Maths Skills

Question 1

What is maths?

Answer 1

The study of quantitative relations

Earlier on in development, maths is focused on children simply understanding number

Question 2

Outline early maths skills in children

Answer 2

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

Question 3

Which dimensions do we need number to understand?

Answer 3

Distance, time, speed, statistics, money and finance, health information

Question 4

Can early maths skills predict overall school success?

Answer 4

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

Question 5

Can having good maths skills predict success in other areas?

Answer 5

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

Question 6

How can we work out how to help children?

Answer 6

By understanding what skills underpin success at maths, and then design effective interventions to support children

Question 7

What can they do from birth?

Answer 7

Discriminate on the basis of small numerosities

Question 8

What can they do at 11 months?

Answer 8

Discriminate increasing from decreasing sequences of numerosities

Question 9

What can they do from 2 years?

Answer 9

Begin to learn sequence of counting words and do one-to-one correspondence in sharing task

Question 10

What can they do from 2.5 years?

Answer 10

Recognise that number words mean more than one

Question 11

What can they do from 3 years?

Answer 11

Count out small numbers of objects

Recognise transformations that affect number

Question 12

What can they do from 3.5 years?

Answer 12

Use the cardinality principle to establish numerosity of set

Question 13

What can they do from 4 years?

Answer 13

Use fingers to aid adding

Question 14

What did Starkey & Cooper (1980) find?

Answer 14

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

Question 15

Outline the possible evidence for an early general magnitude system

Answer 15

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.

Question 16

What are the four informal maths skills that develop before children start school?

Answer 16

1. Non-symbolic quantity understanding
2. Numerical equality
3. Counting
4. Number magnitude
   They set the foundation for more complex maths thinking

Question 17

What is non-symbolic quantity understanding?

Answer 17

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

Question 18

What is numerical equality?

Answer 18

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

Question 19

What is counting?

Answer 19

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

Question 20

What is numerical magnitude estimation?

Answer 20

The understanding that quantities are ordered along a less-to-more dimension
This ability predicts maths achievement

Question 21

What does the cognitive model of maths suggest?

Answer 21

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

Question 22

What are central executive skills?

Answer 22

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

Question 23

What are the language system and visuospatial skills?

Answer 23

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.

Question 24

What do poor visuospatial skills affect?

Answer 24

• Column arithmetic
• Visual attention and monitoring
• Number magnitude and estimation
• Representing numbers in a spatial format

Question 25

What do poor verbal skills affect?

Answer 25

• Counting
• Remembering number facts like times tables
• Math word problems

Question 26

What is dyscalculia?

Answer 26

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

Question 27

What is the debate around the cause of dyscalculia?

Answer 27

Whether it is caused by a core deficit in:
- Numerosity
OR
- Central executive skills

Question 28

Outline the argument for a core deficit with numerosity

Answer 28

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

Question 29

Outline the argument for a core deficit with central executive skills

Answer 29

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