LECTURERS’ AND STUDENTS’ PERCEPTIONS ON THE TEACHING AND LEARNING OF CALCULUS : CASE STUDY OF UiTM SARAWAK 2008 Nor Hazizah Binti Julaihi Universiti Teknlogi MARA
[email protected] Tang Howe Eng (Dr.) Universiti Teknlogi MARA
[email protected] Voon Li Li Universiti Teknlogi MARA
[email protected] Abstract This research seeks to investigate the student’s attitudes towards Calculus and to examine the lecturers’ and students’ perceptions on the teaching and learning of Calculus. The cross-sectional survey method was used in this research since the researchers collected information from a sample that has been drawn from a predetermined population. The instruments included the three set of questionnaires to be answered by the students and the lecturers. The samples comprised Part 1 and Part 2 diploma students in UiTM Sarawak who have enrolled in the respective Pre-Calculus (MAT133) and Calculus I (MAT183) for the semester July – November 2008, and also, the lecturers who have taught the Calculus courses in UiTM Sarawak. The finding shows that students’ attitudes towards the Course of Calculus across gender were not significant. However, there was a significant difference in the attitudes of students towards the Field of Calculus between male and female students. Both MAT133 and MAT183 students seemed to feel, think, and behave similarly about Calculus. There was significant difference in the students’ attitudes towards the Field of Calculus among the four programmes, namely EE111, EC110, AS120 and EH110. Analysis on the students’ perceptions of the difficulty of Calculus questions revealed that students’ perceptions of the difficulty did not change after they attempted the task in 39.27% of the given Calculus questions. However, students’ perceptions changed negatively (questions easier than expected) in 41.28% of the questions and changed positively (questions more difficult than expected) in 19.45% of the questions. The question that was clearly expressed, easy to understand and deemed familiar to the students was perceived as easy question. Considering the aspect of teaching Calculus, experienced lecturers broadened their perceptions on the variety of problems encountered and various strategies were outlined to improve students’ performance in Calculus. Implications from these findings were served as inputs to improve Calculus education and enhance collaborative teaching and learning among researchers, lecturers and students. Key Words: attitudes, perceptions, calculus, teaching and learning
INTRODUCTION The Calculus is the greatest aid we have to the appreciation of physical truth in the broadest sense of the word. …… William Fogg Osgood
1
There has long been concern about Calculus in many parts of the world. In most universities, Calculus courses have always been among the top courses with ‘high-failure rate’. According to Suresh (2002), Calculus was one of the ‘high-failure rate’ courses for engineering students besides Physics and Statistics. Over a third or probably half of the students enrolled in Calculus course(s) each year failed to successfully complete the courses (Douglas, 1998; Lax, 1990). The difficulty in acquiring a good working knowledge of Calculus was well-documented from previous studies (Cipra, 1988; Madison & Hart, 1990; NCTM & MAA, 1987). In UiTM, there have been some concerns raised about the poor performance of diploma students in Calculus courses. According to Professor Dr Zainab Abu Bakar, the Dean of Faculty of Information Technology and Quantitative Sciences (FTMSK), during the Faculty meeting on 2 July 2008, four Calculus courses namely MAT133 (Pre-Calculus), MAT183 (Calculus I), MAT149 (Calculus I) and MAT 199 (Calculus II) were of the five Mathematics courses that had been identified as ‘high-failure rate’ courses. As considered by the top management of UiTM, ‘high-failure rate’ course is a course with the passing percentage of less than 70%. Based on research done in UiTM Sarawak, MAT133 and MAT183 were found to be below 70% benchmark pass for the past 7 semesters; that was from the semester January – May 2004 to the semester January – May 2007 (Tang et al., 2008). MAT133 and MAT183 were taken by part 1 and part 2 diploma students in science and technology based programs, respectively. Inspired by the need to improve students’ performance on Calculus courses, this research was embarked to investigate the students’ attitudes towards Calculus and to examine the lecturers’ and students’ perceptions on the teaching and learning of Calculus. The students’ perceptions of the difficulty of chosen set of questions were also investigated, with the aim of identifying the type of questions that students perceive as easy or difficult. It is hope that the findings obtained from this research can give valuable inputs to the faculty and also the administrators of UiTM, especially in the Sarawak campus to plan and organize various academic programs on Calculus, with an aim to improve students’ performance on Calculus courses. Research objectives The following are the objectives of this research: 1. To investigate the students’ attitudes towards Calculus. 2. To examine the lecturers’ and students’ perceptions on the teaching and learning of Calculus. Research questions Based on the research objectives, this research is carried out to answer the following questions: 1. What are the students’ attitudes towards Calculus across gender, course code and program of studies? 2. What are the students’ perceptions on the learning of Calculus in term of difficulty of questions? 3. What are the lecturers’ perceptions on the teaching and learning of Calculus? 4. What are the lecturers’ perceptions on the students’ Calculus understanding and students’ difficulties in learning Calculus subjects? 5. What are the suggestions given by the lecturers to improve students’ performance in Calculus subjects?
2
Significance of this research The following are the significance of this research to UiTM Sarawak, lecturers, students and the researchers. a) To UiTM Sarawak The findings of this research could serve as inputs for the administrators of UiTM Sarawak to plan and organize various academic programs on Calculus aiming to improve students’ performance on Calculus courses. b) To Lecturers and Students The findings could provide the lecturers with necessary information to improve their teaching in Calculus. As for students, the findings could serve as inputs of the need expected of them. The findings of this research can also provide the information that the students need to know to be successful in their academic performance. c) To the Researchers The findings of this research could serve as inputs for future studies on this area. The data collection and the methods used in this research would be very useful to anyone who is interested in exploring the related field of research. Scope of this research This research focused on attitudes and perceptions of UiTM Sarawak Full-time diploma Students on Calculus courses. The sample involved the students who have enrolled in MAT133 or MAT183 for the semester July – November 2008. MAT149 and MAT199 were not taken into consideration as these two codes were not considered as ‘high-failure rate’ courses in UiTM Sarawak (Tang et al., 2008). In addition, lecturers’ perceptions were also examined from a sample of lecturers who have some experiences in teaching Calculus courses in UiTM Sarawak. It has to stress that the findings are just for this cohort. It cannot be generalized as there is other element of variation in the samples. Definition of terms Listed below are the definitions of terms used in this research. Attitudes : A way of feeling, thinking or behaving towards Calculus. Calculus Course : Mathematics course studying on functions, rates of change, differentiation and integration. Attitudes towards Course of Calculus: Attitudes towards the particular Calculus course. Attitudes towards Field of Calculus : Attitudes towards the use of Calculus course in the field of study. ‘High-Failure Rate’ Course : Mathematics course offered to Full-Time diploma Students in UiTM that has passing percentage below 70%. Perceptions : The process of using the senses to acquire information about the teaching and learning of Calculus.
