



 What is Dyscalculia?  Developmental Dyscalculia  Dyscalculia Symptoms  The NumberSense MMR™ Framework  



What is Dyscalculia? 



Pronounced DISKALKOOLEEAH, dyscalculia comes from Greek and Latin and means ‘counting badly’.
Dyscalculia is a specific learning disorder where the pupil's arithmetical ability is far below that expected for a person of their age, intelligence and education. A dyscalculic pupil can usually perform adequately in all areas except in the acquisition of arithmetic skills. Dyscalculia can arise as a result of a stroke or an injury and is known as acquired dyscalculia. Neuroscience research suggests that dyscalculic individuals may have a specific neural deficiency in the intraparietal sulcus part of the brain and the cells in that part of the sulcus are either weak or damaged. (Butterworth, 2012)
Developmental dyscalculia is encountered due to factors such as cooccurring difficulties, biological conditions, environmental deprivation, poor teaching or a curriculum that is moving too rapidly. This is known as developmental dyscalculia. Developmental dyscalculia is a common cognitive interference; its prevalence in the school population is about 56% (Shalev, 2000). 



Developmental Dyscalculia 



A pupil’s maths acquisition requires the engagement of their visual, auditory, language, memory and tactile pathways to develop meaningful connection to numbers. Some pupils, due to their biological conditions or cooccurring difficulties, find that the cortical pathways, which are known to mediate several dimensions of numbers, have been impaired. Therefore, their cognition of their core number foundational skills may not have been fully harnessed.
Each pupil has a unique neurodiverse profile and, therefore, everyone is uniquely unique. Consequently, the presentation of each pupil's difficulty is not homogeneous. We therefore need to understand where the specific learning difficulties lie, so that a purposeful and intentional intervention can take place.
Dyscalculia is often encountered in a variety of neurological and cooccurring disorders such as attentiondeficit hyperactivity disorder (ADHD), developmental language disorder including dyslexia, epilepsy, and fragile X syndrome. It is also prevalent with other biological conditions including Williams Syndrome, Autism, Turners Syndrome, Duchenne Muscular dystrophy, DiGeorge syndrome and foetal alcohol syndrome. (2)



Identifying Developmental Dyscalculia with Dynamo Maths



Developmental dyscalculia is a condition that affects the ability to access the foundational components of Number Meaning and /or Magnitude. These foundational components form the basis of Number Sense development which is a prerequisite for later maths development. These number sense components are not at the expected level of the person's chronological age, stage of schooling or intellectual abilities.



Components:



Meaning: 
decoding the symbolic Arabic number in its declarative and written form, quantitative representation and place value by the activation of the Approximate Number System (ANS) 
Magnitude: 
perceptual and reasoning skills to order, sequence and estimate. (Esmail 2013) 



The benefits of using the NumberSenseMMR™ framework.



1. 
The grouping of maths ability or components within the NumberSenseMMR™ framework provides a structure to identify pupils at risk of developmental dyscalculia and maths developmental delays. 
2. 
The framework unravels the individual differences that exist in pupils' number sense development and identifies the specific areas of strengths and needs. 
3. 
Dyscalculia presents itself heterogeneously, which means that the range and severity of difficulties experienced varies between dyscalculic learners. 
4. 
No two pupils' Number Sense Development profile is the same as each pupil has a unique mind, a unique nervous system and unique environmental influences. The framework unravels a pupil's individual Number Sense Developmental Profile. 
5. 
The NumberSenseMMR™ framework indicates that the aggregation of marginal gains  the small improvements in the number meaning and magnitude areas, can bring greater progress in the maths areas. This means that little improvement within the many early strands will make a huge difference in securing the relationship part of the pupil’s number sense development. 
6. 
This targeted approach maximises the process of bringing a significant change to the pupil’s development of their number sense 



Where schools adopt a proactive approach, Dynamo Maths Intervention is a frontloaded intervention that can serve as inclusive approach.






Dyscalculia Symptoms 



Pupils may experience some or all of the following common symptoms of dyscalculia. This list is not exhaustive, and can be extended by showing individual components considered within the NumberSenseMMR™ framework.



 
Cannot subitise (the ability to recognise groups of 3/4 without formal mathematical processing. 
 
Cannot count reliably. 
 
Do not associate number words with their symbols. For example they do not associate the word eight with the symbol 8. 
 
Reliance with ‘countingon’ strategies: using fingers rather than mental arithmetic strategies. 
 
Writing number digits the wrong way round. 
 
Difficulty with estimating. 
 
Difficulty placing numbers on a number line. For example, cannot identify that the number 8 should go between 5 and 10 on a number line. 
 
Inability to tell which of two numbers is larger. 
 
