arithmetic and dyscalculia Flashcards
early arithmetic skills
- 5 months + 9 months have arithmetic expectations - look longer at unexpected
- 2-4 years show mental model for non-symbolic skills
- children are more accurate at addition and subtraction in non verbal format
- use of fingers when solving word problems and abstract symbolic problems
- up to 7 yrs, providing manipulatives improves accuracy
- more accurate when problems refer to real situations and use of pictures
strategy for addition problems
-count all, count on from first added, count on from larger, decomposition, retrieval
strategy for subtraction problems
- separate from
- adding
- matching
- counting down/up
distribution of associations network
every time the association between the problem and the answer is strengthened
- more errors with larger operands/numbers bc practised less
- incorrect answers sometimes because operands are related in other ways e.g. 5+6=30
- relational language e.g. more/less - harder to do
overlapping waves model
-children select from a variety of strategies at any time
4 dimensions of strategy use
- repertoire: range of strategies an individual case may use
- distribution: relative frequency of use
- efficiency: accuracy and speed in implementing a strategy
- selection: whether individual makes appropriate choice based on efficiency
choice/no-choice paradigm
- choice: ps choose strategy then report on strategy used - info about reperotire and distribution
- no-choice: ps instructed to use a strategy - info about strategy efficiency
executive function skills
- working memory: ability to monitor + manip info in mind
- inhibition: ability to ignore distractions
- shifting: capacity for flexible thinking and switching attention between tasks
working memory
verbal, visuospatial
- verbal WM strong predictor of arithmetic
- children with math learning difficulties show reduced VM capacity
- dual task: loading WM interferes with ability to carry out procedures when calculating
- WM requried to access arithmetic facts in LTM
inhibition
- might be relevant to inhibit irrelevant info in word problems or in suppressing retrieval of incorrect number facts
- related to math achievement but some studies didn’t
Shifting
correlated to math achievement across ages
language
need good lang skills to learn verbal number words, understand arithmetic
- preschool phonological skills related to numerical
- 3-5 yrs understanding of math lang is predictor of early numerical skills
- children with lang impairment have difficulties with counting, abstract calc and place-value undertstanding
characteristics of math learning disorder (MLD) and developmental dyscalculia (DD)
- not unitary - can be excellent at retrieving facts but struggling understanding principles
- large inter-individual differences
- different developmental trajectories
- low performance on standard math tests
- 3-10% of children have severe math difficulties, but larger number have less severe that affect outcomes
- DD is more severe (lowest 5-10%)
- MLD less severe (bottom 25%)
- dyscalculia is heterogenous condition
comorbidity
50%-66% of children with DD also suffer from additional learning disorder e.g. dyslexia, ADHD, dyspraxia, language delay
counting in MLD/DD
- delay in acquisition of counting principles
- slower to recite
- pseudo errors - counting wrong way
- real errors - double counting
- more likely to report real errors as correct than pseudo
