R6 Core Systems of Number (Feigenson, Dehaene & Spelke, 2004)

What is the main argument of Feigenson, Dehaene & Spelke (2004)?

Humans are born with two innate core systems for representing number.

Who possesses the two core number systems?

Human infants; adults; and many animal species.

What is the role of the core number systems?

They provide the foundation for later mathematical abilities.

Why can't the core systems explain advanced mathematics?

Advanced mathematics requires symbolic learning (e.g. fractions; algebra; negative numbers).

Why is mathematics considered easy?

Humans have innate number systems; and even babies and animals understand basic quantities.

Why is mathematics considered hard?

Advanced concepts require learned symbolic systems.

Name four mathematical concepts not represented by the core systems.

Fractions; negative numbers; square roots; and real numbers.

What are the two core number systems?

The Approximate Number System (ANS) and the Exact Small-Number System.

Which system represents large quantities?

The Approximate Number System (ANS).

Which system represents small numbers exactly?

The Exact Small-Number System.

Which system is ratio dependent?

The Approximate Number System.

Which system is capacity limited?

The Exact Small-Number System.

What is the function of the ANS?

To represent large numerical quantities approximately.

Can the ANS identify exact numbers?

No—it estimates quantities without counting.

Give an example of ANS estimation.

Distinguishing 8 vs 16 but not knowing the exact number.

What experimental method demonstrates the ANS in infants?

Habituation studies.

What happens in a habituation study?

Infants repeatedly view one number (e.g. 8 dots) before seeing a new number (e.g. 16 dots).

What do infants do when shown a new number?

They look longer; indicating they detect numerical change.

What does ratio-dependent performance mean?

Number discrimination depends on the ratio between quantities; not the absolute difference.

Which comparison is easier: 8 vs 16 or 8 vs 12?

8 vs 16 (1:2 ratio).

Why is 8 vs 12 harder?

The ratio is smaller (2:3).

How does ANS precision change with age?

It becomes increasingly accurate.

What ratio can 6-month-olds discriminate?

1:2.

What ratio can 10-month-olds discriminate?

2:3.

Approximately what ratio can adults discriminate?

Around 7:8.

Can the ANS operate across different senses?

Yes.

What types of information can infants discriminate using the ANS?

Dot arrays; sounds; and sequences of events.

What does this suggest about the ANS?

It represents abstract number rather than visual patterns.

What numerical abilities does the ANS support?

Comparing quantities; understanding larger/smaller relationships; and simple arithmetic.

What arithmetic expectation can infants show?

That 5 + 5 is approximately 10.

How does the ANS represent numbers mentally?

As an approximate mental number line.

Why are nearby numbers often confused?

Their mental representations overlap.

What is the function of the Exact Small-Number System?

To represent small numbers exactly.

What is its capacity?

Usually 1–3 objects; sometimes up to 4.

What did the hidden cracker experiment investigate?

Infants' ability to represent exact small numbers.

Which comparisons were infants successful on?

1 vs 2 and 2 vs 3.

Which comparisons did infants fail?

3 vs 4; 2 vs 4; 3 vs 6; and 1 vs 4.

What determined success in this task?

Capacity; not numerical ratio.

What did object-tracking experiments show?

Infants could accurately track up to three objects.

At what number did performance fail?

Four objects.

Besides number; what else can the Exact Small-Number System represent?

Total size; area; and amount of material.

What cracker preference demonstrated this?

Infants preferred one large cracker over two tiny crackers.

Is the Exact Small-Number System approximate or exact?

Exact.

Is it limited by ratio or capacity?

Capacity.

What does it primarily represent?

Individual objects.

Which system represents large numbers?

Approximate Number System.

Which system represents small numbers?

Exact Small-Number System.

Which system is approximate?

ANS.

Which system is exact?

Exact Small-Number System.

Which system estimates quantity?

ANS.

Which system tracks individual objects?

Exact Small-Number System.

Which animals show an Approximate Number System?

Rats; monkeys; and tamarins.

What do these animals demonstrate?

Ratio effects and approximate quantity estimation.

What capacity limit do monkeys show for exact numbers?

Around 3–4 objects.

Which brain region supports the ANS?

The Intraparietal Sulcus (IPS).

What numerical abilities is the IPS involved in?

Number comparison; estimation; and approximate arithmetic.

Damage to the IPS can cause which disorders?

Acalculia and developmental dyscalculia.

What are number-selective neurons?

Neurons that respond most strongly to a preferred number of objects.

Example: A neuron tuned to four objects responds most strongly to…?

Four objects; less to nearby numbers; and very weakly to distant numbers.

Which numerical abilities are present at birth?

Approximate number representations and exact small-number representations.

What mathematical skills are learned later?

Counting; number words; symbols; and arithmetic.

What do the two core systems explain?

Early numerical intuition; infant numerical abilities; similarities across species; and the foundations of mathematics.

What is still needed for higher mathematics?

Language; symbols; education; and culture.

What are the two innate core number systems?

The Approximate Number System (ANS) and the Exact Small-Number System.

Which system is ratio dependent?

ANS.

Which system is capacity limited?

Exact Small-Number System.

What is the capacity of the Exact Small-Number System?

About 3–4 objects.

Which brain area is most associated with the ANS?

Intraparietal Sulcus (IPS).

Which system is shared across infants; adults; and many animals?

Both the ANS and the Exact Small-Number System.

Why are the core systems insufficient for advanced mathematics?

Advanced mathematics depends on symbolic learning; language; education; and culture.