Engineering Mathematics Course Research Articles

Changes in Students’ Approaches to Learning on Engineering Mathematics Courses with Two Different Instructional Models

Changes in Students’ Approaches to Learning on Engineering Mathematics Courses with Two Different Instructional Models

Designing and analysing a teaching proposal about linear algebra through the dialogue of two theories

In this paper we propose a new strategy of dialogue between theories, considering a semiotic cognitive analysis and a praxeological analysis. We examine the implementation of a teaching and learning sequence for introducing eigentheory in a linear algebra course taught during the first year of an engineering degree programme. Initially, the semiotic cognitive analysis based on the Action, Production and Communication space (APC) approach is used in the preliminary, a priori and in vivo phases of the didactic engineering process to propose a teaching strategy that incorporates a variety of semiotic resources. In a second moment, the praxeological analysis intervenes to reformulate the preliminary analysis and to progress on the consideration of a reference epistemological model about eigentheory in a first course of mathematics for engineers. This model is then used in the a priori and a posteriori analysis to integrate the semiotic and epistemological dimensions in the design and implementation of the teaching proposal. The results show the productivity of this new networking strategy and the complementarity of connecting the semiotic with the epistemological analysis.

Enactment and impact analysis of active learning strategies utilized for the basic science courses in the evaluation of engineering students

The new era of teaching learning process demands more clearance of theoretical aspects utilizing visual strategies. Accordingly, this research focuses on usefulness of student team achievement division (STAD) and project based learning (PjBL) as active learning strategies for comprehensive understanding of basic science courses. The study revealed increased effectiveness of learning, encouraging equal participation, active engagement and supportive learning environment for better understanding of concepts in basic science courses. The usefulness of active learning strategies has been studied by conduction of STAD & PjBL activities for the Engineering Mathematics and Engineering Chemistry courses respectively. The appropriate evaluation and comparative analysis done before and after activity allows to elaborate the efficacy of visual strategies utilized for understanding theoretical concepts. Keywords—Active learning tools, Basic Science Courses, Evaluation Rubrics, Project Based Learning, Student Team Achievement Division

DATA ON THE VALUE OF ISLAMIC RELIGIOUS KNOWLEDGE AND SYSTEM OF MATHEMATICAL MODELING EQUATIONS INCREASING THE VALUE OF ISLAMIC RELIGIOUS KNOWLEDGE

The understanding of Islamic Religion of students in the Engineering Mathematics Course, Department of Mathematics, Universitas Islam Negeri Sunan Kalijaga Yogyakarta is quite good, with an average value = 86.4444, median = 84, and mode = 100. The mathematical modeling equation system for increasing understanding of Islamic religion consists of four ordinary differential equations.

Engineering students’ approaches to learning in two student-centred instructional models before and during the COVID-19 pandemic

ABSTRACT In this study, we investigated how well two different student-centred instructional models fostered engineering students’ learning in a time of crisis. We analysed students’ (N = 375) approaches to learning during four engineering mathematics courses in a Finnish university before and during the COVID-19 pandemic. Students’ deep and surface approaches to learning, as well as organised studying, were measured five times during an eight-month period. For the control group the student-centred elements were added to the framework of traditional lecture-based teaching, whereas the intervention group’s instructional model disrupted the structures of traditional teaching more profoundly. Our results indicate that the pandemic and related restrictions were linked to a decrease in students’ deep approach to learning and organised studying, and an increase of surface approach to learning in both groups. However, the intervention group’s instructional model supported the deep approach to learning better than that of the control group.

Why Can the Flipped Classroom Frustrate Students? Experiences from an Engineering Mathematics Course

This paper explores students’ experiences with a flipped classroom in a first-year engineering mathematics course with 118 students. While most students were satisfied with the flipped classroom and expressed appreciation for the flexibility, freedom and independence induced by the teaching method, other students expressed frustrations. Based on two surveys with both open-ended and closed-ended questions, this paper explores possible reasons why a flipped classroom can be a source of frustration. Some students expressed having difficulty adjusting their study habits to the flipped classroom approach as well as having difficulty finding the motivation to watch the required learning videos before in-class activities. While some students experienced the group work associated with the flipped classroom format as a positive aspect of their learning, other students expressed irritation because of group members not meeting prepared for the group assignments. The expressed experiences are discussed in light of the self-determination theory and the self-regulated learning theory. Weaknesses with how the flipped classroom was implemented are also discussed.

