rely on external relational cues. These small interactions help pupils to reset, feel safe and re-engage with learning. They also build trust, which I’ve learned is often the gateway to mathematical risk-taking. This aligns with wider research showing that pupils with ADHD experience more relational turbulence and benefit from warm, responsive teacher–student relationships (Ewe, 2019).
Structured play (externalising motivation)
Towards the end of lessons, I often use an online maths game, such as Blooket. Barkley (2012) notes that pupils with ADHD benefit from immediate, external reinforcement. Quick-fire retrieval games on topics like percentages, indices or trigonometric ratios give pupils fast feedback and a sense of success, ending lessons positively while reinforcing fluency.
Impact on learning outcomes
The impact has been significant. Several students who previously experienced fluctuating performance now show more stable or upward-trending results. For learners whose progress is often disrupted by anxiety or overload, this consistency matters.
I have also noticed:
- greater willingness to attempt challenging questions
- improved persistence with multi-step tasks
- fewer emotional outbursts
- more confident participation at the board
- stronger peer relationships
- a calmer, more predictable classroom climate.
These outcomes suggest that externalising executive functions, exactly as Barkley recommends, creates a learning environment where neurodivergent students can access mathematical thinking more reliably. These adjustments have also benefited the wider class. Clearer modelling, reduced cognitive load, relational warmth and predictable routines support neurotypical students too, creating a calmer environment where more learners feel confident to participate and take risks.
Conclusion
This journey has reshaped my understanding of what equitable mathematics teaching looks like. Supporting neurodivergent students does not mean lowering expectations; it means redesigning the environment so that they can access higher-level thinking on their own terms. By externalising working memory, self-talk, emotional regulation and motivation, I have created a classroom where students with ADHD can thrive academically, socially and emotionally. These changes have strengthened not only students’ confidence but also my own belief that relational, flexible, evidence-informed teaching can transform mathematical learning for those who need it most.
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