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Analysis of students' difficulties in solving trigonometric function problems
Author
Koh, Eric Zhen Feng
Supervisor
Yeo, Joseph Kai Kow
Abstract
Trigonometry is an essential yet challenging Additional Mathematics topic taught in Singapore schools. Majority of Singapore's secondary school students perceived trigonometric function to be tedious and difficult. The aims of the research were to:
1. analyse the degree of understanding of trigonometric function concepts among Secondary 3 Express students in Singapore,
2. identify common errors and misconceptions that these Secondary 3 Express students have when solving trigonometric function problems
For this study, the data collection involved the use of a five-question test was first used to elicit students' performance. The students' test performances were then analyzed to determine preliminarily learning difficulties and degree of understanding. Subsequently, six students were engaged in interview to gain insights into their written answers to achieve triangulation and hence confirmation of the preliminary conclusions.
The numerous successes based on the percentage passes of students suggest that the objectives such as solving trigonometric equations, identifying the relationship of trigonometric graphs and stating amplitude, periodicity and proving simple trigonometric identities, as well as drawing and using the graphs of y = a sin(bx) + c and y = a cos(bx) + c, are generally well understood. In this five-question test, most of the students did well with question involving sketching and stating the number of the points of intersection of two trigonometric graphs. In addition, students were able to apply simple trigonometric identities to prove other trigonometric identities and solve trigonometric equations. As 'for the degree of understanding of trigonometric functions according to the objectives of the Additional Mathematics syllabus as set out by the University of Cambridge Local Examinations Syndicate, the students appeared to concentrate on the procedural aspect of solving trigonometric function problems rather than on conceptual aspect. However, when it came to find trigonometric ratios of any angle which involved some form of conceptual understanding, they performed badly. Another observation made was that students appeared to be less proficient in stating the maximum and minimum point related to composite cosine function. This is not surprising as composite functions were generally more complex. The lack of ability could also be due to students' lack of mathematical knowledge in the transformation of curves which consequently affected their performance. The students made as many procedural errors as conceptual errors in the test. One main reason for this huge number of procedural errors was because the students had forgotten the rules and algorithms relating to trigonometric equation, expressions and identities. Another major factor was due to amplitude, period, maximum and minimum points of the curve. The students failed to interpret the results from the given trigonometric function. The high incidence of procedural errors might also be a result of a lack of practice on the students' part as procedural errors were usually caused while performing algorithms. It may be concluded that students were quite lacking in both their conceptual and procedural understanding of trigonometric function. On a positive note, technical errors accounted for only a small number of errors made in the test. This was largely due to the students' lack of mathematical content knowledge in only two main topics. It might imply that students were not so weak in their mathematics or they could retain what they learnt previously in other topics, which indicated they were prepared for the test. This thesis ends with recommendations for further research and future teaching on this topic trigonometric function.
1. analyse the degree of understanding of trigonometric function concepts among Secondary 3 Express students in Singapore,
2. identify common errors and misconceptions that these Secondary 3 Express students have when solving trigonometric function problems
For this study, the data collection involved the use of a five-question test was first used to elicit students' performance. The students' test performances were then analyzed to determine preliminarily learning difficulties and degree of understanding. Subsequently, six students were engaged in interview to gain insights into their written answers to achieve triangulation and hence confirmation of the preliminary conclusions.
The numerous successes based on the percentage passes of students suggest that the objectives such as solving trigonometric equations, identifying the relationship of trigonometric graphs and stating amplitude, periodicity and proving simple trigonometric identities, as well as drawing and using the graphs of y = a sin(bx) + c and y = a cos(bx) + c, are generally well understood. In this five-question test, most of the students did well with question involving sketching and stating the number of the points of intersection of two trigonometric graphs. In addition, students were able to apply simple trigonometric identities to prove other trigonometric identities and solve trigonometric equations. As 'for the degree of understanding of trigonometric functions according to the objectives of the Additional Mathematics syllabus as set out by the University of Cambridge Local Examinations Syndicate, the students appeared to concentrate on the procedural aspect of solving trigonometric function problems rather than on conceptual aspect. However, when it came to find trigonometric ratios of any angle which involved some form of conceptual understanding, they performed badly. Another observation made was that students appeared to be less proficient in stating the maximum and minimum point related to composite cosine function. This is not surprising as composite functions were generally more complex. The lack of ability could also be due to students' lack of mathematical knowledge in the transformation of curves which consequently affected their performance. The students made as many procedural errors as conceptual errors in the test. One main reason for this huge number of procedural errors was because the students had forgotten the rules and algorithms relating to trigonometric equation, expressions and identities. Another major factor was due to amplitude, period, maximum and minimum points of the curve. The students failed to interpret the results from the given trigonometric function. The high incidence of procedural errors might also be a result of a lack of practice on the students' part as procedural errors were usually caused while performing algorithms. It may be concluded that students were quite lacking in both their conceptual and procedural understanding of trigonometric function. On a positive note, technical errors accounted for only a small number of errors made in the test. This was largely due to the students' lack of mathematical content knowledge in only two main topics. It might imply that students were not so weak in their mathematics or they could retain what they learnt previously in other topics, which indicated they were prepared for the test. This thesis ends with recommendations for further research and future teaching on this topic trigonometric function.
Date Issued
2009
Call Number
QA531 Koh
Date Submitted
2009