mathematical difficulties - DD Flashcards
effect of difficulties with maths as a child on later life
difficulties in maths are common and persist into adulthood
low numeracy skills related to higher rates of unemployment, low salary, increased risk of depression, poorer health
how many adults have low maths skills in England
6.8 million adults in England were estimated to have skills at or below level expected for typical 9-year-old (Department for Education and Skills, 2003)
how many children have severe mathematical difficulties
3-10%
e.g. developmental dyscalculia
larger number of children and adults estimated to have less severe mathematical difficulties, impacting educational and occupational outcomes
is there more research in reading or maths
less research on mathematical disorders (e.g., dyscalculia) compared to reading disorders (e.g., dyslexia)
a lot less research of maths difficulties compared to reading difficulties
what is developmental dyscalculia + how many people have it
specific impairment of mathematical ability
affects approximately 3.5-6.5% of the population
what difficulties are associated with developmental dyscalculia - in early childhood (7)
- number sense
- sorting objects
- recognising patterns or groups
- comparing and contrasting magnitude
- learning to count
- recognising numbers
- matching numbers with amounts
what difficulties are associated with developmental dyscalculia - in school-age children (5)
- solving basic arithmetic problems (addition, subtraction, multiplication division)
- remembering and retaining basic maths facts (e.g., times tables)
- applying knowledge and skills to solve maths problems
- organising maths facts needed to solve a problem
- understanding what’s written on a board or in a textbook
what difficulties are associated with developmental dyscalculia - in teens and adults (3)
- moving on to more advanced mathematical concepts
- grasp mathematical vocabulary
- following multi-step procedures to solve advanced problems:
–> visualise patterns
–> visualise different parts of a maths problem
–> identifying critical information needed to solve problems
warning signs of developmental dyscalculia (9)
- slow to develop counting and maths problem-solving skills
- difficulty reading numbers or recalling numbers in sequence
- frustration when specific computation and organisation skills need to be used
- concept of time issues
- poor sense of direction
- poor long-term memory of concepts
- poor mental maths ability
- difficulty playing strategy games e.g. chess
- difficulty keeping score during games
how DD is diagnosed
performance on standardised maths achievement test
low performance compared to others of same age that can’t be explained by inappropriate education, neurological disorders, or psychiatric disorders = DD
DSM-5 definition of DD (+ 3 specific types)
Specific Learning Disorder
“A neurodevelopmental disorder of biological origin manifested in learning difficulty and problems in acquiring academic skills markedly below age level and manifested in the early school years, lasting for at least 6 months; not attributed to intellectual disabilities, developmental disorders, or neurological or motor disorders”
specify if:
- with impairment in reading
- with impairment in written expression
- with impairment in mathematics
change in definition of DD from DSM-IV to DSM-V
DSM-IV:
Reading Disorder, Mathematics Disorder, Disorder of Written Expression, Learning Disorder Not Otherwise Specified
DSM-V:
Specific Learning Disorder
specific types of reading deficits are described internationally as dyslexia
specific types of mathematics deficits as dyscalculia
change from DSM-IV to DSM-V with IQ discrepancy
DSM-IV = more than 2 standard deviations between maths and IQ
DSM-V = no IQ discrepancy criteria = little evidence that the numerical difficulties of children with developmental dyscalculia differ dependent on IQ level
DSM-V diagnostic criteria of SLD - 3 specifiers and severities
SLD = specific learning disorder
- impairment in reading (word reading accuracy, reading rate or fluency, reading comprehension) = dyslexia
- impairment in written expression (spelling accuracy, grammar and punctuation accuracy, clarity or organisation of written expression)
- impairment in mathematics (number sense, memorisation of arithmetic facts, accurate or fluent calculation, accurate maths reasoning) = dyscalculia
3 levels of severity:
- mild
- moderate
- severe
SLD with impairment in mathematics - DSM-V - 4 criterion
4 criteria must be met:
A
- difficulties learning and using academic skills
- persisted at least 6 months, despite intervention
- presence of at least one of:
–> difficulties mastering number sense, number facts, or calculation
–> difficulties with mathematical reasoning
B
- skills are substantially below those expected for the individual’s chronological age
- skills interfere with academic/occupational performance/activities of daily living
- confirmed by standardized achievement measures and comprehensive clinical assessment
C
- difficulties begin during school-age years
- may not fully manifest until demands exceed capacity (e.g., timed tests, deadlines)
D
- not better explained by other factors (e.g., intellectual disabilities, visual or auditory issues, other mental or neurological disorders)
DD comorbidity
1/2 to 2/3 children with DD have an additional learning disorder
common ones:
- reading difficulties
- ADHD
- language delay
- problems with visuospatial working memory
- motoric deficits
why are comorbid conditions with DD unclear
Additive effect? Shared risk factors?