LITERATURE REVIEW This section provides some theoretical background on the world-wide challenges of Mathematics and Calculus education that have been encountered by students, lecturers, academicians and researchers during their learning and teaching process. Calculus as a ‘killer subject’ Gynnild et al. (2005) had reported a ‘high-failure rate’ of 21.5 – 39.2 per cent in the Basic Calculus course undertaken by engineering students in the Norwegian University of Science and Technology. The low passing rate of Calculus courses had raised concerns among lecturers in the university. Students who failed their Calculus course would need to retake the course in order to progress to the higher level of Calculus or Mathematics course,
3
and this phenomenon had brought much grief to the students concerned. Yudariah and Roselainy (2001) had also revealed similar problems on students’ difficulties in Calculus learning at University Technology of Malaysia (UTM). Additionally, Tang et al. (2008) also reported average passing rate of 68.66% for MAT133 (Pre-Calculus) and 66.46% for MAT183 (Calculus I) from the semester January – May 2004 to the semester January – May 2007 on UiTM Sarawak full-time diploma students. Findings of the research also indicated that student’s performance in SPM Additional Mathematics which comprised Basic Calculus was a significant contributor to the diploma student’s achievement in Calculus course. MAT133 and MAT183 comprised about 60% and 100% of Pre-Calculus and Calculus contents, respectively. The Pre-Calculus topics covered in MAT133 were Coordinates, Graphs and Lines, Functions, System of Equations and Inequalities and Trigonometry, while MAT183 saw the diploma students went through a comprehensive Calculus syllabus consisted of Functions, Limits and Continuity, Differentiation, Applications of Differentiation, Integration and Applications of Integration. Students who did not have a solid foundation of Basic Calculus from secondary school saw themselves struggled to learn the new materials in the Calculus course during their diploma studies. They lose their confidence and were overwhelmed when they attempted to solve word problems in Mathematics and Calculus (Yudariah & Roselainy, 2001). The experiences of fear, struggle and even survival which were faced by these students in learning Calculus were described by a Mathematics teacher as the metaphor, “Mathematics – Calculus is a battle” (Sterenberg, 2008). Students’ attitudes and perceptions towards Calculus According to Ponte (2007), attitudes implied the way people viewed objects and situations and connected them. Di Martino and Zan (2001) defined attitude as the emotional disposition toward Mathematics. Attitudes and beliefs played an important role in the studying of Mathematics and Calculus (McLeod, 1992). Furthermore, Anthony (2000) had identified students’ attitudes as affecting cause towards students’ achievement. Vinner (1997) made the point that most students learned minimally, only to obtain good grades in a particular Mathematics course. They memorized sets of proofs in Mathematics and Calculus, reproduced them in exams and gradually forgotten, as if those proofs would never to be used again (Goulding et.al, 2003). They saw no relationship of Mathematics theories to be used in the real world, especially when teachers did not take the effort to make the connections (Nagasaki & Senuma, 2002). Ponte (2007) reported that the experiences of the students in the classroom had an influence on students’ attitudes towards Mathematics. Doing Mathematics and Calculus had been considered as a dull and routine process of computation for many students. However, when the lecturers took the initiative to orientate, motivate and stimulate the students to do their own Mathematics, they saw how their students established a strong connection between Mathematics and mathematical investigations. The studies showed that the experiences gained by the students in doing mathematical investigations, discussions and reflections with their lecturers had changed the students’ views and attitudes towards Mathematics activities, besides a rise in students’ confidence level of learning Mathematics. Wise (1985) constructed a set of questionnaire with high (~.90) internal consistency for both attitude toward the Course and attitude toward the Field subscale scores (Wise, 1985; Schultz and Koshino, 1998). Tang, et al. (2008) adapted the questionnaire and documented the findings on students’ attitudes towards the Course of Calculus and the Field of Calculus as important factors in determining students’ attitudes towards Calculus. Students who had positive attitudes towards the Field of Calculus were considered as ‘practice-oriented’. They were able to apply the Calculus knowledge they had acquired into their field of study.
4
According to Wood and Smith (2007), students perceived Calculus questions that required conceptual understanding as more difficult compared to questions that required factual recalls or routine procedures. The categories in the taxonomy were consistent with the levels used in Bloom Taxonomy. Wood and Smith reported that the students’ perceptions of the difficulty had changed after they had attempted the task in 37.5% of the given Mathematics questions. Students saw the variations between their perceptions towards Calculus before attempting the task and the actuality. Lecturers’ perceptions towards Calculus Evidence from past research suggested that lecturers’ perceptions towards Mathematics influenced their teaching and students’ learning of Mathematics (Hart, 2002). The curriculum framework for Mathematics might have an effect on students’ attitudes towards Mathematics (Nagasaki & Senuma, 2002). Findings from Tang et al. (2008) revealed that the level of difficulty for Mathematics diploma courses which comprised mainly Calculus, as perceived by Mathematics and Calculus lecturers, had ratings of at least 3.0 (rating “1” = very easy … “5” = very difficult). MAT183 (Calculus I) was perceived 15.8% relatively more difficult as compared to MAT133 (Pre-Calculus). Nagasaki and Senuma (2002) emphasized the importance of attaining the objectives of the Mathematics curriculum as this would affect the attitudes of the students. Students who enjoyed doing Mathematics and Calculus simply because they enjoyed the challenge and achieved well would have more confidence in their studies. Besides the curriculum of Calculus, lecturers-related factor was also important in Mathematics teaching and learning. According to Nagasaki and Senuma (2002), a lecturer who perceived the applications of Mathematics or Calculus theories as un-important would not relate their Mathematics lectures contents to every day life, and this would eventually affect a student’s attitudes. Teachers’ attitudes on the relationship between Mathematics and the real world might have an effect on students’ attitudes. (Nagasaki & Senuma, 2002, p. 88) Australian Mathematics teachers commented that it would be helpful if teachers were in the ability to bridge Mathematics classroom lessons to the real world. I think an effective teacher would be someone who is able to take the curriculum and make it alive for students. Someone who can make it interesting and who can show the relevance of mathematics in today’s society. (Perry, 2007, p. 280) The attitudes of the lecturers should be positive and full of enthusiasm in Mathematics teaching as this would influence the learning process and attitudes of the students. The following statements were made by an Australian Mathematics teacher about good teaching: I think good teaching, as in anything, is an attitude thing. If teachers enjoy it and get into it, the students will respond and reflect your enthusiasm and attitude. I think that is the whole part and parcel of it. If you’re really enthusiastic and have this positive attitude to Mathematics and Mathematics teaching I think it’ll roll over into the students. (Perry, 2007, p. 282) On students-related factor, research had shown that memorization should not play a central role in the learning of Mathematics (Wong, 2007). Findings from a research by Wong
5
(2007) indicated that memorization of facts was deemed important, for example the multiplication table, in order to solve problems quickly. However, students should not be taught to memorize mathematical procedures without conceptual understanding (Porter & Masingila, 2000). According to Tang et al. (2008), students relied heavily on lecture notes as their basis for learning. Students also seemed to work effectively in small groups. Nevertheless, the level of frequency in the usage of concrete materials or equipments to explore Calculus ideas by students was below average. The usage of other instructional systems such as Calculus laboratory and small group projects were also below average. As reported by Ramsden (1984), students’ learning approach varies in accordance to the learning environment exhibited in the classroom. Improvement Strategies in Calculus Education Many educators have been looking into various strategies to improve Calculus education in the tertiary level. According to researchers from Nanyang Technological University (Ahuja et al., 1998), the improvement in Calculus and Mathematics education can be done by curriculum development, effectiveness in teaching strategies, and utilization of technology, creative thinking and up-to-date training to lecturers and facilitators. However, contrary to Dungan and Thurlow (1989), a diversity of teaching styles and the use of technology might not give much difference to students’ attitudes towards Calculus. There appears to be no evidence of association betweens students’ attitudes to mathematics and exposure to alternative teaching approaches or between students’ attitudes to mathematics and new technology. (Dungan & Thurlow, 1989, p. 11) Yudariah and Roselainy (2001) had reported various remedial strategies that were implemented in Universiti Teknologi Malaysia (UTM) to overcome problems faced by its students in the Calculus education. Among the strategies was the setting up of remedial centre and the centre for first year studies, which catered for students who are weak in Mathematics. Remedial help and easy access to lecturers were vital aspects in successful learning as it provided a necessary course support to students (Anthony, 2000). In addition, Yudariah and Roselainy (2001) also suggested materials development which includes module, textbooks and web-based support materials that linked to other learning sites. The cognitive development of students would be taken into account while developing the content of the learning module. The entire development of educational resources must allow independent, self-paced and flexible learning. According to Joiner et al. (2002), Calculus and Maple reformed environment and restrictive classroom environment of the non-computer class affected students’ learning differently. Students preferred the Calculus and Maple reformed class as it provided the space for participation through exploration and collaboration resulting in less abstract with more interaction with the lecturer. Students felt that they enjoyed the reformed class as they had the freedom to work more independently and within their own pace.
