Overview of the NumberSenseMMR™ Framework 

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 provides three dimensions of measurement:

Speed of Processing
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. e.g.:

  • Numbers as symbols
  • Subitising and counting
Number Magnitude:

The perceptual and reasoning skills to sequence, order, compare and estimate.

  • Number comparison
  • Estimation
  • Approximation
  • Ordering
  • Sequencing
Number Relationship (Facts and Reasoning):

Applying arithmetic operations to solving number problems.

  • Place value
  • Number bonds and facts
  • Mental strategies
  • Problem solving
  • Time measurement
  • Multiplication
  • Division
  • Measurement
  • Algebra

Cognitive Capacities

When pupils successfully access the Number Meaning and Number Magnitude components, it gives them the foundation to develop Number Relationships.

Identifying Developmental Dyscalculia with Multiply Screener

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)

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 non-symbolic 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 NumberSenseMMR™ framework depict the activation of the sensory pathways to trigger the process of the ANS and this in turn onsets the development of the skills to subitise, leading to the acquisition of the symbolic numbers. Dehaene’s Triple-Code Model (1995) gives clarity on the dimensions of numbers – shape, sound, quantity (symbolic, non-symbolic, 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 co-occurring conditions, which impede their association to numbers and their application.

At the root level of the framework, the components of visually discriminating objects, subitising, associating the declarative forms to the correct written symbol, one-to-one correspondence and counting are assessed through methods that involve sensory pathways, verbal and non-verbal memory, vocabulary and language. Where pupils show difficulty with these areas, the indicators within the framework identifies this as being at risk of developmental dyscalculia.

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 visuospatial, 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, sequencing forwards and backwards, following a sequence of pattern- all these are areas of number development toward building the flexibility and fluidity in applying the Four Basic Mathematical Operations 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 age-appropriate level within the Number Meaning and Number Magnitude area suggests 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 age-appropriate 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 age-mapped 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 gives 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. In this area, 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 small-step improvements in the Meaning and Magnitude areas bring greater progress in the maths 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 front-loaded 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.

Validation of the NumberSenseMMR™ Framework

A study by University of Oxford was conducted to provide correlating validity of the NumberSenseMMR™ framework. For technical details…