Comparison of Gaps in Mathematics in Engineering Curricula Lecturer Department of Interdisciplinary Studies Faculty of Engineering, University of Ruhuna, Sri Lanka ABSTRACT Students entering the engineering programme struggle to success their mathematics courses. Because there are many applications can be seen especially in engineering faculties. Therefore, engineering faculties have a separate department to teach mathematics for the undergraduate and postgraduate. Most of the fraction of time allocation for the mathematics is higher in the first year and low in subsequent years. The engineering students need to grasp basic principles of mathematics in order to learn engineering subjects. There was an observation of that the mathematics taught at undergraduate level is still not sufficient to grasp some advanced knowledge in certain subjects. Therefore a research was conducted in Faculty of Engineering University of Ruhuna, Sri Lanka aim to compare the gaps of mathematics in the engineering curricular. Multiple choice questionnaires were used to test first year engineering students. Google form of short questionnaire on a adequacy of mathematics at engineering faculties was provided to postgraduate students who has gone abroad for higher studies. Quantitative data was analyzed using descriptive statistics, while qualitative data was analyzed using strategy. Final results showed that mathematical knowledge of the first year undergraduate students were excellent and most of the students scored more than 60% on the test. Only five students got less than 50% marks. Most of the postgraduate students were given good comments for existing curricular and commonly all were asking to add the same modules to the existing engineering curricula. This study further revealed that extra modules should be introduced into the engineering curricular within the existing modules. The result presented in this paper will be helpful to revise the curricular of other engineering faculties too. Keywords: descriptive statistics, extended curriculum program, inductive strategy, knowledge gap. INTRODUCTION Engineering degree program is a four years course in Sri Lanka and it contains three years of mathematics courses. The students are selected to Engineering courses based on students marks achieved in the final school leaving examination that is the Advanced Level (A/L) under the science stream. However, according to the Moyo [6], Wolmarans et al. [9] students entering the engineering courses struggle to success their mathematics courses. Therefore, the students who are going to abroad for higher studies have to struggle with mathematical knowledge gap. Mathematical knowledge gap is defined as the lack of smooth transition from high school mathematics to university first year mathematics for students majoring in science, mathematics and engineering due to the shortcoming of both the high school and the first year university mathematics programs between the knowledge possessed by school leavers and the knowledge required for first year entry into mathematics courses [1]. Mathematics is very important to study in many disciplines. There are many applications can be seen especially in engineering faculties. Each and every Engineering faculties have a separate department to teach mathematics for the undergraduate and postgraduate. Most of the fraction of time allocation for the mathematics is higher in the first year and low in subsequent years. Also, most of the engineering faculties when the students are in the final year mathematics are not normally taught. As such tendency of engineering students are given low priority to learn application of mathematics. Therefore, they consider mathematics as a subject that is not useful as engineers [8]. The engineering students need to grasp basic principles of mathematics in order to teach engineering subjects [4]. However, students do not understand that in most of the engineering subjects involved with some component in mathematics. There was an observation of that the mathematics taught at undergraduate level is still not sufficient to grasp some advanced knowledge in certain subjects [8]. Also, research carried out Shyamali Dilhani and Cyril Kariyawasam [8] found that this subject requires solution of differential and partial differential equations. Especially, most of the undergraduate students who have gone overseas for higher studies are complaining that 49