RESEARCH METHODOLOGY This section briefly describes the design, population and sample, data collection as well as data analysis procedure. This research was a cross-sectional survey research. A cross-sectional survey collects information from a sample that has been drawn from a
6
predetermined population (Fraenkel and Wallen, 1996). Thus, the researchers collected data from a sample of diploma students and Mathematics lecturers in UiTM Sarawak in order to gather information regarding their attitudes and perceptions on the teaching and learning of Calculus respectively. Population and Sample The population of this research consisted of all diploma students taking MAT133 (part 1) and MAT183 (part 2) in UiTM Sarawak. Both MAT133 and MAT183 are Calculus courses; namely Pre-Calculus and Calculus 1 respectively. In this research, all the diploma students who have enrolled in MAT133 (part 1) and MAT183 (part 2) in UiTM Sarawak for semester the July-November 2008 were asked to answer Questionnaire A (questionnaire regarding students’ attitudes towards Calculus courses). Those students came from four different programs, namely EE111 (Diploma in Electrical Engineering), EC110 (Diploma in Civil Engineering), EH110 (Diploma in Chemical Engineering) and AS120 (Diploma in Science). Further, two groups of student who have taken MAT133 (part 1) and another two groups of student who have taken MAT183 (part 2) in UiTM Sarawak for the semester July-November 2008 were asked to express their perceptions on the learning of Calculus. These groups of student were chosen from EE111 program (for MAT133) and AS120 program (for MAT183). The selection of program was through random sampling. These students were asked to answer Questionnaire B. MAT133 is taken by part 1 students whereas MAT183 is taken by part 2 students. Besides this, lecturers who have taught Calculus courses in UiTM Sarawak were also asked to give their perceptions on the teaching and learning of Calculus. Ten Mathematics lecturers from a total of nineteen lecturers had responded to the questionnaire. Two lecturers were not responded to the questionnaire as one was very new and one has no experience in teaching Calculus. Since the selection of the lecturers was on voluntary basis, the lecturers’ perceptions on the teaching and learning of Calculus were focuses on the 52.63% response from the Mathematics lecturers. Instrument In order to meet the research objectives, three set of questionnaires were prepared, whereby two sets of questionnaires were answered by students while the other set of questionnaires were answered by lecturers. Questionnaire A aimed to collect data regarding students’ attitudes towards Calculus. Questionnaire A was modified from Tang et al. (2008), whereby ‘high-failure rate’ Mathematics courses were changed to Calculus courses to be used in this research. Tang et al. (2008) reported an alpha value of 0.874 for the twenty items in the questionnaire. This alpha value indicated that the questionnaire was reliable in measuring students’ attitudes. Questionnaire B sought to examine students’ perceptions on the learning of Calculus. This questionnaire was divided into four sections. Section A examined students’ perceptions of the Calculus difficulty before attempting the given Calculus tasks. Section B examined students’ knowledge in solving difficult Calculus questions. Section C examined students’ perceptions of the Calculus difficulty after completing the given Calculus tasks. Section D examined students’ perceptions on the clarity of the given tasks and previous experiences in the learning of Calculus. Questionnaire B served as a preliminary analysis of students’ perceptions on the learning of Calculus. Questionnaire C sought to examine lecturers’ perceptions on the teaching and learning of Calculus. This questionnaire was divided into Part A and Part B. Part A examined the lecturers’ perceptions on the teaching of Calculus which consisted of three questions. Part B examined the lecturers’ perceptions on students’ Calculus learning, and consisted of three questions.
7
Data Collection Questionnaire A was distributed to all diploma students taking MAT133 (part 1) and MAT183 (part 2) in UiTM Sarawak for the semester July-November 2008. The questionnaires were distributed to the students by the respective lecturers who are teaching MAT133 (part 1) and MAT183 (part 2) in UiTM Sarawak. Questionnaire B was given to the selected groups of students taking MAT133 (part 1) and MAT183 (part 2) in UiTM Sarawak for semester July-November 2008. The selected groups were chosen from EE111 program (for MAT133) and AS120 program (for MAT183). The selected students were asked to answer the given tasks based on the course taken. Questionnaire C was distributed to all Mathematics lecturers in UiTM Sarawak. The lecturers were asked to answer the questionnaire and returned them to the researchers after some time. Data Analysis Procedure The data was analyzed by using Statistical Package for Social Sciences (SPSS) version 12.0. Descriptive statistics, such as mean and standard deviation, were generated to provide an overview of the data. Inferential statistics, such as Mann Whitney U Test and Kruskal Wallis Rank Sum Test, were used to elicit in detail the students’ attitudes towards Calculus. Mann Whitney U Test was used to determine whether there is any significant difference in students’ attitudes between male and female. Also, it was used to determine whether there is any significant difference in students’ attitudes between students taking MAT133 and MAT183. Kruskal Wallis Rank Sum Test was used to determine whether there are any significant difference in students’ attitudes among students from the EE111, EC110, EH110 and AS120 programs. Wilcoxon signed-rank test was used to analyze the pre-scale and post-scale data in Questionnaire B. Means for the related samples were calculated to compare whether there is any significant difference in the pre-scale scores and post-scale scores of the students. Content analysis was carried out on the open-ended questions to categorize the feedback given by the lecturers.
