The number concept

Question 1

what is the number concept

Answer 1

Numerosity, counting, arithmetic

Question 2

what are the 5 counting principle

Answer 2

one-to-one principle
stable-order principle
cardinal principle
order irrelevance principle
abstraction principle

Question 3

what is the one to one counting principle

Answer 3

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

Question 4

what is the stable order counting principle

Answer 4

Tags must be used in the same way

Question 5

what is the cardinal principle

Answer 5

The tag of the final object in the set represents the total number of items

Question 6

what is order irrelevance principle

Answer 6

result the same regardless of order you count items in

Question 7

what is the abstraction principle

Answer 7

these principles can be applied to any collection of objects (including intangible objects)

Question 8

what is implicit knowledge of the principles

Answer 8

Can’t articulate this knowledge, but follow rules

Question 9

when are the five principles attainable by

Answer 9

the age of 5

Question 10

who completed the error detection task

Answer 10

Gelman and Meck

Question 11

what age are tested in the error detection test

Answer 11

3 to 5 year olds

Question 12

what happens during the error detection task

Answer 12

children monitor performance of a puppet

Question 13

Results of error detection test

Answer 13

Pseudo-errors detected as peculiar, but not incorrect
older children performed better but success rates not affected by set size at any age

Question 14

conclusions of error detection tasks

Answer 14

children as young as 3 understand the principles even though they cannot articulate them

Question 15

what did Baroody do

Answer 15

tested order irrelevance and cardinality in 5-7 year olds

Question 16

Baroody method

Answer 16

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?”

Question 17

Baroody results

Answer 17

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

Question 18

Baroody conclusions

Answer 18

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

Question 19

how do tasks affect how children perform

Answer 19

Failure the result of misinterpretation of instructions, not lack of understanding

Question 20

Gelman et al procedure

Answer 20

Baroody replication
Count 3x: 3 opportunities to count first
Altered-question: “How many will there be”
or “What will you get”

Question 21

define empiricism

Answer 21

knowledge comes from experience, develops gradually

Question 22

define nativism

Answer 22

innate understanding of some aspects of number concept, “core knowledge”

Question 23

when are habituation studies used

Answer 23

Can use with very young infants to gauge innate knowledge

Question 24

Wynn conclusions

Answer 24

5-month olds can calculate precise results of simple arithmetical operations
Infants possess true numerical concepts

Question 25

criticisms of Wakeley et al

Answer 25

replications found no systematic preference for incorrect vs correct

Question 26

conclusions from Wakeley et al

Answer 26

Earlier findings of numerical competence not replicated Infants reactions are variable Gradual and continual progress in abilities with age

Question 27

what was Wynn's response

Answer 27

Procedural differences affected attentiveness of infants

Question 28

which view is currently dominant

Answer 28

Nativist view dominant - born with some innate ability which expands with age

Question 29

what age do children seem to have implicit knowledge of counting principles

Answer 29

as young as 3 years

Question 30

why may the evidence of innate abilities be conflicting

Answer 30

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