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The Idea of an Exact Number: Children's Understanding of Cardinality and Equinumerosity
Author(s) -
Sarnecka Barbara W.,
Wright Charles E.
Publication year - 2013
Publication title -
cognitive science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.498
H-Index - 114
eISSN - 1551-6709
pISSN - 0364-0213
DOI - 10.1111/cogs.12043
Subject(s) - cardinality (data modeling) , successor cardinal , cardinal number (linguistics) , mathematics , function (biology) , combinatorics , generating function , enumeration , discrete mathematics , computer science , linguistics , data mining , mathematical analysis , philosophy , evolutionary biology , biology
Understanding what numbers are means knowing several things. It means knowing how counting relates to numbers (called the cardinal principle or cardinality ); it means knowing that each number is generated by adding one to the previous number (called the successor function or succession ), and it means knowing that all and only sets whose members can be placed in one‐to‐one correspondence have the same number of items (called exact equality or equinumerosity ). A previous study (Sarnecka & Carey, 2008) linked children's understanding of cardinality to their understanding of succession for the numbers five and six. This study investigates the link between cardinality and equinumerosity for these numbers, finding that children either understand both cardinality and equinumerosity or they understand neither. This suggests that cardinality and equinumerosity (along with succession) are interrelated facets of the concepts five and six , the acquisition of which is an important conceptual achievement of early childhood.