The Laplace transform as an alternative general method for solving linear ordinary differential equations

<p style='text-indent:20px;'>The Laplace transform is a popular approach in solving ordinary differential equations (ODEs), particularly solving initial value problems (IVPs) of ODEs. Such stereotype may confuse students when they face a task of solving ODEs without explicit initial condition(s). In this paper, four case studies of solving ODEs by the Laplace transform are used to demonstrate that, firstly, how much influence of the stereotype of the Laplace transform was on student's perception of utilizing this method to solve ODEs under different initial conditions; secondly, how the generalization of the Laplace transform for solving linear ODEs with generic initial conditions can not only break down the stereotype but also broaden the applicability of the Laplace transform for solving constant-coefficient linear ODEs. These case studies also show that the Laplace transform is even more robust for obtaining the specific solutions directly from the general solution once the initial values are assigned later. This implies that the generic initial conditions in the general solution obtained by the Laplace transform could be used as a point of control for some dynamic systems.</p>

Non-routine mathematical problem-solving: Creativity, engagement, and intuition of STEM tertiary students

<p style='text-indent:20px;'>This study set out to evaluate an intervention that introduced a period of non-routine problem-solving into tertiary STEM lectures at four tertiary institutions in New Zealand for 683 students. The aim was twofold: to attempt to increase student engagement and to introduce them to the kind of domain-free abstract reasoning that involves critical, creative, and innovative thinking. This study was conducted using a mixed-methods approach, utilizing different types of instruments to gather data: comprehensive student pre- and post-test questionnaires, a content validation survey for the questionnaires, focus group interviews (student participants), open-ended questionnaire (lecturer participants), and naturalistic class observations. The main findings are as follows. Students' behavioural engagement was significantly greater during the intervention. Perceptions of the utility value of the activity improved at the end of the semester for all students. There were no significant changes in students' convergent thinking (problem-solving), intuition, or creativity (originality, fluency, and elaboration traits of the divergent thinking) during the course, probably due to the relatively short timescale of the intervention. However, overall, the results of the investigation suggest that with a relatively small effort, teachers can improve STEM student engagement by devoting a few minutes per lecture on non-routine problem-solving. This is something that can be easily implemented, even by those who primarily teach in a traditional lecturing style.</p>

Microlearning and computer-supported collaborative learning: An agenda towards a comprehensive online learning system

<p style='text-indent:20px;'>With the rise of the COVID-19 pandemic and its inevitable consequences in education, increased demand for robust online learning frameworks has occurred at all levels of the education system. Given the transformative power of Artificial Intelligence (AI) and machine learning algorithms, there have been determined attempts through the design and application of intelligent tools to overcome existing challenges in online learning platforms. Accordingly, educational providers and researchers are investigating and developing intelligent online learning environments which share greater commonalities with real-world classroom conditions in order to better meet learners' needs. However, short attention spans and the widespread use of smart devices and social media bring about new e-learning systems known as microlearning (ML). While there has been ample research investigating ML and developing micro-content, pedagogical challenges and a general lack of alternative frameworks, theories and practices still exist. The present models have little to say about the connections between social interaction, including learner–content, learner–instructor and learner–learner communication. This has prompted us to investigate the complementary aspects of Computer-supported Collaborative Learning (CSCL) as an interactive learning model, along with an embedded ML module in the design and development of a comprehensive learning platform. The purpose of this study is to explore the pedagogical frameworks and challenges with reference to interaction and retention in online learning environments, as well as the theoretical and pedagogical foundations of ML and its applications. In addition, we delve into the theories and principles behind CSCL, the main elements in CSCL, identifying the issues and challenges to be faced in improving the efficacy of collaboration processes and outcomes. In short, we aim to synthesize how microlearning and CSCL can be applied as effective modules within a comprehensive online learning platform, thereby offering STEM educators a relevant roadmap towards progress that has yet to be offered in previous studies.</p>