Solving word problems involving triangles by transitional engineering students: Learning outcomes and implications

Transitional engineering students are those who are academically ineligible to enter a bachelor’s engineering program but are enrolled in an associate engineering program with a university. Successful completion of such an associate engineering program allows the higher achievers to transfer to a full bachelor’s engineering program. The associate engineering program is taken commonly by self-employed tradesmen, technical workers, and young apprentices in regional, rural, and remote (RRR) areas. The foundation engineering mathematics course in the associate engineering program, particularly knowledge and skills in solving word problems involving triangles, plays a key role for the smooth transition of these students to the engineering disciplinary courses. However, there is little we have known about the performances of the transitional engineering students in solving problems involving triangles as the associate engineering programs are not among the mainstream of undergraduate programs. This study analyzed the 27 transitional engineering students’ performances in solving word problems involving triangles assigned to the students in the foundation mathematics course at a regional Australian university and found that the RRR transitional engineering students demonstrated a higher level of study ethics and achievement in solving word problems involving triangles, compared with the RRR student mathematics teachers. This seems mainly due to the professional experiences in delivering real-world projects prior to the start of their mathematics learning. Further research should be expanded to more areas of mathematics to gauge the overall performances of the transitional engineering students in mathematics learning and progression.

Reflection on Experiences of First-Year Engineering Students with Blended Flipped Classroom Online Learning during the COVID-19 Pandemic: A Case Study of the Mathematics Course in the Extended Curriculum Program

The shift to remote learning during the COVID-19 pandemic presented a unique challenge for higher education in developing countries such as South Africa, where resources are distributed unevenly. The Department of Chemical Engineering at a South African university of technology used a flipped classroom blended online learning approach in an engineering mathematics course. This study describes the transition of first-year engineering students from face-to-face learning to flipped classroom blended online learning. The Laurillard conversational framework for teaching learning was used to develop the five components of blended learning pedagogy, this allows students to discover, learn, practice, collaborate, and assess (DLPCA). The chosen assessment strategies made use of adaptive learning technology via the WebAssign platform to provide formative and summative assessments as well as timely feedback to each student. The authors examined the remote teaching and learning approach using three indicators: (i) learning—students’ learning experiences; (ii) assessment—students’ academic performance and integrity; and (iii) students’ challenges. The findings had a positive impact on students’ learning and performance in the mathematics course. The limitation to the study was that the data were collected only from one university of technology and were not compared with other universities in the country. The overall findings of this study indicate that students require time to adjust to online pedagogy to ensure a smooth transition.

The development of sociomathematical norms in the transition to tertiary exam-oriented individualistic mathematics education in an East Asian context

This study investigates social, mathematical, and sociomathematical norms perceived by college students in an engineering mathematics course and examines the students’ sense of mathematics as signals of individual merit. Data sources include a survey and one-on-one interviews with 38 students. The findings help illustrate student perceptions of academic social norms in a large-lecture course represented by the acquisition model of learning in college, detached from communal and collaborative disciplinary practices. Findings provide insights into the local educational context of an East Asian country as a case study when exam-oriented mathematics is institutionalized as normalcy.

Effectiveness and Challenges of Problem-Based Learning Implemented in Engineering Mathematics Courses

Presently, graduates of institutions of higher learning are found to be passive and not competent in carrying out the tasks assigned to them. The number of graduates that fail in a job interview has increased. One of the contributing factors is their ineffective communication skill during the interview, thus failing to exhibit their generic skills abilities in convincing the potential employer. As a proactive move to improve this issue, an initiative was carried out by the Faculty of Engineering and Built Environment (FKAB), Universiti Kebangsaan Malaysia (UKM) to introduce and implement problem-based learning (PBL) activities in the engineering mathematics courses. With the PBL method implemented at the early stage of the study period, the student’s ineffective communication issue can be addressed effectively. It is anticipated that the deployment of the PBL method can generally improve students’ soft skills, especially communication ability in meeting the demand and expectations of industry employers. The objectives of this study are to evaluate the effectiveness of the PBL implementation, thus identifying the benefits and the challenges of the PBL 5 Ladders of Active Learning strategy. In this study, the PBL activity was implemented in the Engineering Mathematics III (Differential Equation) course. To analyse the students’ feedback toward the implementation of the Five Ladders of Active Learning strategy and Self-Directed Learning method, the Rasch Measurement Model application software called Winstep was used. The results showed that the challenges faced during the PBL implementation are the readiness of lecturers as facilitators, the acceptance, and the readiness of students towards the learning process of the 5 Ladders of Active Learning strategy, the conducive learning environment, the crafting and constructing of PBL problems/triggers, the students’ reflection, and the PBL evaluation methods. To ensure that engineering students can master mathematics and generic skills as intended in the program, these challenges must be tackled effectively.

