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Strategies and errors in solving ratio and proportion problems of grade 6 students of an international school in Singapore
Author
Akhila Seshadrinathan
Supervisor
Foong, Pui Yee
Abstract
The purpose of the study was to examine Grade 6 students' strategies and errors in solving ratio and proportion problems. This study was conducted on a group of 36 Grade 6 students of an International school in Singapore. This institution subscribes to the curriculum laid down by the Central Board of Secondary Education (CBSE), India.
An instrument consisting of five word problems on ratio and proportion in the form of a paper and pencil test was designed for the study. These word problems were of four types - missing value, comparison, stretcher and mixtures. The assessment was done based on the students' performance in the paper and pencil test.
The overall achievement of the students in the paper and pencil test was based on the scores obtained in the paper and pencil tests. They obtained an overall average score of 15.64 marks out of a maximum possible score of 20 marks with a standard deviation of 3.83. Based on the scores obtained by the students, they were categorized into 3 groups as Low Achievers (LA) who scored between 6 and 10, Average Achievers (AA) who scored between 11 and 15, and High Achievers (HA) who scored between 16 and 20. The overall performance of the sample can be considered to be 'good' as more than half of the students could be grouped under HA.
Analysis of results showed that the most popular strategy among the students was the algorithm method. A closer study of the students' working showed that they had a tendency to use the algorithm method as a rote procedure. Successful application of this particular strategy did not necessarily imply that the students had the conceptual understanding of the multiplicative relationships. Students with higher scores tended to use a wider variety of strategies.
Among the errors, the most prominent was the use of an illogical strategy or incomplete reasoning implying that the students lacked conceptual understanding of ratio and proportion problems. The mixture problem proved to be the most difficult for the students and this item invoked the largest number of illogical responses.
Taking into account the scores obtained, the strategies used and the errors made, it was possible to assign the students to three levels of proportional reasoning ability. The students at level 1 having scores between 6 and 10 used illogical strategies to attempt a solution. Students at level 2 having a score between 11 and 15 were able to use more strategies compared to the students at level 1 in solving ratio and proportion problems. The students at level 3 who scored between 16 and 20 were able to use a wider variety of strategies to arrive at the solution.
An instrument consisting of five word problems on ratio and proportion in the form of a paper and pencil test was designed for the study. These word problems were of four types - missing value, comparison, stretcher and mixtures. The assessment was done based on the students' performance in the paper and pencil test.
The overall achievement of the students in the paper and pencil test was based on the scores obtained in the paper and pencil tests. They obtained an overall average score of 15.64 marks out of a maximum possible score of 20 marks with a standard deviation of 3.83. Based on the scores obtained by the students, they were categorized into 3 groups as Low Achievers (LA) who scored between 6 and 10, Average Achievers (AA) who scored between 11 and 15, and High Achievers (HA) who scored between 16 and 20. The overall performance of the sample can be considered to be 'good' as more than half of the students could be grouped under HA.
Analysis of results showed that the most popular strategy among the students was the algorithm method. A closer study of the students' working showed that they had a tendency to use the algorithm method as a rote procedure. Successful application of this particular strategy did not necessarily imply that the students had the conceptual understanding of the multiplicative relationships. Students with higher scores tended to use a wider variety of strategies.
Among the errors, the most prominent was the use of an illogical strategy or incomplete reasoning implying that the students lacked conceptual understanding of ratio and proportion problems. The mixture problem proved to be the most difficult for the students and this item invoked the largest number of illogical responses.
Taking into account the scores obtained, the strategies used and the errors made, it was possible to assign the students to three levels of proportional reasoning ability. The students at level 1 having scores between 6 and 10 used illogical strategies to attempt a solution. Students at level 2 having a score between 11 and 15 were able to use more strategies compared to the students at level 1 in solving ratio and proportion problems. The students at level 3 who scored between 16 and 20 were able to use a wider variety of strategies to arrive at the solution.
Date Issued
2006
Call Number
QA117 Akh
Date Submitted
2006