FINDINGS This section reports the findings of the data analysis regarding students’ attitudes towards Calculus, students’ perceptions on the learning of Calculus and also, lecturers’ perceptions on the teaching and learning of Calculus. Students’ Attitudes towards Calculus In examining students’ attitudes towards Calculus, data from 278 respondents were analyzed. Missing values were not being considered in the calculation. Generally, the analysis of students’ attitudes towards Calculus was divided into three parts; naming students’ attitudes across gender, students’ attitudes across course code and students’ attitudes across programs of studies. Students’ Attitudes across Gender Students’ attitudes were evaluated through a five-point Likert 20-item that assessed students’ attitudes towards the Course of Calculus and towards the Field of Calculus. Table 1 shows the output of Mann-Whitney U Test for analyzing students’ attitudes across gender. Table 1 indicates that data from 271 respondents were analyzed for attitudes towards Course
8
subscale whereby data from 272 respondents were analyzed for attitudes towards Field subscale. For gender, data from 277 respondents were used in the analysis. Table 1 Mann-Whitney U Test for Analyzing Students’ Attitudes across Gender Gender Attitude to Male Course Subscale Female Total Attitude to Field Male Subscale Female Total
N 138 133 271 140 132 272
Mean Rank 138.36 133.55
Sum of Ranks 19094.00 17762.00
146.38 126.02
20493.00 16635.00
Table 2 shows the test statistics from Mann-Whitney U Test for analyzing students’ attitudes across gender. The output indicates that the result, with correction for ties and Z-score conversion, was not significant (p> .05) for students’ attitudes towards Course of Calculus between male and female students. However, the result was found to be significant (p< .05) for students’ attitudes towards Field of Calculus between male and female students. Thus, there was no significant difference in the students’ attitudes towards Course of Calculus between male and female students. On the contrary, there was significant difference in the students’ attitudes towards Field of Calculus between male and female students. Table 2 Test Statistics(a) for Analyzing Students’ Attitudes across Gender Attitude to Course Subscale 8851.000 17762.000 -.507 .612 a Grouping Variable: Gender
Mann-Whitney U Wilcoxon W Z Asymp. Sig. (2-tailed)
Attitude to Field Subscale 7857.000 16635.000 -2.142 .032
Students’ Attitudes across Course Code Table 3 shows the output of Mann-Whitney U Test for analyzing students’ attitudes across course code. Table 3 indicates that data from 271 respondents were analyzed for attitudes towards Course subscale whereby data from 272 respondents were analyzed for attitudes towards Field subscale. For course code, data from 278 respondents were used in the analysis. Table 3 Mann-Whitney U Test for Analyzing Students’ Attitudes across Course Code Course Code Attitude to Course MAT133 Subscale MAT183 Total Attitude to Field MAT133 Subscale MAT183 Total
N 153 118 271 154 118 272
Mean Rank 133.18 139.66
Sum of Ranks 20376.50 16479.50
140.56 131.20
21646.00 15482.00
Table 4 shows the test statistics from Mann-Whitney U Test for analyzing students’ attitudes across course code. The output indicates that the result was not significant (p> .05) for students’ attitudes towards Course of Calculus between MAT133 and MAT183 students. The result was also not significant (p> .05) for students’ attitudes towards Field of Calculus
9
between MAT133 and MAT183 students. Thus, there was no significant difference in the students’ attitudes towards Course of Calculus between MAT133 and MAT183 students. There was also no significant difference in the students’ attitudes towards Field of Calculus between MAT133 and MAT183 students. Table 4 Test Statistics(a) for Analyzing Students’ Attitudes across Course Code Attitude to Course Subscale 8595.500 20376.500 -.677 .498 a Grouping Variable: Course Code Mann-Whitney U Wilcoxon W Z Asymp. Sig. (2-tailed)
Attitude to Field Subscale 8461.000 15482.000 -.976 .329
Students’ Attitudes across Programs of Studies Table 5 shows the output of Kruskal-Wallis Rank Sum Test for analyzing students’ attitudes across programs of studies. Table 5 indicates that data from 271 respondents were analyzed for attitudes towards Course subscale whereby data from 272 respondents were analyzed for attitudes towards Field subscale. For programs of studies, data from 278 respondents were used in the analysis. Table 5 Kruskal-Wallis Rank Sum Test for Analyzing Students’ Attitudes across Programs Diploma Program Attitude to Course EE111 Subscale EC110 AS120 EH110 Total Attitude to Field EE111 Subscale EC110 AS120 EH110 Total
N 52 81 92 46 271 53 83 91 45 272
Mean Rank 132.19 124.80 149.75 132.53 156.35 134.70 119.96 149.90
Table 6 shows the test statistics from Kruskal-Wallis Rank Sum Test for analyzing students’ attitudes across programs of studies. The output indicates that the result was not significant (p> .05) for students’ attitudes towards Course of Calculus among EE111, EC110, AS120 and EH110 students. However, the result was significant (p< .05) for students’ attitudes towards Field of Calculus among EE111, EC110, AS120 and EH110 students. Thus, there was no significant difference in the students’ attitudes towards Course of Calculus among EE111, EC110, AS120 and EH110 students. On the contrary, there was significant difference in the students’ attitudes towards Field of Calculus among EE111, EC110, AS120 and EH110 students. Table 6 Test Statistics(a,b) for Analyzing Students’ Attitudes across Programs of Studies Attitude to Course Subscale Chi-Square 4.738 df 3 Asymp. Sig. .192 a Kruskal Wallis Test b Grouping Variable: Diploma Program
Attitude to Field Subscale 8.824 3 .032
10
Students’ Perceptions on the learning of Calculus To examine the students’ perceptions on the learning of Calculus in term of difficulty, questionnaire B was given to 88 students that were chosen randomly from part 1 of Diploma in Electrical Engineering (EE111) and part 2 of Diploma in Science (AS120). Below are the breakdown of the students’ gender, race and their home language. Table 7 The students’ gender Course MAT133 MAT183 Total
Gender Female 10 32 42
Male 27 19 46
Table 8 The students’ race Race Malay Melanau Bidayuh Iban Kayan Bajau Dusun Others Total
Total 37 51 88
Table 9 The students’ home language Frequency 48 7 11 17 1 1 1 2 88
Home Language Malay Melanau Bidayuh Iban Kayan Bajau English & mother tongue Others
Frequency 43 4 8 14 1 1 13 4
In questionnaire B, the students were given two set of questions, each consist of 6 questions (see Appendix). The first set (Task 1) is for MAT133 students and the second set (Task 2) is for MAT183 students. These questions were designed based on the six categories of Bloom’s Taxonomy (Bloom B. S., 1956) and were presented in no particular order (see Table 10). These questions were carefully chosen with the aim of identifying the type of questions that students perceived as easy and difficult. Table 10 Questions represented the categories in Bloom’s Taxonomy Courses Bloom’s Taxonomy Level 1 Knowledge Level 2 Comprehension Application Level 3 Analysis Synthesis Evaluation
MAT133 (Task 1)
MAT183 (Task 2)
Question 6
Question 1
Question 5 Question 3
Question 3 Question 4
Question 2 Question 4 Question 1
Question 2 Question 5 Question 6