Student Centered Post Covid Teaching Using Asynchronous Platform in Malaysia Polytechnic

This paper is focusing on the Engineering Mathematics course that was conducted on an online platform due to the Pandemic of Covid-19. Mathematics instructors are being forced to digitize their course materials, such as videos of lecture topics over the Internet, but lack a detailed survey that addresses how students interact with course content, the tools available during class, and the available equipment at home. This presence challenge has been encountered through before and after class surveys to close the gap on the abovementioned issue through online learning. Throughout this study, the needs of students of the various departments involved were taken into account for the calculation of their satisfaction feedback that was investigated. The survey results also indicate that the problem of Internet coverage over time no longer exists for most students. Only the result of audio equipment instability due to the non-standard good quality of the equipment used during the online learning course was rated 18.3% out of 100%. The engineering mathematics content was delivered as planned and no critical learning issues were identified.

Improving problem-solving skills through technology assisted collaborative learning in a first year engineering mathematics course

PurposeThe purpose of this research study is to explore simple collaborative technique for teaching mathematics and thus improving the problem solving skills of the students. Better pedagogic activities are required to motivate the students to perceive mathematics as a subject that stimulates problem-solving skills required for engineers.Design/methodology/approachThis paper presents a research study on the application of technology-supported collaborative learning in improving the problem-solving skills of first-year engineering students in a mathematics course. The experiment was conducted in a mathematics course “Engineering Calculus” with 286 first-year engineering students in two groups: experimental group (N = 60) and controlled group (N = 226). The academic performance of the students was measured and analyzed with statistical techniques.FindingsFrom the results obtained, it was found that the academic performance of the experimental group was better than the controlled group. Also, interest shown by the students in the topic that dealt with collaborative learning was more than in other topics taught using conventional teaching methods.Research limitations/implicationsThe teachers are required to find effective pedagogical activities to improve the problem-solving skills in mathematics. The research work proposes a collaborative method in mathematics for attaining higher cognitive level in an entry level engineering course. The limitation of this study lies in group formation techniques and the grading policy which deals only with individual assessment scores.Practical implicationsPractice of collaborative learning is made easy with simple technology. A clear strategy for the conduct of collaborative learning sessions has been presented. The solutions recommended are practically feasible and does not require any special infrastructure or specific training.Social implicationsUsing technology in mathematics teaching may not be very easy for all teachers. Especially, for an undergraduate engineering fresher, mathematics may not be a very easy task. This work shall bridge the gap with simple technology-assisted collaborative learning. The teachers need not spend too much time and effort in learning technology for mathematics teaching. The effect of this learning is significant in terms of the performance and satisfaction evaluation.Originality/valueThis work presents a systematic implementation of collaborative learning that shall result in improved problem-solving skills and engaging learning sessions. The statistical analysis methods and the visualization of obtained results shall help in understanding the implications of the presented work. Practice of collaborative learning is made easy with simple technology. The solutions recommended are practically feasible and does not require any special infrastructure or specific training.

Languaging and conceptual understanding in engineering mathematics

The ability to apply mathematical concepts and procedures in relevant contexts in engineering subjects sets the fundamental basis for the mathematics competencies in engineering education. Among the plethora of digital techniques and tools arises a question: Do the students gain a deep and conceptual enough understanding of mathematics that they are able to apply mathematical concepts in engineering studies? This paper introduces the use of languaging exercises in the engineering mathematics course ‘Differential Calculus’ during the spring semester 2020, at Tampere University of Applied Sciences, TAMK. In this study, the students’ conceptual understanding and learning of differential calculus is researched. In the learning process, the languaging method is used to deepen the conceptual understanding of the concepts of differential calculus. Pre-test/post-test setup was used to see the possible gain in conceptual understanding. During the course, students did online assignments, which included languaging exercises. Students described the concepts of differential calculus using natural language, pictures, or a combination of them. The students were also asked to fill in a self-evaluation form to collect their perception of their own knowledge of mathematical skills. Mid-term and final exams summarized the acquired knowledge. The study aimed to enhance the learning outcomes and to gain a deeper understanding of mathematical concepts by exploiting the languaging method.

