Teacher Education, Educational Leadership & Policy ETDs

Publication Date



This study investigated the origins of ordinal and cardinal number concepts in five-, six-, and seven-year old Anglo, Hispanic and Native American children, and the effects of that acquisition on the ability to manipulate the first four natural numbers. The research subjects were Kindergarten and first grade students at rural public schools (Anglo and Hispanic) in New Mexico, and at a contract community school or an independent day school on the Hopi Reservation in Arizona. All the children were tested during the first two weeks of the school year to control for a minimum of school training, and were tested in their dominant language as determined by teachers and parents.

Ordinality is defined as a transitive asymmetric relationship (length and weight) and cardinality as a concept of manyness. The study looked at whether these concepts are acquired sequentially or simultaneously, as determined previously by Brainerd (sequential) and Piaget (simultaneous). Manipulation of number is defined as the ability to add and subtract the first four natural numbers. The study is an extension of the work done by Brainerd in 1973 and 1979.

It was hypothesized that: 1) Anglo and Hispanic children would acquire the two concepts simultaneously; 2) Native American children would acquire the two concepts sequentially (cardinal before ordinal); 3) children showing a simultaneous acquisition would achieve a higher level of addition and subtraction skills than children acquiring the concepts sequentially; 4) there would be a difference in the sequential population between boys and girls; and 5) children acquiring cardinality before ordinality would show a higher level of subtraction than addition.

Ninety Kindergarten and first grade children were selected for testing either by this writer (English speakers) or their teachers (Hispanic and Hopi speakers). Each ethnic group of 30 subjects was evenly divided by sex and grade level. Each child was tested individually with a language pre-test, an ordinal task, a cardinal task, and a test of arithmetic skills.

Document Type




Level of Degree


Department Name

Teacher Education, Educational Leadership & Policy

First Committee Member (Chair)

David Wayne Darling

Second Committee Member

Rafael M. Diaz

Third Committee Member

Catherine Ellen Loughlin

Fourth Committee Member

Patrick B. Scott

Fifth Committee Member

David Hawkins