In order to determine the difficulty of the questions, the students were requested to scale each question twice, before attempting the task (pre-scale) and after completing the task (post-scale). The 5-point Likert-scale, that is from ‘1’ (very easy) to ‘5’(very difficult) were used to scale the questions. Based on results showed in Table 11, it was revealed that students’ perceptions of the difficulty did not change after they attempted the task in 39.27% of the given Calculus questions. However, students’ perceptions changed negatively (questions easier than expected) in 41.28% of the questions and changed positively (questions
11
more difficult than expected) in 19.45% of the questions. Most of the questions were found to be easier than expected except for question 4 and question 5 in MAT183 (see Table 12). Table 11 The differences of scaling before and after answering the questions (in overall). Scale Ties Negative Positive
Percentage (%) 39.27 41.28 19.45
Table 12 The differences of scaling before and after answering each question. Question
1 2 3 4 5 6
Ties 38.33 8.33 41.67 44.44 19.44 41.67
MAT133 Scale Percentage (%) Negative Positive 42.42 24.24 80.55 11.11 50.00 8.33 30.56 25.00 61.11 19.44 41.67 16.67
Ties 44.90 55.10 49.02 43.14 39.22 50.98
MAT183 Scale Percentage (%) Negative Positive 38.78 16.32 32.65 12.25 39.22 11.76 15.69 41.17 19.61 41.17 43.14 5.88
Based on the mean scores of the pre-scale and post-scale showed in Table 13 and 14, questions 6, 3 and 5 in Task 1 were considered difficult before and after doing the questions. Meanwhile, question 6 in Task 2 was considered as very easy whereas questions 2, 4 and 5 were considered difficult before and after doing the questions. Table 13 The scale on the difficulty of question before and after answering the MAT133 questions Pre-scale 4 1 2 6 3 5
Mean 2.57 2.97 3.35 3.43 3.76 4.22
Post-scale 2 4 1 6 3 5
Mean 2.36 2.53** 2.69** 3.14 3.17** 3.33
Significant change indicated by **
Table 14 The scale on the difficulty of question before and after answering the MAT183 questions Pre-scale Mean 6 2.06 3 2.47 1 2.54 2 2.76 4 3.29 5 3.39 Significant change indicated by **
Post-scale 6 1 3 2 4 5
Mean 1.63** 2.18** 2.20** 2.51** 3.63** 3.75**
To investigate the reasons why students chose the scores, they were then asked whether the questions were clearly worded, whether they understood the questions and whether they had seen the similar questions before (see Table 15, Table 16 and Table 17). The mean scores were used in analyzing these Likert scale questions to determine direction the average answer was. Based on the mean scores, the question that was clearly expressed and easy to understand was perceived as easy question, or otherwise.
12
Table 15 Mean scores for MAT133 question analysis (Language and Understanding). Language of the questions. (5-point scale, 1 = very clear, 5 = very hard to understand) Question 1 Question 2 Question 3 Question 4 1.46 1.68 2.86 2.22 Understanding of the questions. (5-point scale, 1 = easy to understand, 5 = very hard to understand) Question 1 Question 2 Question 3 Question 4 2.30 2.65 3.49 2.42
Question 5 3.78
Question 6 2.14
Question 5 3.92
Question 6 3.05
Table 16 Mean scores for MAT183 question analysis (Language and Understanding). Language of the questions. (5-point scale, 1 = very clear, 5 = very hard to understand) Question 1 Question 2 Question 3 Question 4 1.37 1.73 1.96 2.22 Understanding of the questions. (5-point scale, 1 = easy to understand, 5 = very hard to understand) Question 1 Question 2 Question 3 Question 4 1.53 2.20 2.25 2.67
Question 5 2.35
Question 6 1.51
Question 5 2.78
Question 6 1.55
Table 17 Familiarity of the type of questions Question 1 2 3 4 5 6
MAT133 No (%) Yes (%) 2.77 97.22 8.33 91.67 68.57 31.43 8.33 91.67 61.11 38.88 11.11 88.88
MAT183 No (%) Yes (%) 0.00 100.00 0.00 100.00 0.00 100.00 29.41 70.59 31.37 68.63 0.00 100.00
There was a strong link between the familiarity of the type of questions and the difficulty of the questions. The question that was familiar to the students was perceived as easy question before and after the doing the question. Table 17 shows that students were not familiar with question 3 (68.57%) and question 5 (61.11%) in Task 1. Unfamiliarity to the questions might be the reason why the students chose question 3 and 5 as difficult questions before and after doing the questions (see table 13). As for Task 2, the students chose question 4 and question 5 as difficult questions (see table 14) and these questions were perceived by them as unfamiliar questions (see table 17). From the findings, it can be conclude that the question that was clearly expressed, easy to understand and deemed familiar to the students was perceived as easy question. The students were also asked to rank the six Calculus questions in order of difficulty. Based on the results showed in Table 18, the comparison between the ranking scores and the Bloom Taxonomy order show that there was no considerable agreement between the taxonomy categories and the ranking given by the student. According to Wood and Smith (2007), there was no priori reason for the Bloom Taxonomy rankings to reflect difficulty, since the rationale of its development was to reflect conceptual complexity.
13
Table 18 Ranking of questions in order of difficulty. Taxonomy Ranking 6 5 3 2 4 1
MAT133 Students’ Ranking 4 1 3 2 5 6
MAT183 Students’ Ranking 3 2 4 1 5 6
Mean 3.25 3.33 3.42 3.56 3.72 3.72
Mean 2.78 2.96 2.96 3.71 3.96 4.58
Lecturers’ Perceptions on Teaching and Learning of Calculus Ten Mathematics lecturers responded to Questionnaire C that sought to examine lecturers’ perceptions on the teaching and learning of Calculus. The profiles of the lecturers are shown in Figure 1 and Figure 2. Figure 1 shows the number of lecturers who had taught particular Calculus subject. As refer to Figure 1, four lecturers have taught MAT133 (Pre-Calculus), two lecturers for MAT149 (Calculus I), one lecturer for MAT163 (Introductory Mathematics II), four lecturers for MAT183 (Calculus I), one lecturer for MAT193 (Mathematics IIC), three lecturers for MAT199 (Calculus II), two lecturers for MAT235 (Calculus for Engineers), one lecturer for MAT238 (Calculus II for Scientists), one lecturer for MAT242 (Mathematics 3B) and two lecturers for MAT338 (Further Mathematics for Scientist). Number of Lecturers who had Taught Calculus Subjects
Number of Lecturers
M A T1 M 33 A T1 M 49 A T1 M 63 A T1 M 83 A T1 M 93 A T1 M 99 A T2 M 35 A T2 M 38 A T2 M 42 A T3 38
Number of Lecturers
5 4 3 2 1 0
Calculus Subjects
Figure 1. Number of Lecturers who had Taught Calculus Subjects. Figure 2 shows the lecturers’ experience in teaching Calculus subjects. Each one lecturer had taught Calculus subjects for 4 months, 6 months, 1 year, 3 years, 5 years, 6 years and 8 years respectively. Three lecturers had taught Calculus subjects for 2 years. Lecturers' Experience in Teaching Calculus Subjects
Lecturers
Number of
4 3 2
Numbers of Lecturers
1 0 1/3
1/2
1
2
3
5
6
8
Length of Years Teaching Calculus
Figure 2. Lecturers’ Difficulties in Teaching Calculus Subjects. All of the ten Mathematics lecturers encountered difficulties in teaching Calculus subjects. Students are generally very weak in basic mathematics skills required of Calculus subjects. Calculus is a difficult subject which required students to have better understanding
14