the knowledge of mathematics they received as undergraduate is not sufficient to carry out their studies as well as research work. Therefore, most of their supervisors are requested by themselves to follow some undergraduate mathematics courses. Some academics believe that mathematics is a barrier which prevents good students from entering engineering stream [3]. The current technological advances like problem/project based learning, support programs for the students, online support, visual sources, mathematical software programs, online instructional materials, computeraided assessment, flexible, formative and summative assessment (Broadbridge & Henderson, 2008) [2] have increased the importance of mathematic in engineering [5]. How and what mathematics to teach engineering students? This is a problem faced by those who teach mathematics to engineering students. For engineers, mathematics is not just a set of tools, to solve certain well defined problems but it is a mechanism which helps them to approach new problems with confidence [7]. This paper reports on a study carried out at a Faculty of Engineering University Ruhuna, Sri Lanka aim to compare the gaps of mathematics in the engineering curricula. In this study, primary data are collected from Sri Lankan graduates who have gone abroad for higher studies. Secondary data are collected from first year undergraduates (2013 batch) who were studying in the Faculty of Engineering, University of Ruhuna, Sri Lanka. Using both qualitative and quantitative data, findings of the study showed that all the first year engineering undergraduate students had the enough mathematical knowledge and most of the students in the class scored higher than 60%. Findings further revealed that the major drawback is students who are gone for higher studies and they have to self-study or to participate for extra mathematics courses relater to their course work or research work. The insights generated in this study will be help to engineering as well as other institutions looking into designing their curriculum for bridging the knowledge gap. To investigate the matter under study, was guided by the following objectives: To investigate the existence of the mathematical knowledge To evaluate the impact of the engineering curriculum to bridge the knowledge gap of undergraduate and post graduate students 1. MATERIALS AND METHODS The study was carried out at the faculty of engineering, University of Ruhuna in Sri Lanka. The participant of the study were 216 first year undergraduate students and 30 postgraduate students who are reading for their postgraduate degrees in overseas. A purpose of sampling was selected because it felt that first year and postgraduate students had information gained through their experiences in the intervention. Fifteen questions were designed for the multiple choice questionnaire and eight short questionnaire prepared for the survey. Multiple question were designed in such a way that a student would get a marks similar to what they received at the undergraduate level examination. Also, level of the questions was similar to that of the undergraduate engineering mathematics modules. Further, survey questions were based on postgraduate students degree programme and they were requested to give their comments for current engineering mathematics curricula. Submit your manuscript electronically for review. 2. RESEARCH METHODOLOGY The methodology consisted of two parts. First, the undergraduate students answered a formal question paper. This consists multiple choice questions which are related to the first year engineering mathematics module. The five questions captured the knowledge in following areas for undergraduate students. Those are 1. Calculus 2. Coordinate Geometry 3. Trigonometry 4. Complex Analysis 5. Differential Equation. The second was a short questionnaire on adequacy of Mathematics taught at Engineering Faculties. If they had 50
their first degree in Sri Lanka and post graduate education overseas they were asked whether they had to follow any mathematics modules under their programme. Also, eight questions were asked from this students and it consisted about the postgraduate students who had to follow mathematics modules as a requested or opted. Moreover, students opinion about the topics that should be included into engineering curriculum was collected. Also, there was an informal interview with an academic staff who are in different department at the Faculty of Engineering University of Ruhuna. These three components captured both objective and subjective aspects of the research. 3. RESULTS AND FINDINGS The results of the multiple choice questionnaire was shown in the table 1. Figure 1 shows the relationship between the students marks with number of student achieved that marks. In this figure horizontal axis indicates the marks obtained by students and vertical axis shows that the number of students answer for the questionnaire. Table 1: Frequency table of Students participation for questionnaire Number of Students Marks 5 40 4 60 16 67 29 74 45 80 44 87 38 90 35 100 Te s t R e s u lt s 45 44 29 Nu m b er of S tu d en ts 38 35 16 5 4 40 60 67 74 80 87 90 1 0 0 M a r k s Figure 1: Number of students against their marks The figure 1 shows that 45 students (i.e the highest number of population of the students) got 80 marks. The result of the students were skewed to the left and only five students have got 40 marks. Mean of the test result 51