ICLASS LEARNING MANAGEMENT SYSTEM FOR TEACHING ENGINEERING MATHEMATICS DURING COVID 19 A LAGOS STATE UNIVERSITY EPE CAMPUS CASE STUDY

Coronavirus has shocked the world and almost bought the education sector to a stop. The Nigerian government declared a compulsory lockdown on all states of the federal. The Lagos State Government's passion for education consulted Envivo Education, a private company, to develop an Iclass Learning Management System (ILMS) for virtual teaching. This platform was effective in teaching courses, but the peculiarity of engineering is the basic to understand engineering mathematics the bedrock of all concepts. A Motivated Strategies for Learning Questionnaires (MLSQ) survey was administered to all students who took the engineering mathematics courses. The data was collected, and the statistical analysis was done with Minitab. It found out that the ILMS is good for teaching courses, but to understand engineering courses screenwriting and feedback from students should be included.

Analysis of Students’ Errors and Misconceptions in Solving Linear Ordinary Differential Equations Using the Method of Laplace Transform

Laplace transform (LT) is an essential mathematical tool for solving linear ordinary differential equations (ODE) with boundary values, by transforming differential equation into algebraic equations which are easier to manipulate. In this article, we analyse the errors students make and misconceptions they have in solving linear ODE using LT method. The study participants were 81 students enrolled in an engineering mathematics course at a University of Technology in South Africa. The students’ responses to an item based on LT which formed part of an assessment, were analysed. The analysis identified three stages of working that were necessary to reach a solution (introduction of LT and simplification; resolution of expressions using partial fractions (PF); carrying out the inverse LT and manipulations). Within each stage, we distinguished between three types of errors (conceptual, procedural and technical). The results showed that students experienced most problems when working in the PF layer because of the poor background in manipulation of algebraic expressions. It is recommended that students are given opportunities to develop fluency in pre-requisite concepts, so that their efforts at solving problems using LT or other advanced mathematics techniques can be less stressful.

Student Performance Predictions for Advanced Engineering Mathematics Course With New Multivariate Copula Models

Engineering Mathematics requires that problem-solving should be implemented through ongoing assessments; hence the prediction of student performance using continuous assessments remains an important task for engineering educators, mainly to monitor and improve their teaching practice. This paper develops probabilistic models to predict weighted scores ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WS</i> , or the overall mark leading to a final grade) for face-to-face (on-campus) and web-based (online) Advanced Engineering Mathematics students at an Australian regional university over a 6-year period (2013–2018). We fitted parametric and non-parametric D-vine copula models utilizing multiple quizzes, assignments and examination score results to construct and validate the predicted <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WS</i> in independently test datasets. The results are interpreted in terms of the probability of whether a student’s continuous performance (i.e., individually or jointly with other counterpart assessments) is likely to lead to a passing grade conditional upon joint performance in students’ quizzes and assignment scores. The results indicate that the newly developed D-vine model, benchmarked against a linear regression model, can generate accurate grade predictions, and particularly handle the problem of low or high scores (tail dependence) compared with a conventional model for both face-to-face, and web-based students. Accordingly, the findings advocate the practical utility of joint copula models that capture the dependence structure in engineering mathematics students’ marks achieved. This therefore, provide insights through learning analytic methods to support an engineering educator’s teaching decisions. The implications are on better supporting engineering mathematics students’ success and retention, developing evidence-based strategies consistent with engineering graduate requirements through improved teaching and learning, and identifying/addressing the risk of failure through early intervention. The proposed methods can guide an engineering educator’s practice by investigating joint influences of engineering problem-solving assessments on their student’s grades.

