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Secondary three students’ understanding of roots of quadratic equations
Author
Wang, Ming Hwee
Supervisor
Ng, Swee Fong
Abstract
This study explores Secondary 3 students’ levels of understanding of quadratic roots in the algebraic and the graphical representations. Interpretation within only one representation could be conceived as showing surface level understanding. Making bidirectional connections could be conceived as having deeper level understanding of roots.
A paper-and-pencil test designed for this study was administered to investigate students’ levels of understanding of roots of quadratic equations in the multiple representations. Seventy-five students were given 50 minutes to complete a five-item test. Clinical interviews were conducted with eight students from this group. The objective of the interviews was to gain insights into students’ understanding and misconceptions of the representations of roots of quadratic equations.
Analysis of students’ written work was interpretive. Their written responses were classified as exhibiting surface level understanding or deeper level understanding. Interview data was used to corroborate the written work of those who were interviewed. The data analysis examined students’ understanding of roots of quadratic equation within, and between the algebraic and the graphical representations, and identified prior knowledge that hindered students from progressing into deeper level understanding. A framework was constructed to analyze students’ work. Understanding of roots of quadratic equations was viewed in terms of students’ mobility within and between multiple representations of roots. Prior knowledge, as possible prerequisites to a deeper level understanding of roots, was investigated.
The findings indicated that students performed better with algebraic than with graphical representation. Their inability to perform the reversal process, however, indicated that this understanding was procedural. Other than surface level understanding of roots of quadratic equations within the representations, the findings exposed an absence of bi-directional links between the two representations. The connections students made were mostly uni-directional, with the algebraic-to-graphical link stronger than the graphical-to-algebraic. The findings also revealed that prior knowledge, like meanings of letters and the number system, affected students’ understanding of roots of quadratic equations. The findings suggested students’ misconceptions as a function of surface level understanding of representations, meanings of letters and the number system, as well as a lack of reversibility in the representation.
This study discusses the importance of weaving the various representations of
roots. The findings have the potential in translating research findings into practical suggestions for teachers who teach quadratic equations across the different grades in secondary school. It also informed curriculum planner the need to balance the emphasis put on each of the algebraic and graphical representations.
A paper-and-pencil test designed for this study was administered to investigate students’ levels of understanding of roots of quadratic equations in the multiple representations. Seventy-five students were given 50 minutes to complete a five-item test. Clinical interviews were conducted with eight students from this group. The objective of the interviews was to gain insights into students’ understanding and misconceptions of the representations of roots of quadratic equations.
Analysis of students’ written work was interpretive. Their written responses were classified as exhibiting surface level understanding or deeper level understanding. Interview data was used to corroborate the written work of those who were interviewed. The data analysis examined students’ understanding of roots of quadratic equation within, and between the algebraic and the graphical representations, and identified prior knowledge that hindered students from progressing into deeper level understanding. A framework was constructed to analyze students’ work. Understanding of roots of quadratic equations was viewed in terms of students’ mobility within and between multiple representations of roots. Prior knowledge, as possible prerequisites to a deeper level understanding of roots, was investigated.
The findings indicated that students performed better with algebraic than with graphical representation. Their inability to perform the reversal process, however, indicated that this understanding was procedural. Other than surface level understanding of roots of quadratic equations within the representations, the findings exposed an absence of bi-directional links between the two representations. The connections students made were mostly uni-directional, with the algebraic-to-graphical link stronger than the graphical-to-algebraic. The findings also revealed that prior knowledge, like meanings of letters and the number system, affected students’ understanding of roots of quadratic equations. The findings suggested students’ misconceptions as a function of surface level understanding of representations, meanings of letters and the number system, as well as a lack of reversibility in the representation.
This study discusses the importance of weaving the various representations of
roots. The findings have the potential in translating research findings into practical suggestions for teachers who teach quadratic equations across the different grades in secondary school. It also informed curriculum planner the need to balance the emphasis put on each of the algebraic and graphical representations.
Date Issued
2008
Call Number
QA215 Wan
Date Submitted
2008