and a good foundation in basic mathematics. The syllabus for Calculus subjects are relatively packed and have to be covered within a short period of 14 weeks. Generally, lecturers find limited time to teach higher level Calculus and have no time revising basic Calculus with the students. This puts burden on the students especially those with weak mathematical foundation, and also the lecturers as they need to rush in delivering the Calculus content. Lecturers have difficulties in explaining certain Calculus concepts, such as implicit differentiation and application of integration in finding the volume. Students cannot visualize the various Calculus concepts. Lecturers also lack of visualizer to illustrate some of the diagrams especially three dimensional diagrams to the students. In addition, students’ poor attitudes towards Calculus also affect the lecturers’ teaching. Lecturers generally found that students lack of interest when the lecturers delivering Calculus content. Students’ Calculus Understanding Out of ten Mathematics lecturers, seven of them found that students were poor in Calculus understanding. Many students hardly understand certain Calculus topics and tend to memorize Calculus concepts. Students are very weak in basic Calculus, such as integration and differentiation. Majority students were poor in their basic Calculus and need more revision. Two of the lecturers found that students always thinking Calculus as very difficult subject before they even trying to answer Calculus question. This kind of thinking constrains the students from gaining deeper understanding in Calculus. One of the lecturer found that students have some understanding on pre-Calculus and basic algebra but they are normally constrained by fixed rule or formula. They may be able to see the connection between various Calculus fields but some may not be able to see its similarity. Students’ Difficulties in Learning Calculus Subjects All of the ten Mathematics lecturers found that students face difficulties in learning Calculus subjects. Students always have problems in solving derivatives and integrals. They are unable to identify suitable and correct method to solve a particular problem and cannot remember various integration and differentiation techniques due to lacking of exercises. Some of them even face problems in understanding the needs of the questions. In addition, students generally face difficulties in memorizing various important formulas and identities. They cannot memorize all of the formulas required of them. Even sometimes they manage to memorize the required formula, they also face problem in applying the formula to solve particular type of question. Suggestion to Improve Students’ Performance in Calculus Subjects As many researchers (Gynnild et al., 2005; Yudariah and Roselainy, 2001; Tang et al., 2008; Sterenberg, 2008) had reported that students face problems in learning Calculus, therefore, there is an urgent need to explore effective ways to improve students’ performance in Calculus subjects. Based on the feedback received, the following concludes the suggestions given by UiTM Sarawak Mathematics lecturers as an effort to improve students’ performance in Calculus subjects. Generally, the suggestions can be divided into three categories, naming lecturers’ role, students’ role and UiTM top management’s role. Lecturers play important roles to design effective method of teaching Calculus in daily lecture. The suggestion includes lecturers could design teaching activities related to real life situations and formulate Calculus problems in real life contexts. Lecturers must be able to relate Calculus theory and application in daily life and industry when teaching to the students. By doing so, students appreciate what they had learned and be able to master the Calculus skills easily.
15
Furthermore, lecturers could construct a complete module for each Calculus subject. The module compiles all the Calculus topics of the subject and provides various examples, comprehensive exercises and also more problem solving questions for the students. Lecturers should also find more teaching and learning materials for the students. The use of ICT for visualization of various Calculus concepts could also improve the students’ performance in Calculus. For example, the use of Maple 12 and Matlab can help students to develop in-depth understanding on Calculus if used properly in daily lecture. The integration of technology could be an effective way in teaching and learning Calculus if the lecturers could plan the usage properly. Lecturers should be more patient when teaching Calculus concepts to the students. Lecturers should try to help students whenever they need. Students’ interest in studying Calculus need to be built up so that they are confident when answering Calculus question and not easily give up. Sometimes, learning Calculus in small group can be an effective method as students can discuss Calculus concept and communicate better with their peers. As for students’ role, students need to change their attitudes in learning Calculus subjects. Students must practice regular study habits by attending lectures and tutorial as well as attempting all the assignments and exercises in order to master the Calculus concepts. Falling behind tends to be one of the most frequent cause of failure in Calculus. Students must make an effort to consult lecturers whenever they face problems in learning Calculus. As for UiTM top management’s role, a review on the scope of Calculus syllabus by top management is needed to ensure there is a flow on delivering the Calculus concepts. Besides, the Calculus syllabus should also be relevant to the market needs. The scope of the Calculus syllabus should be moderate so that it allows lecturers to instill deeper Calculus understanding to the students. In current situation, lecturers need to rush through the syllabus most of the time. Students do not have enough time to learn and think further as the syllabus is so packed for certain Calculus subjects. When processing new intakes of the students, top management could select students with strong basic Calculus background for programs that need a good command of Calculus. The chosen students must have taken Additional Mathematics and scored at least credit 6 in Sijil Pelajaran Malaysia (SPM). A strong basic Calculus background enables the students to further higher level Calculus without much problem.
CONCLUSION AND RECOMMENDATIONS In this research, students’ attitudes towards the Course of Calculus and students’ attitudes towards the Field of Calculus were used as measurements to determine students’ attitudes towards Calculus. All the students who have taken MAT133 and MAT183 for the semester July – November 2008 were surveyed. Further analysis was also done to seek students’ perceptions on the learning of Calculus. This survey included only part 1 students of Diploma in Electrical Engineering (EE111) for MAT133, and part 2 students of Diploma in Science (AS120) for MAT183. Findings obtained regarding the lecturers’ perceptions towards teaching and learning of Calculus was also studied, with an aim to remedy the ‘high-failure rate’ situation. Students’ attitudes towards the Course of Calculus across gender were not significant. However, there was a significant difference in students’ attitudes towards the Field of Calculus between male and female students. This result indicated that male and female students did not differ much in their opinions and beliefs about the Course of Calculus.