Confusing signs +, , x, ÷ 
 
Difficulty with times tables and mental arithmetic. 
 
Difficulty with everyday tasks such as checking change and reading clocks. 
 
High levels of maths anxiety. 







The NumberSense MMR™ Framework  Identifying Developmental Dyscalculia 



The NumberSenseMMR™ framework provides a structure to identify and understand the components of developmental dyscalculia and maths developmental delays.
It is symbolised by a tree that measures components of number and their development against three broad stages: Meaning, Magnitude and Relationship.



Number Meaning: activation of the approximate number system (ANS) to onset the learning and development of the components of the Arabic number system in its declarative, written, quantitative and place value forms.
Number Magnitude: the perceptual and reasoning skills to sequence, order, compare and estimate.
Number Relationships: applying arithmetic operations to solving number problems.
When pupils successfully access the Number Meaning and Number Magnitude components, it gives them the foundation to develop Number Relationships. 







Development of Number Sense 



The acquisition of arithmetic skills isn’t the domain of just one part of the brain and research suggests that the beginnings of the development of a number sense starts with nonsymbolic numbers and this triggers the Approximate Number System (ANS.)
The ANS system can be activated visually, auditorily and through tactile senses. The roots of the Number Sense MMR™ framework depict the activation of the sensory pathways to trigger the process of the ANS that onsets the development of the skills to subitise, leading to the acquisition of the symbolic numbers. Dehane’s Triple Code Model (1995), gives clarity on the dimensions of numbers – shape, sound, quantity (symbolic, nonsymbolic, quantitative) and place value.
For some pupils, the introduction of these early skills has either been missed or is compromised due to their unique biological or cooccurring condition that impedes their association to numbers and their application.
At the root level of the framework, the developing components of visually discriminating objects, subitising, associating the declarative forms to the correct written symbol, onetoone correspondence and counting are assessed. The assessment harnesses methods that involve sensory pathways, verbal, nonverbal memory, vocabulary and language. It then profiles the pupil's number sense development and identifies indicators that show if the pupil is at risk of developmental dyscalculia or maths delays.
A significant amount of research in the area of dyscalculia is associated with difficulties in accessing the magnitude from numbers. An important skill that underpins the ability to access magnitude from numbers is in the application of numbers using visiospatial, perceptual and reasoning skills. This area of development is depicted in the trunk area of the symbolic representation of the tree and the framework detects the profile of the pupil in accessing components of magnitude with numbers.
The skills of comparing two numbers or quantities, approximating, estimating, using mathematical vocabulary and language, ordering numbers, forwards and backwards sequencing and following a sequence of patterns  all these are areas of number development towards building the flexibility and fluidity in applying the four rules meaningfully and within problem settings.
.
The NumberSenseMMR™ framework indicates that the aggregation of marginal gains  the small improvements in the number meaning and magnitude areas, can bring greater progress in the maths areas. This means that little improvement within the many early strands will make a huge difference in securing the relationship part of the pupil’s number sense development.
Pupils performing below ageappropriate level within the Number Meaning and Number Magnitude area suggest symptoms of dyscalculia.
Where pupils show difficulty at an age appropriate level, the indicators within the framework detect this at the trunk level as being at risk of developmental dyscalculia
Pupils performing below ageappropriate level within the Relationship area suggests maths developmental delay.
The NumberSenseMMR™ framework can be used to develop number sense milestones according to the pupil’s age and the curriculum. It profiles the strengths and agemapped gaps in the pupil's learning and development.
Each of the stages in the NumberSenseMMR™ framework has a range of components and the ease and agility in which the meaning, magnitude and relationship of numbers are extracted give an overall profile of the pupil’s number sense development. The ultimate aim is to have pupils who can apply their knowledge of numbers efficiently and with fluidity within different contexts. This is the top end of the tree within the NumberSenseMMR™ framework  Number Relationship area. This area focuses on the pupil's understanding of number concepts, recalling number facts and applying these to solve problems using mental and written strategies within different contexts. Research shows that the smallstep improvements in the Meaning and Magnitude areas bring greater progress in the Relationship areas.
The NumberSenseMMR™ framework can also serve as an inclusive model and can be used as early as age 5. The advantage of this approach is that pupils struggling can be identified quickly and early at school. This preventative approach with a frontloaded intervention is invaluable as this can build capacity in the pupil’s formative years and teachers can take advantage of the brain's malleability and plasticity.
A study by the University of Oxford was conducted to provide correlating validity. NumberSenseMMR ™ validation technical details...





 What is Dyscalculia?  Developmental Dyscalculia  Dyscalculia Symptoms  The NumberSense MMR™ Framework 


