Hansong XUE1,*, and Stephen TAY En Rong2
1Science, Mathematics and Technology, Singapore University of Technology and Design (SUTD)
2Department of the Built Environment, College of Design and Engineering (CDE), National University of Singapore (NUS)
Sub-Theme
Others
Keywords
Student-centered learning; assessment; active learning; higher-order thinking ; engagement
Category
Lightning Talks
Introduction
In the teaching and learning of mathematics, ordinary differential equations (ODEs) is an important topic that mathematically explains observed phenomena in engineering and sciences. However, students find ODEs abstract and unrelatable to their experience (Santos et al., 2020). Furthermore, while a guided inquiry approach for ODEs was reported, the link to personal experience was still lacking (Hyland et al., 2023). To help draw upon authentic contexts and student engagement, work on scenario-based student generated questions (sb-SGQA) was developed (Tay, 2024). Through sb-SGQA, students become active constructors of knowledge rather than passive recipients, which fosters autonomy and encourages the development of higher order thinking skills (Yu & Wu, 2020). Subsequently, the incorporation of reflection in the sb-SGQA approach led to the employment of Contextualised Learning via Enquiring, Answering, and Reflecting (CLEAR). Hence, this study seeks to explore the impact of CLEAR through the following research questions (RQ):
RQ1: Does the CLEAR approach help students relate ODEs to observed phenomena beyond the classroom?
RQ2: How do students perceive the CLEAR approach?
Methodology
The CLEAR approach was implemented during the Spring Semester of AY2025 in the graduatelevel course “Applied Mathematics for Engineering” at the Singapore University of Technology and Design. Students, in groups of 2, were tasked to develop CLEAR assignments that utilise ODEs concepts and principles to a context they could draw upon from life experience. To help with scaffolding, a sample contextualised CLEAR assignment was provided (Figure 1). A total of 10 graduate students were enrolled in the class. As the course was taught for the first time, a control was not available for comparison. Consequently, data for discussion would rely on analysis of students’ work (RQ1) and feedback from students (RQ2).
.
Results and Discussion
An analysis of the contexts developed by the students revealed that students were able to meaningfully relate ODEs to real-world phenomena beyond the classroom (Table 1). Deep-diving into one such assignment, heat transfer for nuclear fuel was used as a relevant and authentic context for the application of ODEs (Figure 2), along with reasonable answers to the questions developed (not shown in abstract). This finding addresses RQ1 and responds to the concerns raised in a previous study (Santos et al., 2020).
List of contexts students developed questions and answers for through CLEAR. Note that 9 contexts were shown as the 4th context was duplicated by another group
.
Subsequently, student feedback was analysed to gain insight into their perception of the CLEAR approach. Table 2 presents the semester feedback, reproduced as provided. In general, graduate students appreciated the concepts taught to beyond the classroom (Feedback No. 1, 4, 5 and 6). One appreciated how approximations are commonly used (Feedback No. 3), and another enjoyed the learning process (Feedback No. 2). These results help to answer the second research question, indicating that students were generally positive.
Student feedback on the use of CLEAR
.
.
Conclusion and Significance
This study employed the use of CLEAR to teach ODEs to graduate students. While regarded as a challenging subject that students always struggle to relate to, the results of this study revealed that students were able to develop a variety of meaningful contexts for the application of ODEs. In addition, perceptions were generally positive, with a comment indicating that the process was enjoyable. These findings provide helpful anecdotal evidence that could inspire new approaches to teaching ODEs in classes. Furthermore, as the approach does not have associated hardware and software costs, the CLEAR approach can be reasonably scaled, potentially across a wide range of other courses and disciplines.
Limitations and Future Work
A limitation of the study lies in the small class size of 10 students, which prevents meaningful quantitative analysis. Moreover, the cohort comprises students from five different academic departments, each bringing varied academic backgrounds. Moving forward, aggregated results across multiple cohorts could be used to improve the sample size for meaningful comparisons.
References
Hyland, D., Paul, v. K., & and Nolan, B. (2023). Student perceptions of a guided inquiry approach to a service-taught ordinary differential equations course. International Journal of Mathematical Education in Science and Technology, 54(2), 250-276. https://doi.org/10.1080/0020739X.2021.1953627
Santos, L. B., Xavier, P. H. F., Santos, J. V. C., & Sampaio, R. R. (2020). Teaching of ordinary differential equations using the assumptions of the PBL method. Int. J. Eng. Pedagog., 10(3), 7-20. https://doi.org/10.3991/ijep.v10i3.12015
Tay, E. R. S. (2024). A four-year journey in implementing scenario-based student generated questions and answers (sb-SGQAs) across Departments, Colleges, and Institutions. SoTL-Asia Talk Series
Yu, F.-Y., & Wu, W.-S. (2020). Effects of student-generated feedback corresponding to answers to online student-generated questions on learning: What, why, and how? Computers & Education, 145, 103723. https://doi.org/10.1016/j.compedu.2019.103723