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Student errors in integrating rational functions at A-level
Author
Ng, Kin Yee
Supervisor
Toh, Tin Lam
Abstract
Students working towards the A-level examination in a three-year institute in Singapore tend to be able to perform adequately when tasked to carry out differentiation on various functions, but tend to make more errors in integration than in differentiation. Students, especially those in remedial programmes at the institute, have complained that they did not know how to think when faced with a question on integration or how to decide what to do to integrate.
This study is an attempt to list students’ errors and to categorise them according to errors in algebra or errors in interpreting visual presentation of rational functions.
Ideally, students should fit mathematics into appropriate schema which they could use to solve problems, and theoretically, more useful schemas tend to be those frameworks which incorporate several or many concepts in mathematics. Differentiation and integration should fit together naturally into one schema as one is the reverse process of the other. However, students tend to find differentiation easier to deal with successfully than integration and students do not always use the link between the two to identify how to integrate or how to check whether they had integrated correctly. Furthermore, remedial- level students tend to be misled or confused easily by mathematical representations and symbolism. This confusion could be a factor in causing these students to make errors in integration.
This study focused on a small sample of students and the common errors they made in integrating rational functions. A short test was administered and a small group of students was interviewed. The identified errors were compared across students and within the individual student so as to establish students’ thinking patterns. The identification of errors in this way and the interviews carried out were to help identify students’ integration schema and their perceptions and interpretations of rational functions.
As the sample size was small, the results of this study may not be generalisable. However, the data may guide teachers in designing lessons or remedial lessons for less able students or for students facing difficulties in integration. An example would be the selection of appropriate examples which could help students build patterns, plus a consistent approach to carrying out integration. Another two examples would be the consistent selection of terms used in teaching and repeated emphasis on the meaning of mathematical symbols.
This study is an attempt to list students’ errors and to categorise them according to errors in algebra or errors in interpreting visual presentation of rational functions.
Ideally, students should fit mathematics into appropriate schema which they could use to solve problems, and theoretically, more useful schemas tend to be those frameworks which incorporate several or many concepts in mathematics. Differentiation and integration should fit together naturally into one schema as one is the reverse process of the other. However, students tend to find differentiation easier to deal with successfully than integration and students do not always use the link between the two to identify how to integrate or how to check whether they had integrated correctly. Furthermore, remedial- level students tend to be misled or confused easily by mathematical representations and symbolism. This confusion could be a factor in causing these students to make errors in integration.
This study focused on a small sample of students and the common errors they made in integrating rational functions. A short test was administered and a small group of students was interviewed. The identified errors were compared across students and within the individual student so as to establish students’ thinking patterns. The identification of errors in this way and the interviews carried out were to help identify students’ integration schema and their perceptions and interpretations of rational functions.
As the sample size was small, the results of this study may not be generalisable. However, the data may guide teachers in designing lessons or remedial lessons for less able students or for students facing difficulties in integration. An example would be the selection of appropriate examples which could help students build patterns, plus a consistent approach to carrying out integration. Another two examples would be the consistent selection of terms used in teaching and repeated emphasis on the meaning of mathematical symbols.
Date Issued
2008
Call Number
QA308 Ng
Date Submitted
2008