Clear evidence for genetic risk
practical implications of comorbidity with DD
less able to use compensatory mechanisms due to additional co-occurring deficits
interventions then may need to be tailored for those with or without comorbid conditions
2 theories of DD
domain-specific
- underlying core deficit is a numeral deficit
domain general
- impairment in non-numerical mechanisms
ANS
ANS = approximate number system
mental system responsible for representing and processing numerical magnitude information
deficits seen in domain-specific theory of DD
domain-specific DD - ANS deficit
deficit in ANS system
deficit in representing large nonsymbolic numerosities → developmental dyscalculia
DD reflects problem with processing magnitude
more precise ANS = faster/more sold number word and/or Arabic digit acquisition
task for ANS
are there more blue or yellow dots (slide 21)
children with maths learning disability (ALD) had poorer ANS acuity
issue with domain specific ANS deficit theory of DD
several studies fail to find ANS deficit in children with developmental dyscalculia
domain specific DD - symbolic processing deficit
deficit in symbolic representations
“Access deficit” - difficulties accessing numerical magnitude representations from symbols
assumes symbolic number representations shape the ANS
symbolic magnitude processing task
present with 2 numbers, say which is bigger
longer response times for symbolic comparison in children with DD - no difference in accuracy, just speed
numerical stroop task
shown 2 numbers which are physically and numerically different sizes
either asked to say physically larger number or numerically
can have congruent (physically and numerically larger number) and incongruent trials (physically larger is numerically smaller)
result:
smaller or absent size congruity effect in children with DD
because they do not automatically process numbers, they can ignore the numerical value and easily pick the physically larger number
transcoding tasks
present with a number verbally then have to write it down
results:
DD make more mistakes with transcoding than NT peers
e.g. may have issues with placeholing e.g. write 1000100101 rather than 1111
domain general theory - WM deficit
Working memory: Ability to hold information in memory while processing new information
verbal working memory
visuospatial working memory
–> keeping track of place-value alignment
–> visuospatial representation of numbers (e.g., mental number line)
deficits in visuospatial working memory both at the behavioural and neural level for children with dyscalculia
would make sense at a neural level with specific brain area deficits with VS WM
task of visuospatial working memory
have to tap sqaures in reverse order to pattern shown (like simon game but backwards)
impairments seen in those with DD
serial order in WM task
have to say names of animals on cards in right order - remember and repeat them in correct order
DD have impairments in serial order WM
domain general theory - attentional/executive deficits
attentional/executive functions important for mathematics
- inhibition
- shifting
some evidence that these functions might be impaired in children with developmental dyscalculia
flaws with 2 theories of DD
domain specific:
- core deficit in symbolic processing?
domain general:
- core feature? or comorbidity?
- all about WM and attention, so maybe it’s all about poor EF, which one causes the other or are they just comorbid
- could it be a brain region which has issues spanning both WM and maths ability
heterogeneity at behavioural, cognitive, and biological level as a core feature of DD
Caused by several subtypes of dyscalculia? Comorbidities with learning disorders? Diagnostic issues? Different trajectories of development?
