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Differences in performance and choice of heuristics in mathematical problem solving among secondary three male gifted pupils in Singapore
Author
Rajaram Ramasubban
Supervisor
Foong, Pui Yee
Abstract
This study examines the differences in the performances in the mathematical problem-solving processes among gifted pupils. The main objective of the study was to investigate differences in problem-solving performance in non-routine mathematical problems among three groups of gifted pupils - the highly gifted, averagely gifted and less than averagely gifted pupils. A second objective was to study the differences in the choice of heuristics among the gifted pupils.
This study is presented in three parts : i) a literature review of giftedness and mathematical problem-solving, ii) a report on the present research which includes a pilot study, the main study and a quantitative and qualitative analysis of the data collected and iii) research findings derived from the data of the differences among the three groups gifted pupils and its implications for mathematics teaching in gifted education programme classrooms.
The sample for the main study consisted of 73 Secondary Three pupils enrolled in the Gifted Education Programme at Raffles Institution, a leading independent school in Singapore.
A Problem-Solving Achievement Test was designed by the researcher using tasks developed by the Shell Centre of Mathematics, Nottingham University (1984). Responses to the Test were marked based on the Analytic Scoring Scale developed by Charles, Lester and O'Daffer (1987). Qualitative analyses of the written protocols were also done. To assess the suitability of the Problem-Solving Achievement Test, a pilot study was done on a group of 24 pupils using two sets of three mathematical problems each. Eventually, four problems that were sufficiently challenging were selected for the main study.
In summary, the findings of the main study showed that the highly gifted pupils were able to understand the requirements of a problem better because they were able to retrieve the relevant domain specific knowledge relevant to the problem from their memory and apply it. In contrast, the other two groups of pupils had a weaker grasp of the mathematical knowledge. The averagely gifted pupils understood the problems in terms of what was explicitly stated in the problem and the less than the averagely gifted pupils showed more lapses in mathematical knowledge and missed important pieces of information necessary for full understanding of the problem requirements.
Having understood a problem in terms of mathematical principles and ideas, the highly gifted used content-related strategies to solve the problem. They were also more proficient in executing the heuristics skilfully and made relatively fewer computational errors. The averagely gifted applied more general strategies such as drawing a diagram and constructing a table and the less than averagely gifted pupils used weaker strategies such as trial and error and were not able to solve the problems as well because of poor execution of the heuristics.
The findings have significant implications as to how mathematical problem-solving is taught in the gifted programme classrooms. There is obviously a range of ability levels even within the gifted group of pupils and the teaching approach must suit the type of pupils that are being taught.
This study is presented in three parts : i) a literature review of giftedness and mathematical problem-solving, ii) a report on the present research which includes a pilot study, the main study and a quantitative and qualitative analysis of the data collected and iii) research findings derived from the data of the differences among the three groups gifted pupils and its implications for mathematics teaching in gifted education programme classrooms.
The sample for the main study consisted of 73 Secondary Three pupils enrolled in the Gifted Education Programme at Raffles Institution, a leading independent school in Singapore.
A Problem-Solving Achievement Test was designed by the researcher using tasks developed by the Shell Centre of Mathematics, Nottingham University (1984). Responses to the Test were marked based on the Analytic Scoring Scale developed by Charles, Lester and O'Daffer (1987). Qualitative analyses of the written protocols were also done. To assess the suitability of the Problem-Solving Achievement Test, a pilot study was done on a group of 24 pupils using two sets of three mathematical problems each. Eventually, four problems that were sufficiently challenging were selected for the main study.
In summary, the findings of the main study showed that the highly gifted pupils were able to understand the requirements of a problem better because they were able to retrieve the relevant domain specific knowledge relevant to the problem from their memory and apply it. In contrast, the other two groups of pupils had a weaker grasp of the mathematical knowledge. The averagely gifted pupils understood the problems in terms of what was explicitly stated in the problem and the less than the averagely gifted pupils showed more lapses in mathematical knowledge and missed important pieces of information necessary for full understanding of the problem requirements.
Having understood a problem in terms of mathematical principles and ideas, the highly gifted used content-related strategies to solve the problem. They were also more proficient in executing the heuristics skilfully and made relatively fewer computational errors. The averagely gifted applied more general strategies such as drawing a diagram and constructing a table and the less than averagely gifted pupils used weaker strategies such as trial and error and were not able to solve the problems as well because of poor execution of the heuristics.
The findings have significant implications as to how mathematical problem-solving is taught in the gifted programme classrooms. There is obviously a range of ability levels even within the gifted group of pupils and the teaching approach must suit the type of pupils that are being taught.
Date Issued
1997
Call Number
QA63 Raj
Description
Pg. 137 is missing
Date Submitted
1997