MATHS SKILLS

Question 1

What is the focus of maths early on in development? And why are early maths skills so important?

Answer 1

Understanding number

Number is a central dimension of human experience in order to understand other dimensions
e.g. distance, speed, time.

Question 2

How are early maths skills thought to arise?

Answer 2

Some innate knowledge, experience, informal learning and imitation.

Question 3

What do early maths skills rely on?

Answer 3

A broad array of skills - learning is cumulative - early learning sets the foundation for later learning.

Question 4

What other skill can maths skills have a knock on effect to?

Answer 4

Reading

Question 5

Why are early maths skills so important?

Answer 5

Number = a central dimension of human experience - in order to understand other dimensions e.g. distance, speed, time

in order to understand:
Statistics,
Money and finances,
Health information

Early maths skills predict overall school success

Question 6

What do early maths skills predict?

Answer 6

Overall school success
- DUNCAN et al (2007) - maths skills @ school entry predict maths achievement throughout school and in other academic subjects and social skills.

• KOPONEN et al (2013) - maths skills @ school predict reading achievement

Predicts success in other areas:
- AGARWAL + MAZUMDER (2013) - associated w/successful financial decision making

Predicts SES? - RITCHIE + BATES (2013)

Question 7

At what age are children able to count effectively?

Answer 7

3 1/2 years - the cardinality principle (enables successful counting)

Question 8

What is the cardinality principle?

Answer 8

When you count a set of objects, the last number you say corresponds to how many objects there are.

Question 9

Why would we need to use habituation in researching children’s developing maths skills?

Answer 9

Because infants can’t tell you what they’re thinking + don’t have the motor skills to show you.

Using habituation - showing an infant a stimulus over and over again until they start looking away
- tells the researcher that they’ve extracted all the information they need so they don’t need to look at it anymore.

Look at the infants’ eye movements.

Up until the age of about 10-12 months when you can start to use more complex paradigms.

Question 10

4 informal maths skills that develop before children start school

Answer 10

1. Non-symbolic quantity understanding
2. Numerical Equality
3. Counting
4. Numerical magnitude estimation

These set the foundation for more complex maths thinking.

Question 11

Describe the maths skill: Non-symbolic quantity understanding

Answer 11

Knowledge of the magnitude of a set of items without the need to use verbal or symbolic names.

Provides a foundation for learning verbal labels and for arithmetic.

The ability to know the number of a set of objects without counting them = subitizing (this tends to be quantities of less than 5)

3 and 4 year old’s non-symbolic quantity skills predict their maths achievement scores 6 months later.

Question 12

Describe the maths skill: Numerical Equality

Answer 12

The understanding that sets of different objects that have the same number have something in common (e.g. 2 balls and 2 dogs)

This emerges very early on in development, perhaps even @ around 6 months of age.

Question 13

Describe the maths skill: Counting

Answer 13

By age 3, children can count to 10 successfully.

They also begin to understand counting principles of:

1. One-to-one correspondence
2. Stable order
3. Cardinality
4. Order irrelevance
5. Abstraction

Children need to be able to do these^ in order to be classed as able to count successfully.

Question 14

Describe the maths skill: Numerical Magnitude Estimation

Answer 14

The understanding that quantities are ordered along a less-to-more dimension.

e.g. number line

Also that this doesn’t matter whether the numbers refer to distance, weight or hours, if the unit is the same.

This ability predicts maths achievement.

Question 15

How does working memory support children’s maths thinking?

Answer 15

Central executive skills (executive functions) support conceptual and procedural skills.

Central executive skills:

• high level cognitive skills involved in coordinating and executing goal-directed behaviour
• WM - the system allowing us to process and maintain information.

The skills ^ support the learning of maths, help construct maths knowledge and facilitate the solving of mathematical problems.

Language system + visuospatial skills

Question 16

How does inhibitory control support children’s maths thinking?

Answer 16

Inhibitory control = the system allowing us to suppress distracting information.

Inhibitory control is needed when fraction understanding + numerical information conflict.

Question 17

How do modality-specific skills support children’s maths thinking?

Answer 17

The modality specific systems (the specific type of info you are holding in your head) support the maintenance and processing of information specific to either verbal or visuospatial information (although, these abilities are not necessarily related skills).

Poor visual-spatial skills will affect:

• Column arithmetic
• Visual attention and monitoring
• Number magnitude and estimation
• Representing no.’s in a spatial format.

Poor verbal skills will affect:

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

Question 18

What is dyscalculia?

Answer 18

Also known as mathematical learning difficulty…

A specific learning disorder characterised by impairments in learning basic arithmetic facts, processing numerical magnitude and performing accurate and fluent calculation.

Question 19

A fact/feature of children with dyscalculia’s reading skills…

Answer 19

Despite having poor maths scores, children with dyscalculia have average, or above average IQ + reading scores.

Question 20

What causes dyscalculia?

Answer 20

Numerosity OR central executive skills.

Question 21

Numerosity as a cause of dyscalculia…

Answer 21

Children with dyscalculia couldn’t use subitizing in a dot-matching task therefore difficulties could be tied to the child’s understanding of numerosity.

Suggests that poor performance is unlikely to be due to factors that are known to affect school attainment (ie. poor teaching or absences from school).

T/F, dyscalculia - caused by a weak intuitive grasp of umbers + difficulties with understanding basic numerical concepts.

Question 22

Evidence for a core deficit with central executive skills in patients with dyscalculia

Answer 22

May arise from a more general deficit in cognitive skills ie. a deficit in working memory or inhibitory control.

Children may use immature strategies because they cannot successfully represent this information in WM.

They also might retrieve the wrong maths strategy or information due to poor inhibitory control.

Memory span in children with dyscalculia is usually lower than controls and is correlated with maths difficulties.