Maths Skills Flashcards
What is maths?
The study of quantitive relations
Numbers make it possible for people to understand and manipulate quantities in very precise ways
Early maths skills are thought to arise through….
Innate knowledge
Experience
Informal learning
Imitation
Maths understanding is…
Cumulative, early learning sets the foundation for later learning
We need to understand number in order to understand….
Distance Time Speed Statistics Money and finance Health information (dietary information or medicine dosage)
Early maths skills predict overall school success
Maths skills at school entry predicted maths achievement throughout school, above and beyond general cognitive ability
Maths skills at school entry predict ____ achievement more than _____ skills
Reading
Literacy
Agarwal & Mazumdea (2013)
Maths skills are associated with successful financial decision making
Berkman et al (2011)
Low maths skills are linked to ill health, due to understanding of medical information
Ritchie & Bates (2013)
Good maths skills in early childhood predicts college completion and SES age 42 after controlling for IQ and years in education
About _____ of 10 year olds do not have proficient maths skills
64%
Cardinality principle
The last number you say is how many items there are
Develops around 3.5
Number sense in infancy - dots
Show infants a series of dots until they look away
Then show them the same number of dots or different
4 month olds looked longer at quantities which were different from before
Recognise that it had changed, recognise different quantities
Specific to quantities between 0-4
Number sense in infancy - crackers
10 and 12 month olds are presented with two boxes, one with two crackers and one with three
Infants will crawl to the one with the most crackers but are random when the quantity is more than 4
Lourenco & Longo (2010)
Infants may have a general magnitude system for time, space and number
Infants were shown that small objects were white with dots and big objects were black with stripes
Looked longer when they were shown an incongruent array
Four informal maths skills develop before children start school
Non-symbolic quantity understanding
Numerical equality
Counting
Numerical magnitude estimation
Non-symbolic quantity understanding
Knowledge of the magnitude of a set of items without the need to use verbal or symbolic names
Subitizing
Knowing the number of a set of objects without counting them (less than 5)
Numerical equality
Sets of different objects that have the same number have something in common
Counting
By age 3 most children can count to 10 successfully
Counting principles
One-to-one correspondence - each object must be labelled by a single number word
Stable order - should be recited in an order
Cardinality - number of objects in a set corresponds to the last number stated
Order irrelevance - objects can be counted in any order
Abstraction - any set of objects or events can be counted
Numerical magnitude estimation
The understanding that quantities are ordered on a less-to-more dimension
Regardless of whether the number is distance, weight or time
Cognitive model of maths - Geary (2004)
Difficulties in maths may be caused by cognitive difficulties further downstream
Central executive supports conceptual and procedural skills
Modality-specific systems represent the information (visuospatial and language system)
Central executive skills
High-level cognitive skills involved in coordinating and executing goal-directed behaviour
Working memory
Inhibitory control
Modality-specific systems
Support the maintenance and processing of information specific to either verbal or visuospatial information
They aren’t necessarily linked
Poor visuospatial skills will affect…
Column arithmetic
Visual attention and monitoring
Number magnitude and estimation
Representing numbers in spatial format
Poor verbal skills will affect…
Counting
Remembering facts like times tables
Dyscalculia
A specific learning disorder characterised by impairments in learning basic arithmetic facts, processing numerical magnitude and performing accurate and fluent calculations
Often have higher than average IQ
How many children have dyscalculia?
Around 5-8%
As widespread as dyslexia
What causes dyscalculia?
Deficit in…
Numerosity OR
Central executive skills
Dyscalculia explained by deficit in numerosity
Children with dyscalculia do not subitize in a dot-matching task, they count them
Dyscalculia explained by deficit in central executive skills
May use counting strategies as they cannot successfully represent the information in working memory
Might retrieve the wrong strategy as they cannot inhibit other information
Memory span in children with dyscalculia is usually lower than controls and is correlated with maths difficulties
Age 0 milestone
Can discriminate on the basis of small numerosities
Age 11 months milestone
Discriminates increasing from decreasing sequences of numerosities
Age 2 milestone
Begins to learn sequence of counting words
Can do one-to-one correspondence in a sharing task
Age 2 and 6 months milestone
Recognises that number words mean more than one
Age 3 milestone
Counts out small numbers of objects
Can recognise transformations that affect number
Age 3 and 6 months milestone
Can use cardinality principle to establish numerosity of a set
Age 4 milestone
Can use fingers to aid adding
