Typical and atypical development in numeracy learning
In considering typical and atypical development in numeracy learning, refer back to Year 1, Module 2 of the Masters in Educational Practice (MEP) ‘Learner and adolescent development 0–19, Topic 1: Typical and atypical development’. It is crucial for teachers to have an appreciation of what typical development in numeracy learning looks like in a classroom so they can be aware of learners whose development may deviate from the rest of the class.
What is meant by ‘typical’ development?
The graph below is an example of a normal bell curve/distribution curve. The majority of learners in the classroom sit under the typical range, i.e. within the red section.
Learners who present with typical development in numeracy learning appear to start with ‘number sense, an intrinsic ‘feel’ for quantities and numbers’ (Butterworth and Yoe, 2004). They can move beyond the ones-based approach to quantities in number.
For further reading around mathematical development, refer to David C. Geary’s website (external link) for a reference list of publications on this topic.
What is meant by ‘atypical’ development?
Learners are usually considered atypical if they are exhibiting numeracy learning behaviours that are emerging in a way or at a pace that is noticeably different from their peers.
More able and talented
These learners deviate from the majority of their peers and sit on the right side of the distribution curve. In Wales, these learners are referred to as ‘more able and talented’ in numeracy, which means that they require enriched and extended opportunities to develop their numeracy ability. They are learners who achieve above the expected level in the end-of-key-stage teacher assessments. The Welsh Government has worked closely with the National Association for Able Children in Education (NACE) (external link) in developing quality standards and the Challenge Award for supporting more able and talented learners (see links below).
Learners with dyscalculia
These learners also deviate from the majority of their peers but sit on the left side of the distribution curve, with prevalence estimates for severe difficulties (disorders) in learning about numbers and arithmetic (dyscalculia) reported as between of 3.6 and 6.5 per cent [i.e. between 1.5 and 3+ standard deviations below the mean] (Lewis, Hitch and Walker, 1994; Gross-Tsur, Manor and Shalev, 1996).
What is meant by delay and disorder?
- Numeracy skills that are slow to emerge (delay) – the learner develops numeracy skills in the same way as other learners, but later.
Disorder (e.g. dyscalculia)
- The learner may have some numeracy skills but not others or the way the skills develop are different than usual, e.g. they struggle to move beyond a ones-based concept of number. In considering this, it is important to be clear that we distinguish between delay and disorder.
- If a learner who is exposed to the same levels of ‘appropriate and sufficient’ teaching as other learners does not learn the skill, then this is likely to indicate significant difficulties.
In considering learners who are experiencing learning difficulties in numeracy, Chinn (2012) proposes that we include those learners whose achievement in mathematics is at the bottom 20–25 per cent (approx. 1 standard deviation below the mean).
Prevalence estimates for severe difficulties (disorders) in learning about numbers and arithmetic (dyscalculia) are between of 3.6 and 6.5 per cent [i.e. between 1.5 and 3+ standard deviations below the mean] (Lewis, Hitch and Walker, 1994; Gross-Tsur, Manor and Shalev, 1996) – this is similar to estimates of disorders of literacy development (dyslexia).
- Identify a learner in your care who can be described as ‘typically developing’ in numeracy learning. What are the numeracy behaviours they are exhibiting?
- Identify a learner in your care who can be described as ‘atypically developing’ in numeracy learning. What are the numeracy behaviours they are exhibiting?
Identification of delay and disorder
In school, delay in acquiring numeracy skills can be identified by:
- screening learners
- teachers or parents/carers conversing and recognising ‘red flags’ in the development of the learner’s numeracy skills, i.e. signs or symptoms causing concern compared to other learners of a similar age. A good relationship with families is key here
- possible risk factors, e.g. the presence of other developmental disorders such as Dyslexia (Lewis, Hitch and Walker, 1994), ADHD (Gross-Tsur, Manor and Shalev, 1996; Ramaa and Gowramma, 2002); difficulties with working memory, spatial representation, language, motor functioning, executive functioning – planning and checking (Geary, 2007)
- another family member with significant numeracy difficulties.
- Is numeracy screening with learners undertaken in your school?
- What information is transferred from a previous school or educational setting to ascertain the learner’s developmental stage in numeracy learning?
- How is this information used to inform teaching practices?
Anxiety and numeracy
Anxiety can block both the willingness to learn numeracy (motivation) as well as the capacity to do so. Working memory is linked with achievement in numeracy and anxiety can adversely affect working memory. Chinn (2012) offers an interesting discussion of mathematics anxiety in his book ‘More Trouble With Maths’. Chinn goes as far as to suggest that when diagnosing dyscalculia, then some investigation of anxiety should be made.
- How might you recognise anxiety about numeracy in one of your learners?
- Consider two ways in which you might address ‘numeracy’ anxiety in your learners.
Chinn, S. (2012) More trouble with maths: A complete guide to identifying and diagnosing mathematical difficulties. Routledge, David Fulton Book.
Geary, D. C., Hoard, M. K., Byrd-Craven, J., Nugent, L. & Numtee, C. (2007) ‘Cognitive Mechanisms Underlying Achievement Deficits in Children with Mathematical Learning Disability’, Child Development, 78(4), pp.1343-1359.
Gross-Tsur, V., Manor, O. and Shalev, R. S. (1996) ‘Developmental dyscalculia: Prevalence and demographic features’. Developmental Medicine and Child Neurology, 1(38), 25-33.
Lewis, C., Hitch, G.J. and Walker, P. (1994) ‘The Prevalence of Specific Arithmetic Difficulties and Specific Reading Difficulties in 9- to 10-year-old Boys and Girls’. Journal of Child Psychology and Psychiatry, Volume 35, Issue 2, pp. 283-292.
Ramaa, S. and Gowramma, J. P. (2002) ‘A systematic procedure for identifying and classifying children with Dyscalculia among primary school children in India’. Dyslexia, 8, 67-85.