Dyscalculia: Mathematical Difficulties

Dyscalculia is defined as a specific difficulty in understanding mathematics, but in particular numeracy.

The difficulty is experienced irrespective of the individual's overall cognitive ability. It is considered that:

  • it is a developmental difficulty which a child is born with as opposed to acquires following birth
  • between 3 and 5% of the population experience mathematical difficulties,
  • unlike literacy difficulties (which is predominantly a male-dominated difficulty) there are equal numbers of boys and girls who experience numeracy difficulties

At present, the consensus for formal diagnosis is still up for debate, but a diagnosis can be obtained from a specialist teacher who has specialised in the field of mathematical development.

The identification of mathematical difficulties should look at the profile of strengths and difficulties of the individual and dig deep to look below the surface.

Individuals experience mathematical difficulties for a number of reasons and it is only when the underlying cause is teased out that successful approaches to intervention can be determined.

Mathematical difficulties can often be the result of a primary difficulty, such as dyslexia and detailed assessment must be conducted to determine the reason for the mathematical difficulties occurring.

It is not associated with mathematical notation and recording. 

The primary difficulties in dyscalculia are considered to be:

  • A lack of an intuitive sense of number - the fiveness of five - understanding magnitude, meaning and relationship to other values and numbers
  • Difficulties in seeing the pattern or rule
  • Difficulty in generalisation and making connections
  • Difficulty in remembering number facts
  • Difficulty in transferring between the concrete and the abstract forms
Early Years:
  • Difficulty in counting
  • Difficulty in remembering the order and names of numbers e.g. may say 1, 2, 5, 7
  • Doesn’t naturally associate numbers with the corresponding number of items (give me three)
  • Doesn’t associate the final count to represent the total number or size of the collection
  • Has difficulty counting a collection of different objects
  • Difficulty in counting on from a number other than 1, goes back to 1 each time
  • Difficulty understanding concept of quantity: which is more/less?
  • Difficulty in understanding the concept of 7 being 1 more than 6, 8 being 1 more than 7 and so on 
Primary Years:
  • Continued errors in counting, particularly the ‘teens’ and across the decade 
  • ‘Teen’ and ‘ty’ confusion 
  • Has difficulty ordering numbers 
  • May write numbers the wrong way round e.g. 23 instead of 32, or mis-interpret digits e.g. confusing 3 and 5, 2 and 5, 1 and 7 , or reversing digits 
  • Continued difficulty in understanding the concept of how many more/less? 
  • May continue to use inefficient counting as a method for calculating and return to 1 each time rather than count on 
  • Has difficulty seeing the pattern or rule e.g. 23,33,43 
  • Difficulty in remembering number facts 
  • Difficulty in learning times tables
  • May confuse symbols such as + and x 
  • Difficulty in learning number bonds, odd and even numbers 
  • Difficulty in deriving information from a known e.g. if 6+4=10, 6+5 must be 11 
  • Inaccurately remembering number facts 
  • Difficulty in partitioning number, commutativity (3+5=5+3) and that addition is the opposite of subtraction 
  • Applying rules too liberally without a thorough understanding 
  • Misconceptions may occur possibly due to over-generalisation 
  • Difficulty with understanding and interpreting place value (e.g. one hundred and two is written 1002) 
  • Difficulty in following word problems 
  • Difficulty in multi-stepped problems, may lose way 
  • Difficulty in understanding coin values 
  • Difficulty in giving change 
  • Difficulty in learning to tell the time
Secondary Years:

At this stage it is very clear when a pupil is experiencing substantial difficulties in reasoning and understanding numerical operations. Mathematics relies upon the ability to use a range of strategies, make connections between operations and see the pattern or rule. If an individual continues to experience substantial difficulty in understanding basic numerical concepts, such as fractions and percentages, preferring to learn a rule, they should be assessed for dyscalculia.
  • Continued difficulties in calculating, relying upon inefficient method of counting 
  • Difficulties in algebra due to difficulties in generalisations and understanding equivalence 
  • Difficulty in multi-stepped activities due to memory difficulties 
  • May find interpreting word problems tricky and not know what operation to assign to the problem
  • Continued difficulty in deriving information from the known e.g. 25 + 75 = 100, 100-75 = 25, 2.5+7.5 =1.0 and so on.
  • Using the appropriate strategy for a particular context -relies upon inefficient strategies, such as counting
  • May lose place easily when calculating resulting in errors 
  • Difficulties in understanding and using money (coin values, giving change) 
  • Difficulties in understanding decimal notation due to place value difficulty 
  • Difficulty in application of mathematical concepts such as in measure and capacity 
  • Time-related concepts difficult to understand 
  • Problems with percentages, fractions and decimals
Beyond Secondary:
The impact of ongoing difficulties will impact many walks of life including:

  • Limiting ability when managing home finances and shopping 
  • Limiting ability to estimate time, read timetables etc 
  • Restricting employment prospects to work that does not involve too much mathematics, such as required in engineering, plumbing, electrician, medicine, teaching, retail and so on 
  • Reduced ability to measure items (weight, capacity, length and distance) restricting employment roles
            Possible Access Arrangements:
Very rarely would a mathematical difficulty require a specific access arrangement in its own right. However, any co-occurring difficulties or the underlying root cause for the difficulty occurring may require additional access arrangements.
     Extra timeprocessing difficulties, slow reading, slow writing, comprehension difficulties
     reader/computer readerstudents with exceptionally slow reading or poor reading comprehension
     prompterstudents with distractibility or poor concentration
     Supervised Rest breaksstudents who experience visual stress, test anxiety, poor concentration
    Coloured overlays or modified papersstudents who experience visual stress or spatial awareness difficulties

     Scribeillegible writing or visual impairment