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Mathematical reasoning of secondary two students in proportion
Author
Renuka Ramakrishnan
Supervisor
Chua, Boon Liang
Abstract
Proportion is a comparison between two rates or ratios, each of which is coordinated between two variables. Proportional reasoning is the ability to analyse mathematical situations involving proportion and construct logical arguments.
Mathematical reasoning in proportion plays a pivotal role in students’ understanding of various topics in mathematics and sciences at the primary, secondary and tertiary levels. Definitions of proportional reasoning, types of proportional reasoning tasks, rubrics to assess proportional reasoning are available in the literature, but thus far little research has been done on the topic of proportion on secondary school students in Singapore. In light of the paucity on this issue, the purpose of this study was to determine the levels of proportional reasoning manifested by 30 Secondary Two Express students, comprising 17 boys and 13 girls, from one secondary school in Singapore. In addition, the aim of this research was to uncover some of the students’ difficulties in proportional reasoning and to identify the possible causes of these difficulties. In order to do so, this study adopted a mixed method research design. The students were assessed based on a self-designed pen-and-paper test entitled MR PROP, consisting of 10 questions, using a coding scheme which was modified from the literature. Three students were subsequently interviewed.
Findings of this study showed that most students were able to reason proportionally for all three levels of difficulty. The percentage of successful responses for the Basic questions was predictably higher than the Intermediate and Advanced questions. It was also found that majority of the students were able to reason at Levels 3 and 4. Level 2 reasoning was the least evident in students’ responses. Some of the difficulties faced by students were: 1) An unclear expectation of some tasks, (2) Lack of experience to handle justification questions, and (3) Inability to operate on a letter as a generalised number. It has also been highlighted that a lack of exposure to explanation questions in the classrooms has been the main cause of these difficulties.
Findings from the present study were then used to propose some limitations of the study as well as implications for teaching and future research.
Mathematical reasoning in proportion plays a pivotal role in students’ understanding of various topics in mathematics and sciences at the primary, secondary and tertiary levels. Definitions of proportional reasoning, types of proportional reasoning tasks, rubrics to assess proportional reasoning are available in the literature, but thus far little research has been done on the topic of proportion on secondary school students in Singapore. In light of the paucity on this issue, the purpose of this study was to determine the levels of proportional reasoning manifested by 30 Secondary Two Express students, comprising 17 boys and 13 girls, from one secondary school in Singapore. In addition, the aim of this research was to uncover some of the students’ difficulties in proportional reasoning and to identify the possible causes of these difficulties. In order to do so, this study adopted a mixed method research design. The students were assessed based on a self-designed pen-and-paper test entitled MR PROP, consisting of 10 questions, using a coding scheme which was modified from the literature. Three students were subsequently interviewed.
Findings of this study showed that most students were able to reason proportionally for all three levels of difficulty. The percentage of successful responses for the Basic questions was predictably higher than the Intermediate and Advanced questions. It was also found that majority of the students were able to reason at Levels 3 and 4. Level 2 reasoning was the least evident in students’ responses. Some of the difficulties faced by students were: 1) An unclear expectation of some tasks, (2) Lack of experience to handle justification questions, and (3) Inability to operate on a letter as a generalised number. It has also been highlighted that a lack of exposure to explanation questions in the classrooms has been the main cause of these difficulties.
Findings from the present study were then used to propose some limitations of the study as well as implications for teaching and future research.
Date Issued
2016
Call Number
QA9 Ren
Date Submitted
2016