Individual digital learning recommendations for pre-courses in mathematics
Karin Landenfeld & Jonas Priebe
Hamburg University of Applied Sciences, Germany
Previous school knowledge in the STEM subjects, especially mathematics, is not sufficient for many degree programmes to ensure a good entry into the degree programme. In order to support the preparation as well as possible, individually and specific to the degree programme, we work with a blended learning concept, which is appropriately supported by an online learning environment. The students and teachers benefit from the digital diagnostic knowledge tests specific to the degree programme and the topic-specific learning recommendations. On the one hand, we present the concept and the digital learning environment with which the students learn with learning videos, many interactive exercises and visualisations. On the other hand, we show results of knowledge tests and the corresponding learning recommendations before and after the pre-course as well as a comparison between different study programmes in electrical engineering from several semesters.
Enhancing Multivariate Calculus Learning using Matlab
School of Industrial Engineering, Università Carlo Cattaneo – LIUC, C.so Matteotti 22, 21053 Castellanza, Italy
Mathematical software is considered a powerful tool for supporting the teaching and learning of mathematics, Höltta and Hyötyniemi (2003). The use of toolboxes and plots allows students to visualize mathematical concepts and better understand traditional content, Hadjerrouit (2019). Multivariate calculus, which deals with elements living in the plane and space, such as level curves and gradient flows, is one of the mathematical topics
that benefit greatly from visualization. However, students often struggle with these concepts and teachers find it difficult to represent them on the blackboard. While students may rely on illustrations in textbooks, this approach can lead to a superficial understanding of the material, Lipsman and Rosenberg (2017). To promote a more active learning experience, students can draw, manipulate, and analyze the geometric shapes of multivariate calculus using software tools, Freeman (2014). By doing so, they can assess their knowledge and competencies, enhance their skills, and take a more holistic approach to the subject.
This work aims at presenting a literature review to understand the approaches used when introducing mathematical software in traditional math courses to support learning. Despite the benefits of using software, teachers face challenges in designing and implementing these approaches. In first-year engineering courses, for example, classes can consist of hundreds of students, making it difficult to guide all of them in using the software.
Challenges also arise in terms of coding skills prerequisites and available time for coding activities.
To address these challenges, this work illustrates some preliminary results using MATLAB software, Mathworks (2022), in the multivariate calculus module of the first-year Analysis course of the Industrial and Management Engineering Bachelor’s degree at LIUC. In this case, the opportunity to use MATLAB was offered to only a subset of the class during extra-class time. A questionnaire was administered to this sample of students, and the results were analyzed. A discussion is presented comparing the performance of students who used MATLAB with that of the rest of the class, to identify the positive and negative aspects of this approach. However, a potential risk is that this approach may create a distortion in the class group, as those participating in the extra-curricular activity may be more motivated to study, while the rest of the class may not be participating despite potentially needing the learning approach more and expected to benefit more from it.