Profile, Performance and Language in Engineering Mathematics

There is a global concern for retention and success of students in higher education engineering programmes, in particular for students from under-represented communities. Low success in engineering programmes can be partly attributed to students failing mathematics or being unable to articulate mathematics in other engineering courses. This research explores how understanding the academic preparedness of engineering students in relation to their performance in university mathematics can direct curriculum changes to improve student success, driven by the research question: “How can the analysis of student data contribute to understanding student performance in calculus?” Data from engineering students in an extended curriculum programme at the University of Cape Town (UCT) were analysed to generate profiles from variables including gender, home language and performance in university admissions tests. Profiles were related to performance in three consecutive engineering mathematics courses. To determine which variables had the greatest explanatory power on engineering mathematics scores, relative importance analysis was applied. There was no evidence that weaknesses in terms of pre-university mathematics performance held students back from succeeding in the first two engineering mathematics courses at UCT, at least within the support context of the extended curriculum programme. When analysing according to engineering mathematics performance levels (e.g., fail versus first-class pass), academic literacy and, to a lesser extent, quantitative literacy emerged as having greater relative importance than pre-university mathematics in explaining the variance in engineering mathematics scores. The findings imply that interventions to improve the success of engineering students should include developing academic literacy practices, potentially in first- and second-year mathematics courses. We reflect on how the relative importance analysis of student data strengthens similar findings from other research on the importance of language in mathematics by highlighting the most important variables explaining students’ mathematics performance.

Factors Influencing Success in Advanced Engineering Mathematics Courses: A Case Study

Several studies have been conducted to understand the predictors of academic performance of various levels of high school and undergraduate students as quantified by the grade point average. This study focuses specifically on engineering students as they differ from other undergraduate students in their background and expectations. We focus on quantifying essential predictors of the performance of engineering students in an advanced mathematics course. We collected data from 72 participants recruited from engineering students enrolled in the advanced engineering mathematics (AEM) course in a research university. We chose this course to represent a standard engineering mathematics course covering several essential topics. We consider several factors in our analysis, such as cellphone usage and the academic background, e.g., the academic year, number of minors, and majors, performance in prerequisite courses. We perform several regression analyses to understand the effects of cellphone usage, course schedule, and academic background on performance in the AEM course and its prerequisites. In particular, we use the stepwise regression technique using forward selection and backward elimination procedures. We discovered a few interesting findings in this case study. Firstly, for the participants in this study, we find that the daily average “screen time” on their cellphones is not a statistically significant predictor of student performance. This finding contradicts some prior studies on this participant and may indicate adaption and integration of the technology by the new generation of students in recent years. We also found that the lecturing schedule was not an influential factor for their academic performance. These findings are especially relevant during the COVID-19 pandemic, as they suggest that advanced engineering students have adapted to the use of technology and are flexible concerning lecture schedules. Another unexpected finding is that this study brings new evidence that the number of minors taken by the participants is a negative predictor of their grade in the AEM course. This observation may indicate that course-work from non-major classes may adversely impact their performance in mathematical engineering courses.

Implementation of Learning Management System (LMS) in mathematics learning

The world of education during a pandemic is forced to use an online learning system. This is evidenced by the issuance of regional and central regulations relating to online learning rules. There are many platforms that can be used to do online learning, one of which is edmodo. The edmodo platform can be used more flexibly with the help of laptops and cellphones that students often use, besides that, it does not require much quota. The research method used is a mix method by combining quantitative and qualitative methods. The population of this study is students from University of Serang Raya. The object of the research was students of civil engineering, unsera in engineering mathematics courses. The result of this research is that the experimental class is better than the control class in terms of the mean value. The application of learning uses a learning management system, namely students upload assignments, download material, collect assignments and ask questions in the comments column related to the material provided by the lecturer.

Finnish university students’ views of different relationships in first-year engineering mathematics courses

Integration is seen as a main factor for students to stay in university and eventually graduate. In conventional lecture-based teaching, students might avoid asking for academic help from teachers, which weakens the student–teacher relationship and distances students from the faculty. To decrease distance and ease integration, more student-centred methods are widely adopted. This article concerns the use of specific tutors and a learning space called Math Shack in engineering mathematics teaching and learning at Tampere University in Finland. The aim of this study was to examine how students experience relationships and roles within first-year engineering mathematics courses and determine if Math Shack affected their experiences. The analysis was based on the material from a drawing assignment (N = 695) which was collected from first-year engineering mathematics students. Drawings were categorized as data-driven. The results showed that Math Shack tutors were experienced as more approachable than assistants; however, assistants were experienced as middlemen. Though there were no major differences in experiences whether students had been in Math Shack or not, assistants were experienced slightly differently.