16
However, male students tend to be more positive in attitude towards the Field of Calculus than the female counterparts. For the analysis across course code, there were no significant difference in the attitudes of students, both towards the Course of Calculus and the Field of Calculus. Both MAT133 and MAT183 students seemed to feel, think, and behave similarly about Calculus. In studying the students’ attitudes across programmes, no significant difference was found for the attitudes of students towards the Course of Calculus. Nevertheless, there was significant difference in the students’ attitudes towards the Field of Calculus among the four programmes, namely EE111, EC110, AS120 and EH110. With regards to students’ perceptions on Calculus learning, students’ perceptions of the difficulty did not change after they attempted the task in only 39.27% of the given Calculus questions. However, students’ perceptions changed negatively (questions easier than expected) in 41.28% of the questions and changed positively (questions more difficult that expected) in 19.45% of the questions. Most of the questions were found to be easier than expected except for question 4 and question 5 in MAT183. It may be partly due to the students’ poor understanding on the language used, which resulted into wrong interpretation of questions. Moreover, students’ unfamiliarity on these types of questions (application and synthesis) may also explain the reason behind their expectations. Students may underestimate or overestimate the hardness of the questions at first glance. This may be due to the questions’ appearances. The questions look quite hard or easy enough, but closer inspection of the questions revealed the exact nature of the questions. In Task 1 for MAT133, the categories of questions which were considered as difficult before and after attempting the task were of type application (question 3), comprehension (question 5) and knowledge (question 6). Contrary, in Task 2 for MAT183, the categories of questions which were considered as difficult before and after attempting the task were of type analysis (question 2), application (question 4), and synthesis (question 5). Students’ rankings scores on task difficulty were found to differ from the orders of Bloom Taxanomy. This result was consistent to Wood and Smith (2007), which stated that the rationale of its development was to reflect conceptual complexity and not difficulty. Generally, questions which were deemed familiar to students, in which simple language was used, were perceived as easy questions. The differences in the students’ perceptions of difficulty before attempting the task and its reality, as was categorized by the Bloom Taxonomy had provided an understanding and opportunity for further improvement in the Calculus teaching and learning. From the perspectives of the lecturers who have taught Calculus courses for at most three years, the difficulties in Calculus teaching were due to several factors such as packed syllabus, insufficiency of technology-enabled classrooms and students’ weaknesses in basic mathematical skills. In the teaching of certain Calculus topics such as the applications of integral Calculus, the use of visual aid was deemed valuable in helping students to understand abstract Calculus concepts. Unfortunately, due to the lack of technology resources and packed syllabus, lecturers often did not have the time and capacity to meet the attention and needs of every student required of them. Lecturers perceived students’ minimal understanding and difficulties in Calculus learning were linked to their attitudes towards Calculus. The process of learning Calculus seemed to be so difficult to them, that they simply memorized the concepts, formulas and procedures with the hope that by doing so, they could actually solve Calculus problems. Most of the times, they failed because there was no conceptual understanding leading to incorrect applications of theorems and formulas. Few suggestions had been recommended by the lecturers in order to remedy the problems faced by students and lecturers in the teaching and learning of Calculus. Calculus
17
lessons could be designed to connect facts and theories to real life situation. The use of Mathematics software such as Maple and Mathematica would be an added advantage to enhance students’ understanding of Calculus as well as to encourage independence in learning. The content and scope of the syllabus for Calculus courses should be reviewed and amended in terms of quantity and continuity of prior knowledge. By providing a comprehensive instructional system, which includes complete module of Calculus subjects, students can be encouraged to learn independently. Besides the lecturers’ roles, lecturers believed that students also need to change their attitudes towards Calculus. It is indeed crucial to enhance students’ motivation, whereby the students’ support unit can play a part to provide personal and academic counseling. It is suggested that only those students with the grade of at least credit 6 in both SPM Additional Mathematics and SPM Mathematics are allowed to enroll in Science-based programs. The findings of this research provide an important scope of how students and lecturers perceived the Calculus teaching and learning in diploma level for progressing Calculus education research in this direction. REFERENCES Ahuja, O. P., Lim-Teo, Suat, K., & Lee, P. Y. (1998). Mathematics teachers’ perspective of their students’ learning in traditional calculus and its teaching strategies. Journal of the Korea Society of Mathematical Education Series D, 2(2), 89–108. Anthony, G. (2000). Factors influencing first-year students’ success in mathematics. International Journal of Mathematical Education in Science and Technology, 31(1). Bloom B. S. (1956). Taxonomy of Educational Objectives, Handbook 1: The Cognitive Domain. New York: David McKay Co Inc. Cipra, B. (1988). Calculus; Crisis looms in mathematics’ future. Research News. 239. 14911492. Di Martino, P. & Zan, R. (2001). Attitude toward mathematics: Some theoretical issues. In M. van den Heuvel-Panhuizen (ed.), Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education, 3, 209-216. Douglas, R. G. (1998). Today’s Calculus Course are too watered down and outdated to capture the interest of students. The Chronicle of Higher Education. 34, B1-B3. Dungan, J. F., & Thurlow, G. R. (1989). Students’ attitudes to mathematics: A review of the literature. The Australian Mathematics Teacher, 45(3), 8 – 11. Fraenkel, J. R. & Wallen, N. E. (1996). How to Design and Evaluate Research in Education. 3rd. ed. USA: McGraw-Hill, Inc. Goulding, M., Hatch, G., & Rodd, M. (2003). Undergraduate mathematics experience: Its significance in secondary mathematics teacher preparation. Journal of Mathematics Teacher Education, 6, 361 – 393. Gynnild, V., Tyssedal, J., & Lorentzen, L. (2005). Approaches to study and the quality of learning. Some empirical evidence from engineering education. International Journal of Science and Mathematics Education, 3, 587-607. Hart, L. C. (2002). Pre-service teachers’ beliefs and practice after participating in an integrated content/methods course. School Science and Mathematics, 102 (1), 4-15. Joiner, K. F., Malone, J. A., & Haimes, D. H. (2002). Assessment of classroom environments in reformed calculus education. Learning Environment Research, 5, 51-76. Lax, P. D. (1990). Calculus reform: A modest proposal. Undergraduate Mathematics Education Trend, 2(2), 1. Madison, B. L., & Hart, T. A. (1990). A challenge of numbers: People in the mathematical sciences. Washington, DC: National Academy Press. McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 576 – 596). New York: Macmillan. Nagasaki, E., & Senuma, H. (2002). TIMSS Mathematics Results: A Japanese Perspective. D. F. Robitaille & A. E. Beaton (eds.), Secondary Analysis of the TIMSS Data, 81-93.
18
National Council of Teachers of Mathematics & Mathematics Association of America (NCTM/MAA) (1987). Curiculum for grades 11-14. In L.A. Steen (Ed.), Reshaping collage mathematics: A project of the committee on the undergraduate program in mathematics (MAA notes 13, pp. 91-102). Washington DC: The mathematical Association of America. Perry, B. (2007). Australian teacher’s views of effective mathematics teaching and learning. ZDM Mathematics Education, 39, 271-286. Ponte J. P. (2007). Investigations and explorations in the mathematics classroom. ZDM Mathematics Education, 39, 419-430. Porter, M. K., & Masingila, M. O. (2000). Examining the effects of writing on conceptual and procedural knowledge in calculus. Educational Studies in Mathematics, 42, 165-177. Ramsden, P. (1984). The context of learning. In F. Marton et al. (Eds.). The experience of learning. Edinburgh: Scottish Academic Press.
Schultz, K. S., & Koshino, H. (1998). Evidence of reliability and validity of Wise’s Attitudes Toward Statistics scale. Psychological Reports, 82, 27-31. Sterenberg, G. (2008). Investing teachers’ images of mathematics. J Math Teacher Education, 11, 89 – 105. Suresh, R. (2002). Persistence and attrition in Engineering: Understanding the nature of students’ experience with barrier courses. PhD. dissertation, University of New York. Tang H. E., Voon L. L., & Nor H. J. (2008). The impact of ‘high-failure rate’ Mathematics courses on UiTM Sarawak full-time diploma students’ academic performance. Research Report, Universiti Teknologi MARA, August 2008. Vinner, S. (1997). The pseudo-conceptual and the pseudo-analytical thought processes in mathematics learning. Educational Studies in Mathematics, 34, 97 – 129. Wise, S. L. (1985). The development and validation of a scale measuring attitudes toward statistics. Educational and Psychological Measurement, 45, 401-405. Wong, N. Y., (2007). Hong Kong teachers’ views of effective mathematics teaching and learning. ZDM Mathematics Education, 39, 301–314. Wood, L. N., & Smith G. H. (2007). Perceptions of difficulty. Research Report, University of Technology, Sydney, Broadway, Australia. Yudariah, M. Y., & Roselainy A. R. (2001). Mathematics education at Universiti Teknologi Malaysia (UTM): Learning from experience. Jurnal Teknologi, 34(E), 9-24. APPENDICES QUESTIONNAIRE A
UNIVERSITI TEKNOLOGI MARA KAMPUS SAMARAHAN QUESTIONNAIRE ON CALCULUS COURSES AND ME Name: Student No: (A) Please circle where applicable. 1. Gender: 1 Male
2 Female
19
(B) Please tick (√) in the appropriate column. Strongly Strongly Disagree Disagree Neutral Agree Agree ———— ———— ———— —— — 1. I would like to continue my Calculus learning in an advanced course. ———— ———— ———— ———— — 2. I feel that Calculus will be useful to me in my future profession. ———— ———— ———— ———— — 3. The thought of being enrolled in a Calculus course makes me nervous.
