# THE DEVELOPMENT OF ORDINATION, CARDINATION AND NATURAL NUMBER

http://hdl.handle.net/10150/282315
Title:
THE DEVELOPMENT OF ORDINATION, CARDINATION AND NATURAL NUMBER
Author:
Skorney, James Robert
Issue Date:
1980
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
This study investigated domains within the tasks of ordination, cardination and natural number. In addition, it examined the sequencing of the development of established domains between ordination, cardination and natural number. One hundred and forty-eight children were individually given a test designed to ascertain the presence of arithmetic related skills. The task of cardination was designed to detect the ability to associate numbers with sets containing a group of elements ranging from one to five. The task of ordination was designed to detect the ability to associate a number with a relative position within a group of ordered objects. The task of natural number assessed children's ability to add numbers with a sum equal to five or less. Latent structure analysis was used to analyze the results. Four different models were used in order to establish domains within each task. The four models that were used tested independence, equiprobability, ordered relations and asymmetrical equivalence. The results showed two domains for cardination. One item in a set constituted one domain while three and five items in a set constituted a second domain. The domain for ordination included relative positions one, three and five. In regards to natural number, the results showed a permeable domain. There was some indication of ordering but it was not strong enough to yield separate domains. The same models were then used to compare across the different tasks. The results showed that the easiest cardination domain developed before ordination and natural number. The results also showed that the ordination task was equivalent to one of the natural number tasks. All of the other comparisons between cardination, ordination and natural number yielded asymmetrically equivalent relations. That is, there was an ordering but the ordering was not strong enough to establish separate domains.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Degree Grantor:
University of Arizona
Bergan, John R.

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleTHE DEVELOPMENT OF ORDINATION, CARDINATION AND NATURAL NUMBERen_US
dc.creatorSkorney, James Roberten_US
dc.contributor.authorSkorney, James Roberten_US
dc.date.issued1980en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThis study investigated domains within the tasks of ordination, cardination and natural number. In addition, it examined the sequencing of the development of established domains between ordination, cardination and natural number. One hundred and forty-eight children were individually given a test designed to ascertain the presence of arithmetic related skills. The task of cardination was designed to detect the ability to associate numbers with sets containing a group of elements ranging from one to five. The task of ordination was designed to detect the ability to associate a number with a relative position within a group of ordered objects. The task of natural number assessed children's ability to add numbers with a sum equal to five or less. Latent structure analysis was used to analyze the results. Four different models were used in order to establish domains within each task. The four models that were used tested independence, equiprobability, ordered relations and asymmetrical equivalence. The results showed two domains for cardination. One item in a set constituted one domain while three and five items in a set constituted a second domain. The domain for ordination included relative positions one, three and five. In regards to natural number, the results showed a permeable domain. There was some indication of ordering but it was not strong enough to yield separate domains. The same models were then used to compare across the different tasks. The results showed that the easiest cardination domain developed before ordination and natural number. The results also showed that the ordination task was equivalent to one of the natural number tasks. All of the other comparisons between cardination, ordination and natural number yielded asymmetrically equivalent relations. That is, there was an ordering but the ordering was not strong enough to establish separate domains.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectNumber concept.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineEducational Psychologyen_US
thesis.degree.grantorUniversity of Arizonaen_US