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ERIC Number: ED422186
Record Type: RIE
Publication Date: 1998
Pages: 52
Abstractor: N/A
Reference Count: N/A
ISBN: N/A
ISSN: N/A
Children's Construction of the Operation of Addition.
Grobecker, Betsey
Six- to eight-year-old children (N=42) who were identified by their teachers as within the average range of ability in mathematics were individually tested on three different mathematics tasks. On the flashcard task and the nonverbal task where children replicated the number of buttons placed under a box, the same 14 addition problems with sums up to 20 were used. The third task investigated children's understanding of the associativity of length where they had to determine if string segments of various length, number of cuts, and different spatial orientations were of equal length. These data were analyzed using Rasch statistics which places both the items and the children along a hierarchical scale of difficulty. The results indicated that within each of the tasks there existed a sequential construction of increasingly complex cognitive abilities which was measured by providing the correct answers and the strategy types used. Further, a comparison between the flashcard, nonverbal, and associativity of length tasks elicited a developmental relationship between the ability to generate more sophisticated strategies to solve mathematics problems and the evolution of operational structures as measured on the Piagetian associativity task. These findings were discussed relative to the dispute as to whether mathematical knowledge consists of the internal construction of relationships or the mapping of standard mathematical symbols onto a preexisting mental model of number and number transformation. Remedial implications of the findings follow. Contains 49 references. (Author)
Publication Type: Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A