Over the past 18 months two committees, the SpLD Assessment Standards Committee (SASC) and the British Dyslexia Association dyscalculia and mathematics learning difficulties committee, have been actively working on a new definition for dyscalculia and assessment guidelines to support diagnostic assessment. The assessment guidance was published in December 2019 and can be accessed here http://bit.ly/SASCDyscalculia.

This article introduces the new definition and offers a personal perspective on the need for a continued and enhanced focus on understanding barriers to learning mathematics.

The newly published definition of dyscalculia is:

**Dyscalculia is a specific and persistent difficulty in understanding numbers which can lead to a diverse range of difficulties with mathematics. It will be unexpected in relation to age, level of education and experience and occurs across all ages and abilities.**

**Mathematics difficulties are best thought of as a continuum, not a distinct category, and they have many causal factors. Dyscalculia falls at one end of the spectrum and will be distinguishable from other mathematics issues due to the severity of difficulties with numbersense, including subitising, symbolic and non-symbolic magnitude comparison and ordering. It can occur singly but can also co-occur with other specific learning difficulties, mathematics anxiety and medical conditions.**

At the heart of the definition is a core deficit model – in other words, dyscalculia is a specific difficulty in understanding numbers. This does not exclude other challenges that may exist around mathematics learning, nor does it suggest that these difficulties will not cause problems in the learning of mathematics. Recognising maths difficulties as a continuum may be slightly disingenuous as this indicates a uni-dimensional domain, when in fact difficulties should be considered across a range of areas, each of which can impact on doing and learning maths. Indeed, I often explain maths difficulties as a ‘blob’ with dyscalculia lying as a specific subset within this.

A significant driver for creating a consensus definition has been a desire to allow a more informed debate round mathematical learning difficulties, particularly in the learning environment, which will, with the help of evidence-based guidance, allow teachers to recognise some of the barriers, at least those that relate to the development of mathematical cognition, to better understand why a learner may be struggling; to start to help to unpick the learner. Or, the question that Brian Butterworth (2019, pg 9) recognises as being needed to be asked;

Why is this child failing to understand what his or her classmates understand?

In the last 20 years, the study of dyscalculia and maths learning difficulties has moved forward at some pace, with excellent and compelling arguments around mathematical cognition and the nature of impairments put forward by contributors from across the globe. Without doubt, we have a sound understanding of many aspects of the development of mathematical thinking, and a strong evidence base for a specific impairment in a ‘sense of number’ or ‘sense of magnitude’ (Leibovich et al., 2013, Butterworth, 2019).

In considering a definition, what is being defined must be measurable, and there should be sufficient consensus amongst peers that what is being measured has a direct relationship with what has been defined. This creates tension around any measurement of cognition or psychometric testing and provides a strong argument against labelling – how sure are we that what we see directly relates to what we seek to measure? Or are we fitting the measurement to what we want to see? So, there is a potential dichotomy between seeking information to help a child develop skills and understanding because they clearly have a learning barrier and trusting that any assessment we undertake is providing us with accurate and insightful information.

One approach is to think of the ability to ‘do’ maths as a subset of the ability to ‘learn’ maths. A sense of number relates to a set of skills which develop from an innate ability to make magnitude comparisons. Included within this sense of number are non-symbolic and symbolic magnitude comparisons, the capability to subitise efficiently, estimation skills, ordering and an aptitude for seeing how numbers work. We can think of the ability to ‘do’ maths as a measure of the efficiency of a person’s sense of number. If someone has a weak sense of number in comparison to their peers, they will be less efficient in developing a range of mathematical knowledge and skills.

The core components of a sense of number; subitising, symbolic and non-symbolic magnitude comparisons, and ordering (both cardinal and ordinal), can all be measured discreetly and with an acceptable level of validity. Therefore, it is possible to observe an impairment in ‘sense of number’ through appropriate and reliable testing

Learning maths requires more than an efficient ‘sense of number’. Abilities around working memory, speed of processing, literacy, attention and fact recall can all have a significant impact on learning mathematics and need to be considered in any assessment. The impact of resilience, anxiety and mindset also play a role in learning. However, these factors are not domain-specific. They are common to other specific learning difficulties such as dyslexia, dyspraxia and ADHD and therefore may be considered to be domain-general difficulties, even if their impact is seen most specifically in the mathematics classroom.

The manifestations of difficulties with mathematics in the classroom are many and varied and have always created challenges in supporting learners who struggle with number.

Our intuition allows us to recognise the danger signs in the classroom: difficulty recalling facts, slow processing, avoiding work, forgetting what was done and seemingly remembered before lunch, the shock and fear of going to the ‘dark side’ of the decimal point, being able to cut up a pizza and happily sharing the pieces with their friend but not grasping fractions in an abstract form, and that shrug when you ask “does your answer seem right to you?”.

Our observation allows us to recognise that people learn differently, have different strengths and weaknesses, understand subject knowledge in different ways, and exhibit different behaviours in the learning environment. Some learners get low marks because they withdraw from learning; others seem to work as hard as they realistically can but make slow if any progress.

It seems reasonable that the foundation of good teaching is a sound understanding of the learner drawn from meaningful and insightful ongoing assessment, focusing not only on their subject knowledge and skills but their attitudes, motivations and metacognitive abilities; this, in turn, can lead to personalised learning, guiding the learner forward most efficiently and effectively. Finally, we need to take account of emotion, as all learning is an emotionally mitigated activity – know the learner, teach for the learner, and make their experience positive and safe. So far, so good, but this entails the analysis of broad and often unobtainable data – not helped by a lack of certainty about the questions we are asking of our data.

The purpose of the definition is to allow for better questions to be asked of any data collected. The definition allows the collection of more granular information about an individuals strengths and weaknesses around mathematical cognition. As the guidance that supports the definition asks for a holistic examination of a learners knowledge and skills, it is intended that assessors and teachers will be able to build a detailed picture which will help inform personalised learning.

Moving forward, there will be challenges and debates. Elliot and Grigorenko have challenged what they describe as the cultural meme of dyslexia. The concern is that understandings of both the causation and manifestation of dyslexia is wooly. Indeed, I would be inclined to agree that there is a difference in understanding between professionals and the wider population about what difficulties with reading and spelling look like and some misinformation and conflabulation has not helped. It has been the intention of the committees involved to pay heed to the ‘dyslexia debate’ and to be precise about what dyscalculia is. This will undoubtedly create difficulties around labelling and concerns that a diagnosis of a Specific maths Learning Difficulty is somehow less significant than a diagnosis of dyscalculia. This is not the case, any maths difficulty can have a significant impact if significant, unrecognised or ignored. Dyscalculia merely describes a specific sub-type that needs to be considered taking account of the difficulties in developing efficient numbersense. The dyscalculic is likely to need support with their lack of numbersense alongside scaffolding inefficient working memory, but the learner who has working memory problems but no evidence of an impairment in their sense of number will also require support.

What is important is the debate now moves into the open for the next stages. So over to you, the practitioners to pick through the bones and to make comment. Equals Online is an excellent forum for debate such as this and we hope that you will engage with us to make the definition work equitably.

Butterworth, B. (2019). *Dyscalculia. From science to education*. Abingdon. Routledge. Pg 9.

Elliott, J.G. & Grigorenko, E.L. (2014). The dyslexia debate. New York: Cambridge University Press.

Leibovich, T., Katzin, N., Harel, M., and Henik, A. (2017) From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition. *Behaviour and Brain Sciences 1–62. *