The development of maths skills Flashcards
Whats maths?
The study of quantitative relations, in early dev focused on cs understanding numbers
Where is early maths though to arise from?
Through innate knowledge, experience, informal learning and imitation
- maths learning is cumulative
Why are maths skills so important ?
- number is a central dimension of human experience
- we need to understand number in order to understand other dimensions like
- TIME
- DISTANCE
- SPEED
daily life: - STATISTICS
- MONEY AND FINANCE
- HEALTH INFO e.g. diet info/medicines
Why are early math skills so important ?
1) early math skills predict overall school success
- maths skills predicted achievement throughout school
- math skills @ school entry predict reading achievement more than literacy skills
2) good math skills predicts success in other areas
- financial decision making
- effects on understanding medical info = link to ill health which limits SES
- good maths in early childhood= predicts college completion and SES
What are the individual differences in maths skills?
- childrens maths skills are very poor
= 64% of 10yrs dont have proficient maths skills
what does understanding skills that underpin success at maths help us do?
work out how we can help cs through designing effective interventions to support children
At what age can cs discriminate on the basis of small numerosities ?
0
what age can discriminates increasing from dreacreasing sequences of numerosities ?
11months
What age do cs begin to learn sequences of counting words and do one to one correspondence in a sharing task?
2yrs
what age can cs recognise that number words mean more than one ‘grabber’?
2yrs 6mnths
what age can cs count small numbers of objects and recognise transformations that affect number?
3yrs
what age can cs use the cardinality principle to establish numerousity of set ?
3yrs 6 months
What age can children use fingers to aid adding?
4yrs
what does Feigenson, Carey & Hauser 02 demonstrate?
number sense in infancy 10/12mnths presented w two boxes - 1 = 2 crackers - other = 3 crackers FOUND: infants will crawl to the one with the most crackers BUT random when quantities more than 4
What study demonstrates number sense in infancy?
Starkey & Cooper 1980
- 4mth old infants looked longer at quantities that were different from before
SUGGESTING they recognised the quantity changed
SO UNDERSTAND DIFFERENT QUANTITIES
BUT only w nos less than 4
= infants can discriminate between nos less than 4
What evidence is there for an early general magnitude system?
= for time, space and number - small objects = shown for less time, and should have less amount compared to big objects - more = more across dimensions = big size= more quantity= lasts longer lourenco and longo 10
What 4 informal maths skills develop before children start school?
1) Non-symbolic quantity understanding
2) Numerical equality
3) Counting
4) Number magnitude
= foundation for more complex maths thinking
What does non-symbolic quantity understanding refer to ?
-Knowledge of the magnitude of a set of items without the need to use verbal or symbolic names
= foundation for learning verbal labels for arithmetic
- 3/4yrs non-symbolic quanity skills predict their maths achievement scores 6mths later = libertus, feigenson & halberda 13
What is subitizing?
the ability to know the number of a set of objects without counting them
What is number equality ?
understanding that sets of different objects that have the same no. have something in common e.g. twoness
= emerges early dev around 6mnths wynn 95
At what age can most children count to 10 successfully ?
3yrs old
= whnn 1990
What happens at age 3 regarding counting?
1) one to one correspondence = each object must be labelled by a single number word
2) stable order= nos should be recited in order
3) cardinality = the no of objects in a set coresponds to the last no stated
4) order irrelevance - objects can be counted in any order
5) abstraction - any set of objects/events can be counted
what can counting skills at age 5 predict?
Maths achievement at age 8
= aunola et al 04
what is numerical magnitude estimation?
the understanding that quantities are ordered along a less-to-more dimension
e.g. 6 is smaller than 8
= predicts maths achievement
- may seem easy but not
What is the cognitive model of maths? What does it show?
geary 04
how cognitive skills support maths
modality specific systems represent the info, central executive skills support the conceptual and procedural skills,
- idea that difficulties in mathmatical domain are caused by cognitive difficulties further downstream
What are the cogntive executive skills of the cognitive model of maths?
- coordinating and executing goal-directed behaviour
- involve WM = process and maintain info and inhibitory control
= the system allowing us to suppress distracting info
= help solve maths problems
what is the language speech system and vidsuospatial skills?
modality specific systems support maintenece and processing of info
- could have good executive function but bad on this= limits ability to represent a particc type of info
how does the central executive skills help deal with verbal info/problems?
-WM = comprehend the word and keep track of info
-Inhibitory control= inhibits tendency to subtract immediately e.g.when hear phrase ‘flew away’
also ignores extraneous info
how does the central executive skills help deal with verbal info/problems with nos in them instead of words?
sally has 20 marbels. she has 10 more marbels than anne. how many marbels does anne have?
inhibitory control= add when see more than
how does the central executive skills help deal with visual fractions?
inhibitory control= needed to understand numerical info conflict
e.g. inhibit the fact that although 1/2 is the numerically bigger fraction , 3/9 by themselves are bigger than 1 and 2
how will poor visual-spatial skills affect the central executive modality specific skills?
1) column arithmetic
2) visual attention and monitoring
3) number magnitude and estimation
4) representing numbers in a spatial format
how will poor verbal skills affect central executive modality specific skills?
1) counting
2) remembering no facts like times tables
3) math word problems
may struggle w verbal labels so use visual formats like counting w fingers
What is dyscalculia? also known as mathematical learning difficulty
specific learning disorder characterised by impairments in learning basic arthmetic facts, processing numerical magnitude and performing accurate and fluent calculation
_________ is a specific learning disorder characterised by impairments in learning basic arithmetic facts , processing numerical magnitude and performing accurate and fluent calculation
dyscalculia
= maths learning difficulties
how many children have dyscalculia ?
5-8% of school children
= as widespread as dyslexia
what causes dyscalculia
debate about if its deficit in:
numerosity or central executive skills
not being able to subitize and instead counting to 3 in a dot-matching task suggests dyscalculia is caused by__________
a core deficit with numerosity
not being able to complete dot -matching tasks even before big school suggests that dyscalculia is caused by _________
numerosity
= a weak intuitive grasp of numbers
taking longer to decide if 9 is larger than 2 than that 9 is larger than 8 shows..
imature strategies
= a core deficit with numerosity
a core deficit with central executive skills can be seen by:
- using immature strategies like using fingers to count as cannot successfully represent this information in WM
- retrieve wrong maths strategy or info due to poor inhibitory control
- mem span usually lower than controls which is correlated w maths difficulties
children with _______ tend to get better attainment scores through school in maths and other subjects
good early maths skills
children with ______ are more likely to have a higher SES in adulthood
good early maths skills
the ability to do maths is supported by ________, ______, and ________
- working memory
- inhibitory control
- the ability to represent verbal and visuospatial info
________ is a mathametical learning disability
dyscalculia
