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Pupils' understanding of area
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Type
Thesis
Author
Tan, Chu Sing
Supervisor
Plant, Eric
Abstract
Measurement is a fundamental concept not only in mathematics and science but is also a very important idea with many practical everyday applications. The present study is concerned with an essential aspect of measurement, namely the "measurement of an amount of surface" which is used in this study as a workable definition of the concept of area at the level of primary school pupils.
In the contemporary Singapore primary school system, children are streamed into one of three courses: the Normal Bilingual Course designated the Normal course, Extended Bilingual Course (Extended course) or Monolingual course after Primary Three. The course to which children are allocated depends on performance in the school examinations from Primary one to three. A child who is streamed into the Normal course (N course) will take a three-year course from Primary 4N to 6N before he sits for the Primary school Leaving Examination (PSLE) at Primary 6N. At the same time, a child who is in the Extended course will take a five-years course from Primary 4E to 8E before he sits for PSLE at primary 8E. For a child in the Monolingual course (M course) he too will take a five-year course from Primary 4M to 8M before he sits for Primary School Proficiency Examination (PSPE) at Primary 8M.
The Singapore New Primary School mathematics syllabus (Normal course) requires pupils to learn about area from Primary 4N to Primary 6N. This research focuses on the Primary 5N and Primary 6E pupils whom where taught "Formula of area of the rectangle" at Primary 4N and 5E levels as outlined in the mathematics syllabus. By testing pupils using a paper-and-pencil test, the results have been examined in order to consider the extent to which pupils have an understanding of area. The items in the test are designed to permit a description of four levels of development which pupils seem to attain as they develop a full understanding of the idea of area. These are designated as follows:
(i) Understanding of area vocabulary
(ii) Sorting and matching
(iii) Conservation of area
(iv) Measurement of area
The whole study consists of two pilot tests and one main study. The aim of the first pilot study was to develop a set of appropriate test items. A split-half multiple-choice test of twenty-two items was produced. The split half method permitted a comparison of the questions as two parallel sets. Multiple-choice items were used. The test items were scored 1 or 0, according as they were correct or incorrect. A Kuder-Richardson formula 20 (KR20) was used to calculate reliability and internal consistency. The reliability estimate of KR20 for the first pilot test was found to be 0.61. By using the Nuttall and Skurnik's criterion, the suitability of the test items was determined. Two best-items were reconstructed and an additional twelve test-items were added. A second pilot study then comprised thirty-four questions. The reliability estimate of the test as indicated by KR20 was improved to 0.81. All the test-items satisfied the Nuttall and Skurnik's criterion. The test was therefore validated and considered adequate for the main study.
In the main study, a total of two hundred and eighty-two pupils from Primary 5N and Primary 6E levels were given the validated test. The value of the KR20 at this stage was 0.84. The pupils were also divided into three different ability groups, namely high, average and low, based on their test scores.
In order to examine some pupil responses in greater detail, clinical interviews were conducted with a sample of pupils from the three ability groups. In this way, a comparison was made between interview outcome and scores in the written test in order to check the evidence for the four levels of development. The evidence and data analysis together with the conclusions and implications of the investigation are presented in the study.
In the contemporary Singapore primary school system, children are streamed into one of three courses: the Normal Bilingual Course designated the Normal course, Extended Bilingual Course (Extended course) or Monolingual course after Primary Three. The course to which children are allocated depends on performance in the school examinations from Primary one to three. A child who is streamed into the Normal course (N course) will take a three-year course from Primary 4N to 6N before he sits for the Primary school Leaving Examination (PSLE) at Primary 6N. At the same time, a child who is in the Extended course will take a five-years course from Primary 4E to 8E before he sits for PSLE at primary 8E. For a child in the Monolingual course (M course) he too will take a five-year course from Primary 4M to 8M before he sits for Primary School Proficiency Examination (PSPE) at Primary 8M.
The Singapore New Primary School mathematics syllabus (Normal course) requires pupils to learn about area from Primary 4N to Primary 6N. This research focuses on the Primary 5N and Primary 6E pupils whom where taught "Formula of area of the rectangle" at Primary 4N and 5E levels as outlined in the mathematics syllabus. By testing pupils using a paper-and-pencil test, the results have been examined in order to consider the extent to which pupils have an understanding of area. The items in the test are designed to permit a description of four levels of development which pupils seem to attain as they develop a full understanding of the idea of area. These are designated as follows:
(i) Understanding of area vocabulary
(ii) Sorting and matching
(iii) Conservation of area
(iv) Measurement of area
The whole study consists of two pilot tests and one main study. The aim of the first pilot study was to develop a set of appropriate test items. A split-half multiple-choice test of twenty-two items was produced. The split half method permitted a comparison of the questions as two parallel sets. Multiple-choice items were used. The test items were scored 1 or 0, according as they were correct or incorrect. A Kuder-Richardson formula 20 (KR20) was used to calculate reliability and internal consistency. The reliability estimate of KR20 for the first pilot test was found to be 0.61. By using the Nuttall and Skurnik's criterion, the suitability of the test items was determined. Two best-items were reconstructed and an additional twelve test-items were added. A second pilot study then comprised thirty-four questions. The reliability estimate of the test as indicated by KR20 was improved to 0.81. All the test-items satisfied the Nuttall and Skurnik's criterion. The test was therefore validated and considered adequate for the main study.
In the main study, a total of two hundred and eighty-two pupils from Primary 5N and Primary 6E levels were given the validated test. The value of the KR20 at this stage was 0.84. The pupils were also divided into three different ability groups, namely high, average and low, based on their test scores.
In order to examine some pupil responses in greater detail, clinical interviews were conducted with a sample of pupils from the three ability groups. In this way, a comparison was made between interview outcome and scores in the written test in order to check the evidence for the four levels of development. The evidence and data analysis together with the conclusions and implications of the investigation are presented in the study.
Date Issued
1987
Call Number
QA135.5 Tan
Date Submitted
1987