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Development of subtraction skills by primary school children in Singapore
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Type
Thesis
Author
Chu, Chiu Wai
Supervisor
Wong, Khoon Yoong
Abstract
Subtraction concepts and algorithmic skills form part of the basic mathematical skills that children in Singapore are taught when they are in Primary 1 to Primary 3. In a survey conducted by the Singapore Ministry of Education (1982b), particular attention was drawn to the drop in percentages of children having attained mastery (an attainment of 80%) in subtraction skills. The percentage for Primary 1 was 86.4%, but it dropped to 53.1% in Primary 2. The percentage for Primary 3 was 74.1%. A poor mastery of the algorithmic skills may be a hindrance to the child's understanding of other mathematical skills.
This study attempted to investigate the order of acquisition of subtraction skills by children, the sequence of complexity of the subtraction skills and the types of errors committed by the children. The information obtained from this study can have important implications for the teaching of these skills especially when a comprehensive set of specific instructional objectives is used as a guide for lesson plans and test construction. The error types identified will provide information the misconceptions that children have on performing subtraction skills.
A criterion-reference test on subtraction facts and algorithmic skills was designed for this study. Up to 4-digit numbers used in the test items which consist of a varied combination of number of digits, renaming and the involvement of 0 digit in the renaming. This test was given to a sample of 381 Primary 1 to 3 children in two primary schools of average academic ability.
The data obtained were subjected to two statistical analyses to determine the homogeneous groups of items at various facility bands and the scalability of these groups. The results of the two statistical analyses showed that there was an order of acquisition of subtraction skills by the children. This order was similar to that suggested by other researchers like Gagne(1965) and Cox(1975), and that presented in the Singapore primary Mathematics Syllabus.
The complexity of the subtraction skills could be described in terms of the basic facts, horizontal and vertical format of presentation of the item, number of digits, number of renaming,involvement of the 0 digit in the renaming and the column position of the renaming. The vertical format of presentation was found to be more difficult than the horizontal format. The difficult than the horizontal format. The difficulty of an item was increased when the number of digits or trending was increased and when the 0 digit was involved in the renaming. Renaming at a middle digit was also more difficult than renaming at the right-most digit. This sequence of complexity was similar to the sequence in a set of specific instructional objectives compiled by some teachers from a group of primary schools in Singapore.
Altogether 25 error types were identified and the three common errors were basic subtraction factors, subtract smaller digit from larger digit when the smaller digit is in the minuend, and do not reduce the digit in minuend by 1 after a renaming. The errors could be classified as basic fact errors, conceptual errors and procedural errors. A wide range of conceptual errors (22 types) were found. these errors involved renaming and the 0 digit. They suggest a lack of understanding on the place value in the deanery system and the role of the 0 digit in the renaming procedure.
The results of this study have important implications to the teaching and redemption of subtraction skills. The subtraction skills need to be taught in the order identified in this study so that the children can acquire the skills according to their levels of cognitive development. The sequence of complexity of subtraction skills can be used as a guide in compiling specific instructional objectives to be used for teaching and test design. Effective strategies are also needed to help children understanding the basic concepts like place value so that they can master the basic arithmetic skills.
This study attempted to investigate the order of acquisition of subtraction skills by children, the sequence of complexity of the subtraction skills and the types of errors committed by the children. The information obtained from this study can have important implications for the teaching of these skills especially when a comprehensive set of specific instructional objectives is used as a guide for lesson plans and test construction. The error types identified will provide information the misconceptions that children have on performing subtraction skills.
A criterion-reference test on subtraction facts and algorithmic skills was designed for this study. Up to 4-digit numbers used in the test items which consist of a varied combination of number of digits, renaming and the involvement of 0 digit in the renaming. This test was given to a sample of 381 Primary 1 to 3 children in two primary schools of average academic ability.
The data obtained were subjected to two statistical analyses to determine the homogeneous groups of items at various facility bands and the scalability of these groups. The results of the two statistical analyses showed that there was an order of acquisition of subtraction skills by the children. This order was similar to that suggested by other researchers like Gagne(1965) and Cox(1975), and that presented in the Singapore primary Mathematics Syllabus.
The complexity of the subtraction skills could be described in terms of the basic facts, horizontal and vertical format of presentation of the item, number of digits, number of renaming,involvement of the 0 digit in the renaming and the column position of the renaming. The vertical format of presentation was found to be more difficult than the horizontal format. The difficult than the horizontal format. The difficulty of an item was increased when the number of digits or trending was increased and when the 0 digit was involved in the renaming. Renaming at a middle digit was also more difficult than renaming at the right-most digit. This sequence of complexity was similar to the sequence in a set of specific instructional objectives compiled by some teachers from a group of primary schools in Singapore.
Altogether 25 error types were identified and the three common errors were basic subtraction factors, subtract smaller digit from larger digit when the smaller digit is in the minuend, and do not reduce the digit in minuend by 1 after a renaming. The errors could be classified as basic fact errors, conceptual errors and procedural errors. A wide range of conceptual errors (22 types) were found. these errors involved renaming and the 0 digit. They suggest a lack of understanding on the place value in the deanery system and the role of the 0 digit in the renaming procedure.
The results of this study have important implications to the teaching and redemption of subtraction skills. The subtraction skills need to be taught in the order identified in this study so that the children can acquire the skills according to their levels of cognitive development. The sequence of complexity of subtraction skills can be used as a guide in compiling specific instructional objectives to be used for teaching and test design. Effective strategies are also needed to help children understanding the basic concepts like place value so that they can master the basic arithmetic skills.
Date Issued
1987
Call Number
QA115 Chu
Date Submitted
1987