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A study of concept levels in three aspects of transformation geometry
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Type
Thesis
Author
Tay, Choon Hong
Supervisor
Plant, Eric
Abstract
This study has been directed essentially towards the construction of a detailed test with which to examine various possible levels of intellectual awareness of the concepts and principles involved in the study of transformation geometry. This is an important topic in the present secondary mathematics school syllabus for Singapore schools. The data and findings have been collected from Secondary Three Express Stream pupils in a school in a typical Housing Development Estate area.
The study has focussed on the three basic and significant ideas which are considered to be necessary to an initial study of transformation geometry. These are:
● reflected symmetry,
● rotational symmetry,
● enlargement.
An attempt has been made to devise test items which might reveal or suggest levels of mental awareness with respect to the three important topics which are listed above. At the same time the data was treated with some contemporary analytical statistical methods to try to suggest an ascending hierarchical sequence of levels of development within these topics and concepts.
The statistical techniques which have been used are described and illustrated in detail. The findings and evidence are presented for consideration both as relevant to mathematical education and in pupils' developmental awareness in learning some significant aspects of an important school mathematical topics.
The findings also present evidence to caution educators about the care with which it is necessary to construct test items. The effect of the use of grid behind an item to measure the pupils' awareness of line symmetry is shown and lends to contradict traditional assumption. The findings also point to the need to consider carefully the impact of concrete operational thinking even with pupils who are usually regarded as at the stage of formal reasoning.
Each item is examined in detailed with regard to the aspect of transformation which is being tested. Linkages of items are suggested and conclusions are drawn from the actual evidence of pupils' results. A final set of items for a test is justified from the data.
The study has focussed on the three basic and significant ideas which are considered to be necessary to an initial study of transformation geometry. These are:
● reflected symmetry,
● rotational symmetry,
● enlargement.
An attempt has been made to devise test items which might reveal or suggest levels of mental awareness with respect to the three important topics which are listed above. At the same time the data was treated with some contemporary analytical statistical methods to try to suggest an ascending hierarchical sequence of levels of development within these topics and concepts.
The statistical techniques which have been used are described and illustrated in detail. The findings and evidence are presented for consideration both as relevant to mathematical education and in pupils' developmental awareness in learning some significant aspects of an important school mathematical topics.
The findings also present evidence to caution educators about the care with which it is necessary to construct test items. The effect of the use of grid behind an item to measure the pupils' awareness of line symmetry is shown and lends to contradict traditional assumption. The findings also point to the need to consider carefully the impact of concrete operational thinking even with pupils who are usually regarded as at the stage of formal reasoning.
Each item is examined in detailed with regard to the aspect of transformation which is being tested. Linkages of items are suggested and conclusions are drawn from the actual evidence of pupils' results. A final set of items for a test is justified from the data.
Date Issued
1986
Call Number
QA461 Tay
Date Submitted
1986