was 83.36 and median of the test result was 87. This implied that students mathematics knowledge were averagely at the higher level. Also, with the survey data of postgraduate students did not have any problem with knowledge of mathematics while they were undergraduate students. However, they were requested to add some modules related to their current studies. For some unidentified reason most of the students asked to include the same module because they were not in the same specialized field. It was not important whether the student is doing Master of Science, Engineering or doctor of philosophy. 30 students were participated for this survey and summary of the results were shown in the table 2. Table 2: Summary of the results of short answer questionnaire Question asked on adequacy of Mathematics taught at Engineering faculties Were you requested (or you opted) to follow courses/modules in mathematics: Responses Yes No 36% 64% If yes what were the modules: Discrete Mathematics Random Variables and Stochastic Processes Numerical Methods for Engineers Advanced Mathematics for Engineers Optimization Numerical Methods in Structural Analysis Operations Research Applied Statistics In your opinion what are the More on Linear Algebra topics that should be included in our engineering mathematics Some basics of Discrete Mathematics and Random Variables and Stochastic Processes. curriculum: Queuing theory The use of software to solve mathematical problems. Laplace principle (large deviations theory). Advance integration Tensor analysis Dynamic simulation mathematic Graph Theory Advanced Engineering Dynamics Mathematics related to quantum mechanics. Mathematical modelling of natural systems with applications Optimization. 52
This survey results depicted that the current topics in our engineering curriculum can be satisfied. However, they were requested to add more modules related to their higher studies. It will be very important to all the engineering faculties to do curriculum revision. Major finding was majority was asking to include optimization techniques into the current syllabus of the faculty. Some comments of the survey data are shown in below. Engineering students did not have any idea why they should learn some mathematics modules. Therefore purpose of studying mathematics should be well explained. More modules related to Mathematical modeling are very useful. The curriculum is broadly acceptable, but the depth and intensity of study needs to be increased. Toward the latter years (3rd and 4th years) advanced mathematics courses need to be introduced as technical electives/core courses. The syllabuses must be also incorporated the usage of software and completion of applied projects rather than only theoretical aspects of mathematics and manual problem solving. Students need to be guided to understand further knowledge of the practical dimensions and applications of the material being taught. This comparison was justified because the multiple choice questionnaire and the survey on mathematics taught in engineering faculties were of similar difficulty. At the informal interviews the academic staff members who are in different department indicated that student cannot relate the mathematics they learned to their engineering subjects. The general consensus was that they prefer more applications oriented mathematics than theoretical mathematics. CONCLUTIONS, IMPLICATIONS AND SIGNIFICANCE It is concluded that the types of mathematics taught at the engineering faculty is useful for engineers of certain disciplines. Also, existing mathematics curriculum is acceptable with some changes. The following recommendations are made to change existing mathematics curriculum. Mathematics curriculum should be prepared in consultation with the engineering faculty staff. Curriculum should be prepared in consultation with the students who has been studying for postgraduate. Syllabi need to be oriented towards practical dimensions and application of the material. This research is very useful for those who are planning and designing mathematics curriculum at the engineering faculty level. Even though the knowledge of mathematics has satisfied undergraduate level. ACKNOWLEDGMENT I appreciate the support extended by academic staff and students of the faculty of Engineering, University of Ruhuna, Galle, Sri Lanka in carrying out this research work. In addition, I appreciate Sri Lankan postgraduate students who are in overseas for higher studies. Without their great support this will not success. REFERENCES 1 Basitere M and Ivala E Problem Based Learning and Authentic Assessment in Digital Pedagogy: Embracing the Role of Collaborative Communities The Electronic Journal of e-learning Volume 13 Issue 2 2015, (pp68-83) available online at www.ejel.org 2 Broadbridge, P. & Henderson, S. (2008). Mathematics education for 21st century engineering students. Final Report. Australian Mathematical Sciences Institute. Available: http://www.amsi.org.au/. 3 Devitt, F., & Goold1, E., (2012). The role of mathematics In engineering practice and in the formation of engineers SEFI 40th Annual conference, National University of Ireland Maynooth, Ireland. 53
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