%0 Journal Article %1 Ollive01 %A Olive, John %D 2001 %J The Mathematics Educator %K ijmte2006 mythesis sequences %N 1 %P 4-9 %T Children's Number Sequences: An Explanation of Steffe's Constructs and an Extrapolation to Rational Numbers of Arithmetic %U http://jwilson.coe.uga.edu/DEPT/TME/Issues/v11n1/2olive.html %V 11 %X In regarding young children as mathematicians we need to pay close attention to how children develop their mathematical thinking. It would be misleading to assume that young children think mathematically in the same way as adult mathematicians. Children have to develop their mathematical structures and their ways and means of operating mathematically. These structures and operations have to be constructed from the childﾒs own activities. They cannot be given to the child "ready made." One of the most fundamental mathematical structures that a child develops early on in life is that of a number sequence. The basic activity that leads to the construction of a number sequence is that of counting. The activity of counting, however, does not occur all at once for a child. Steffe, von Glasersfeld,. Richards and Cobb (1983) indicated in their research of young childrenﾒs counting activities that early counting progresses through five distinct types of activity, from the counting of perceptual unit items to the counting of abstract unit items. They liken this progression to Piagetﾒs concept of öbject permanence" (p.117). A childﾒs number sequence, however, is not a static structure. It also progresses through several developmental changes that are brought about through adaptations in the childrenﾒs counting activities as they encounter more complex numerical situations. Following their work on childrenﾒs counting types, Steffe and Cobb (1988) further developed the notion of children's abstract number sequences from their teaching experiments with first and second grade children. They described the development of three successive number sequences: the Initial Number Sequence (INS), the Tacitly Nested Number Sequence (TNS) and the Explicitly Nested Number Sequence (ENS). What follows are my attempts to clarify my own thinking about these hypothetical number sequences and an extrapolation from these sequences to a Generalized Number Sequence (GNS) and subsequently to the Rational Numbers of Arithmetic (RNA).

@article{Ollive01, abstract = {In regarding young children as mathematicians we need to pay close attention to how children develop their mathematical thinking. It would be misleading to assume that young children think mathematically in the same way as adult mathematicians. Children have to develop their mathematical structures and their ways and means of operating mathematically. These structures and operations have to be constructed from the childﾒs own activities. They cannot be given to the child "ready made." One of the most fundamental mathematical structures that a child develops early on in life is that of a number sequence. The basic activity that leads to the construction of a number sequence is that of counting. The activity of counting, however, does not occur all at once for a child. Steffe, von Glasersfeld,. Richards and Cobb (1983) indicated in their research of young childrenﾒs counting activities that early counting progresses through five distinct types of activity, from the counting of perceptual unit items to the counting of abstract unit items. They liken this progression to Piagetﾒs concept of "object permanence" (p.117). A childﾒs number sequence, however, is not a static structure. It also progresses through several developmental changes that are brought about through adaptations in the childrenﾒs counting activities as they encounter more complex numerical situations. Following their work on childrenﾒs counting types, Steffe and Cobb (1988) further developed the notion of children's abstract number sequences from their teaching experiments with first and second grade children. They described the development of three successive number sequences: the Initial Number Sequence (INS), the Tacitly Nested Number Sequence (TNS) and the Explicitly Nested Number Sequence (ENS). What follows are my attempts to clarify my own thinking about these hypothetical number sequences and an extrapolation from these sequences to a Generalized Number Sequence (GNS) and subsequently to the Rational Numbers of Arithmetic (RNA).}, added-at = {2010-08-05T08:58:11.000+0200}, author = {Olive, John}, biburl = {https://www.bibsonomy.org/bibtex/2241ac6e001d40436847c5db00a984af2/yish}, citeulike-article-id = {532458}, comment = {good explanation of the Piaget / Steffe stages in development of the number sequence concept.}, interhash = {07ba6fb7c3271d457adf507fd6234778}, intrahash = {241ac6e001d40436847c5db00a984af2}, journal = {The Mathematics Educator}, keywords = {ijmte2006 mythesis sequences}, number = 1, pages = {4-9}, priority = {2}, timestamp = {2010-08-05T08:58:12.000+0200}, title = {Children's Number Sequences: An Explanation of Steffe's Constructs and an Extrapolation to Rational Numbers of Arithmetic}, url = {http://jwilson.coe.uga.edu/DEPT/TME/Issues/v11n1/2olive.html}, volume = 11, year = 2001 }