The number concept Flashcards
what is the number concept
Numerosity, counting, arithmetic
what are the 5 counting principle
one-to-one principle
stable-order principle
cardinal principle
order irrelevance principle
abstraction principle
what is the one to one counting principle
One and only one tag or “counting word” for each item in the set
what is the stable order counting principle
Tags must be used in the same way
what is the cardinal principle
The tag of the final object in the set represents the total number of items
what is order irrelevance principle
result the same regardless of order you count items in
what is the abstraction principle
these principles can be applied to any collection of objects (including intangible objects)
what is implicit knowledge of the principles
Can’t articulate this knowledge, but follow rules
when are the five principles attainable by
the age of 5
who completed the error detection task
Gelman and Meck
what age are tested in the error detection test
3 to 5 year olds
what happens during the error detection task
children monitor performance of a puppet
Results of error detection test
Pseudo-errors detected as peculiar, but not incorrect
older children performed better but success rates not affected by set size at any age
conclusions of error detection tasks
children as young as 3 understand the principles even though they cannot articulate them
what did Baroody do
tested order irrelevance and cardinality in 5-7 year olds
Baroody method
Children shown 8 items
Count them left to right and then indicate the cardinal value of set
Can you make this number 1
We got N counting this way, what do you think we would get counting the other way?”
Baroody results
All but 1 child could recount in the opposite direction
BUT, only 45% of 5yr-olds, and 87% of 7yr-olds were successful in prediction task
Baroody conclusions
Understanding of order-irrelevance develops with age
Young children’s understanding of principles overestimated
how do tasks affect how children perform
Failure the result of misinterpretation of instructions, not lack of understanding
Gelman et al procedure
Baroody replication
Count 3x: 3 opportunities to count first
Altered-question: “How many will there be”
or “What will you get”
define empiricism
knowledge comes from experience, develops gradually
define nativism
innate understanding of some aspects of number concept, “core knowledge”
when are habituation studies used
Can use with very young infants to gauge innate knowledge
Wynn conclusions
5-month olds can calculate precise results of simple arithmetical operations
Infants possess true numerical concepts
criticisms of Wakeley et al
replications found no systematic preference for incorrect vs correct
conclusions from Wakeley et al
Earlier findings of numerical competence not replicated
Infants reactions are variable
Gradual and continual progress in abilities with age
what was Wynn’s response
Procedural differences affected attentiveness of infants
which view is currently dominant
Nativist view dominant - born with some innate ability which expands with age
what age do children seem to have implicit knowledge of counting principles
as young as 3 years
why may the evidence of innate abilities be conflicting
Task and procedure have large impact on results and age at which we see these abilities
