Maths Skills Flashcards
What is maths?
The study of quantitative relations
Earlier on in development, maths is focused on children simply understanding number
Outline early maths skills in children
Thought to arise through some innate knowledge, experience, informal learning and imitation , and rely on a broad array of skills
It is cumulative, early learning sets the foundation for later learning
Which dimensions do we need number to understand?
Distance, time, speed, statistics, money and finance, health information
Can early maths skills predict overall school success?
Maths skills at school entry predicted maths achievement throughout school, above and beyond general cognitive ability and social skills
Maths skill at school entry also predicts reading achievement more than literacy skills
Can having good maths skills predict success in other areas?
Maths skills are associated with successful financial decision making, through its effects on understanding medical information - linked to health, which then limits a person’s SES
Having good maths skills in early childhood predicts college completion and SES after controlling for IQ and years in education
How can we work out how to help children?
By understanding what skills underpin success at maths, and then design effective interventions to support children
What can they do from birth?
Discriminate on the basis of small numerosities
What can they do at 11 months?
Discriminate increasing from decreasing sequences of numerosities
What can they do from 2 years?
Begin to learn sequence of counting words and do one-to-one correspondence in sharing task
What can they do from 2.5 years?
Recognise that number words mean more than one
What can they do from 3 years?
Count out small numbers of objects
Recognise transformations that affect number
What can they do from 3.5 years?
Use the cardinality principle to establish numerosity of set
What can they do from 4 years?
Use fingers to aid adding
What did Starkey & Cooper (1980) find?
That 4 month old infants looked longer at quantities that were different from before
Suggesting that they recognise the quantity has changed and so understand different quantities
But only with numbers less than 4
Outline the possible evidence for an early general magnitude system
If they are shown that smaller objects were white with dots and bigger objects were black with stripes, they expected the same colour pattern mapping to hold for duration and numerosity.
What are the four informal maths skills that develop before children start school?
- Non-symbolic quantity understanding
- Numerical equality
- Counting
- Number magnitude
They set the foundation for more complex maths thinking
What is non-symbolic quantity understanding?
The knowledge of the magnitude of a set of items without the need to use verbal or symbolic names
The ability to know the number of a set of objects without counting them is called subitizing
3 and 4 year olds non symbolic quantity skills predict their maths achievement scores 6 months later
What is numerical equality?
The understanding that sets of different objects that have the same number have something in common
This emerges very early on in development, maybe even at around 6 months of age
What is counting?
By age 3 most children can count to 10 successfully and begin to understand the following principles:
1. One-to-one correspondence - each object must be labelled by a single number word
2. Stable order - numbers should be recited in order
3. Cardinality - the numbers of objects in a set corresponds to the last number stated
4. Order irrelevance - objects can be counted in any order
5. Abstraction - any set of objects or events can be counted
Counting skills at age 5 predict maths achievement at 8
What is numerical magnitude estimation?
The understanding that quantities are ordered along a less-to-more dimension
This ability predicts maths achievement
What does the cognitive model of maths suggest?
The idea that deficits or difficulties in maths overall are caused by cognitive difficulties further downstream
- Central executive skills support conceptual and procedural skills
- Modality-specific systems represent the information
What are central executive skills?
High level cognitive skills involved in coordinating and executing goal-directed behaviour
Involve WM and inhibitory control
They support the learning of maths, help construct maths knowledge and facilitate the solving of mathematical problems
What are the language system and visuospatial skills?
They support the maintenance and processing of information specific to either verbal or visuospatial information
A child may have good executive function skills but have limitations in these two systems which limits their ability to represent a particular type of information.
What do poor visuospatial skills affect?
- Column arithmetic
- Visual attention and monitoring
- Number magnitude and estimation
- Representing numbers in a spatial format
What do poor verbal skills affect?
- Counting
- Remembering number facts like times tables
- Math word problems
What is dyscalculia?
A specific learning disorder characterised by impairments in learning basic arithmetic facts, processing numerical magnitude and performing accurate and fluent calculation
Despite poor maths scores, children have average or above average IQ and reading scores
What is the debate around the cause of dyscalculia?
Whether it is caused by a core deficit in:
- Numerosity
OR
- Central executive skills
Outline the argument for a core deficit with numerosity
Children are able to perform tasks such as dot counting before they begin school, which suggests that poor performance is unlikely to be due to factors that are known to affect school attainment
Researchers have argued that dyscalculia is caused by a weak intuitive grasp of numbers and difficulties with understanding basic numerical concepts
Outline the argument for a core deficit with central executive skills
They may use immature strategies like using their fingers to count because they can’t represent this information in WM
They might also retrieve the wrong maths strategy or information due to poor inhibitory control
Memory span in children with dyscalculia is usually lower than controls
