- Analysis of students' difficulties in solving integration problems

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# Analysis of students' difficulties in solving integration problems

Author

Seah, Eng Kiat

Supervisor

Edge, Douglas Richard Montgomery

Abstract

Integration is part of the Additional Mathematics syllabus required for the Singapore-Cambridge General Certificate in Education Ordinary Level Examination and is a topic that students generally find difficult to understand. The aim of this study was to pursue an answer to the following general questions :

1. Given the various objectives with respect to integration in the calculus component of the Additional Mathematics syllabus, what is the degree of understanding of integration concepts among Secondary Four school students in Singapore?

2. What are common errors and misconceptions that secondary school students have with respect to integration?

For this study, the data collection involved the use of a six-question test to determine students' performance, degree of understanding and to identify students' learning difficulties. After an analysis of the data collected from the diagnostic test, seven students were interviewed to clarify and elaborate their written answers. Data collected from the interviews also provided information on students' degree of understanding of integration and students' learning disabilities.

With respect to students' performance, students in this study did well with questions involving integration of sums of terms in powers x excluding 1 / x and functions of the form (ax + b)n . They were also adept at evaluating definite integrals. Questions involving integration of trigonometric functions were not as easy for students. The most difficult questions involved applying integration to evaluate plane areas. With regards to application of differentiation and integration to kinematics problems, students fared better when the functions involved were polynomial rather than trigonometric functions.

As for degree of understanding, the students seemed to focus on the procedural aspects of integration far more than on the conceptual aspects. Nevertheless, students generally lacked both conceptual and procedural understanding of integration.

Students committed a large number of conceptual errors, particularly when applying integration to evaluate plane areas. They made about twice as many procedural errors. The procedural errors were mainly due to their confusion over the algorithms for performing integration and differentiation, and also because of their failure to put the constant c in indefinite integrals. However, the largest numbers of errors committed were technical errors which were primarily attributed to the students' lack of mathematical content knowledge in other topics required for integration.

The study concluded with a discussion on the implications for teaching.

1. Given the various objectives with respect to integration in the calculus component of the Additional Mathematics syllabus, what is the degree of understanding of integration concepts among Secondary Four school students in Singapore?

2. What are common errors and misconceptions that secondary school students have with respect to integration?

For this study, the data collection involved the use of a six-question test to determine students' performance, degree of understanding and to identify students' learning difficulties. After an analysis of the data collected from the diagnostic test, seven students were interviewed to clarify and elaborate their written answers. Data collected from the interviews also provided information on students' degree of understanding of integration and students' learning disabilities.

With respect to students' performance, students in this study did well with questions involving integration of sums of terms in powers x excluding 1 / x and functions of the form (ax + b)n . They were also adept at evaluating definite integrals. Questions involving integration of trigonometric functions were not as easy for students. The most difficult questions involved applying integration to evaluate plane areas. With regards to application of differentiation and integration to kinematics problems, students fared better when the functions involved were polynomial rather than trigonometric functions.

As for degree of understanding, the students seemed to focus on the procedural aspects of integration far more than on the conceptual aspects. Nevertheless, students generally lacked both conceptual and procedural understanding of integration.

Students committed a large number of conceptual errors, particularly when applying integration to evaluate plane areas. They made about twice as many procedural errors. The procedural errors were mainly due to their confusion over the algorithms for performing integration and differentiation, and also because of their failure to put the constant c in indefinite integrals. However, the largest numbers of errors committed were technical errors which were primarily attributed to the students' lack of mathematical content knowledge in other topics required for integration.

The study concluded with a discussion on the implications for teaching.

Date Issued

2003

Call Number

QA308 Sea

Date Submitted

2003