———— ———— ———— ———— —
4. Calculus seems very mysterious to me. ———— ———— ———— ———— — 5. Most people would benefit from taking a Calculus course. ———— ———— ———— ———— — 6. I have difficulty seeing how Calculus is related to my field of study.
———— ———— ———— ———— —
7. I see being enrolled in a Calculus course as a very pleasant experience. ———— ———— ———— ———— — 8. Calculus is not really useful because it tells me what I already know anyway. ———— ———— ———— ———— — 9. I wish that I could avoid taking my Calculus course.
———— ———— ———— ———— —
10. Calculus is too Calculus-oriented to be of much use to me in the future.
———— ———— ———— ———— —
11. I get upset at the thought of enrolling in another Calculus course. ———— ———— ———— ———— — 12. I feel frightened when I have to deal with mathematical formulas. ———— ———— ———— ———— — 13. I am excited at the prospect of actually using Calculus in my future job. ———— ———— ———— ———— — 14. Studying Calculus is a waste of time.
———— ———— ———— ———— —
15. Calculus thinking can play a useful role in everyday life.
———— ———— ———— ———— —
16. Dealing with numbers makes me uneasy.———— ———— ———— ———— — 17. Calculus is too complicated for me to use effectively.
———— ———— ———— ———— —
18. Calculus thinking will one day be as necessary for efficient citizenship as the ability to read and write. ———— ———— ———— ———— — 19. Calculus will be useful to me in comparing the relative merits of different objects, methods, programs, etc. ———— ———— ———— ———— — 20. Calculus training is relevant to my performance in my field of study. ———— ———— ———— ———— — Thank you for your cooperation!
20
QUESTIONNAIRE B Task 1 (for MAT133 students) 1. Determine the possible values of x if
x 3 1. Express your answer using interval 2x 4
notation and number line. 2. Identify the values of x and y if given
x y 4i . 2 i 2i
3. Use long division method to find the quotient and remainder when f(x) = x3 – 5x2 + 6x divided by (x+2). 4. The points X, Y and Z have coordinates (-2,3),(5,4) and (4,11) respectively. Find an equation of line that passes through the midpoint of XZ and perpendicular to the line XY. 5. Discuss the following equations : y2 = -12x 6. State the radius and the centre of the circle with equation x2+ y2 - 6x + 2y - 6 = 0.
Task 2 (for MAT183 students) 1. By using the first principle, find f ( x ) for the function f ( x ) 2 . x
2. Consider the graph of the piecewise function, y = f(x) as shown below.
State the domain and the range of f(x). 3. Given the function 2 x 1 g( x ) 6
, ,
0x3 x 3
Discuss the continuity at x = 3. 4. Determine the slope of the line that is tangent to the curve 2 x 2 5 y 3 at the point (1, 0). 5. Find the equation of the tangent line to the curve 6 y 2 3x 2 1 at the point (1, 3). 2 6. Evaluate lim x 4 . x 2
x2
21
Section A : Students’ perceptions of the difficulty BEFORE attempting task. 1. I would rate the question as : (Please tick one answer for each question.) Scale Very easy Easy Question 1 2 1 2 3 4 5 6
Moderate 3
Difficult 4
Very Difficult 5
Section B : Answer all the questions stated in Section A. Task 1 to be answered by MAT133 students and Task 2 to be answered by MAT183 students. Section C : Students’ perception of the difficulty AFTER completing task. 1. I would re-rate the question as : (Please tick one answer for each question.) Scale Question 1 2 3 4 5 6
Very easy 1
Easy 2
Moderate 3
Difficult 4
Very Difficult 5
2. Rank the questions in order of difficulty. Very easy
Very Difficult
Section D : Students’ perceptions on the clarity of questions and previous experiences. Based on the questions stated in the task, answer the following. 1. The language of the question is : (Please tick one answer for each question.) Scale Very clear Clear Question 1 2 3 4 5 6
1
2
Moderate
Hard
3
4
Very hard to understand 5
22
2.
The question is : (Please tick one answer for each question.) Scale Very easy to Easy understand Question 1 2 1 2 3 4 5 6
Moderate
Hard
3
4
Very hard to understand 5
3. I have done the similar questions before. (Please tick one answer for each question.) Answer No Yes Question 0 1 1 2 3 4 5 6
*************************************************************************** Student’s Particular Name
: ……………………………….
Sex
: ……………………………….
Race
: ……………………………….
Home Language
: ……………………………….
23
QUESTIONNAIRE C
UNIVERSITI TEKNOLOGI MARA NEGERI SARAWAK KAMPUS SAMARAHAN JALAN MERANEK KOTA SAMARAHAN 94300 SARAWAK
Dear Colleagues, This questionnaire is designed to gather the information on lecturers’ perceptions on Calculus. The findings of this research will be used to generate ideas to overcome the problems in Calculus. As such, your input in this research is very important and your kind cooperation to complete the questionnaire is very much needed. All the information contributed will be regarded with the highest esteem and confidentiality is assured. Your participation and cooperation in the survey is deeply appreciated. We will be most grateful if you can send the completed questionnaire to the following names on or before 12 September 2008. Thank you.
Researchers : 1. Mdm. Nor Hazizah Julaihi 2. Dr. Tang Howe Eng 3. Ms. Voon Li Li
-
Jabatan Sains Kuantitatif (Mailbox : 187) Jabatan Sains Kuantitatif (Mailbox : 8) Jabatan Sains Kuantitatif (Mailbox : 316)
PART A: LECTURER’S PERCEPTION ON TEACHING CALCULUS
1. List out the Calculus subject(s) that you have taught (subject code & name).
24
2.
Indicate the length of year(s) you teach Calculus in UiTM.
3. Do you face difficulty in teaching Calculus? If yes, please list out the difficulty. If no, please list out the effective method that you use to teach Calculus.
PART B: LECTURER’S PERCEPTION ON STUDENTS’ CALCULUS LEARNING
1. What do you think of your students’ Calculus understanding?
2. Do the students face difficulty in learning Calculus? If yes, what are the problems normally faced by the students? If no, which aspect of Calculus the students like most?
3. What is your suggestion to further improve students’ performance in Calculus?
THANK YOU FOR YOUR KIND COOPERATION
25
