Number Concept DVML

What is the number concept?

Numerosity, counting, arithmetic

5 counting principles (Gelman and Gallistel)

One to one principe

Stable order principle

Cardinal principle

Other irrelevance principle

Abstraction principle

One to one principle

One and only one tag or counting word for each item in the set

Stable order principle

Tags must be used in the same way eg 123, 132

Cardinal principle

The tag of the final object in the set represents the total number of items eg knowing the word ‘two’ refers to sets of two entities

Order irrelevance principle

Result the same regardless of order you count items in

Abstraction principle

These principles can be applied to any collection of objects. Not labelling

Children knowledge of 5 principles

Can’t articulate this knowledge but follow rules

Attainable by age 5

Error detection test

German and Meck (1983)3-5 year olds tested on 3 principles one to one, stable order, cardinal. Children monitor performance of puppet, don’t have to count themselves

Very high accuracy on correct trials, high accuracy on incorrect trials. Children as young as 3 understand the principles

Gelman and Meck (1983)

Concluded children as young as 3 understand the principles even thought they can’t articulate them due to higher accuracy on correct trials and a bit lower accuracy on incorrect trials

Baroody (1984)

Understanding of order-irrelevance develops with age. Young children’s understanding of principles overestimated

Give “N” task knower levels

Child asked to give ‘N’ number of items

Up to 4-knowers called ‘subset’ knowers. Only know how a subset of knowers work.

Switch to CP-knower. Can solve flexibility across sets, not restricted. Really knows how counting works

Where does our numerical knowledge come from?

Empiricism: knowledge comes from experience, develops gradually

Nativism: innate understanding of some aspects of number concept “core knowledge”

habituation

Less likely to notice a stimulus overtime. Can use with very young infants to gauge innate knowledge

Procedure example: habituation to 4 dots, followed by expect 2 dots. Understand basic discrimination of numerosity?

Wynn (1992)

32 5 month olds. Looking time procedure - shown different mathematical outcomes.

Can calculate precise results of simple arithmetical operations

Wakely et al (2000)

Replication of Wynn but showed 3-1 = 1 or 2. Incase preferred answers is the greater numbers.

No systematic preference for incorrect vs correct. Infants reactions are variable.

Wynn responded by saying procedural differences affected attentiveness of infants.

Nativist view

Most dominant

Born with some innate ability to hug expands with age and experience

Experience of numbers

Number talk from parents is related to later performance in school

Conclusions

Children as young as 3 seem to have implicit knowledge of counting principles

Evidence of innate abilities: numerosity (habituation studies), arithmetical operations.

Born with limited ability, then expands with age

Task and procedure have large impact on results and age at which we see these abilities.