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Thesis

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Rumiati 2010, 'An investigation of the number knowledge of first and second grade children in an Indonesian school', MEd., Southern Cross University, Lismore, NSW.

Copyright Rumiati 2010

Abstract

A model of stages in the construction of the numerical counting scheme (Steffe & Cobb, 1988) and a model of levels in base-ten arithmetical strategies (Cobb & Wheatley, 1988) have been adapted by the Mathematics Recovery Program (Wright, Martland & Stafford, 2006) to document children’s progress in arithmetical learning. Using the assessment theories, techniques and tools developed by this Program, this study investigates number knowledge of children in the first and second grades of an Indonesian school. Forty children, twenty from each grade, were selected for videotaped interviews. Each interview addressed six areas: strategies in early arithmetical learning, structuring numbers 1–20, base-ten arithmetical strategies, numeral identification, forward and backward number word sequences, number word after and number word before. In order to gain an additional picture of their number knowledge, a series of written tests and a children’s questionnaire were administered, and informal conversations with teachers were undertaken.

The interview results show that, in terms of the model of stages in early arithmetical learning, sixteen first-graders and six second-graders were at the advanced Countingby- ones stage, while four first-graders and fourteen second-graders were at the facile stage. With regard to the model of levels in the knowledge of base-ten arithmetical strategies, five first-graders and four second-graders were at the initial level, fifteen first-graders and eleven second-graders were at the intermediate level, and five secondgraders were at the facile level.

Other findings were that five first-graders used the Chisanbop method and twelve children, nine from the second grade and three from the first grade, used the erroneous algorithm ‘subtract smaller from larger’. While the use of fingers seemed to be vestigial for several students, most children were observed to use fingers to support their counting. Their strategies were likely to mirror the teaching approaches used in their school, home and out-of-school number lessons. The overall findings give rise to concerns about current number teaching practices in this school which emphasise the standard written algorithm in the first and second grades. The findings support notions that the teaching of the standard algorithm in the first and second grades could be harmful. Results also suggest that using the Chisanbop method could be a barrier to children using their own informal algorithms.

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