Advanced^2 Engineering Mathematics (A2EM)

Background and justification of the project

The project Advanced Advanced Engineering Mathematics (A2EM) aims at the development of advanced learning modalities for the course Advanced Engineering Mathematics (AEM, 4BM00). AEM is lectured in Q1 and is a core course in the curriculum of the Mechanical Engineering M.Sc. program. The course attracted approximately 160 students in 2018-2019. The number of participants of the course has increased significantly over the years, in accordance with the growth of the student population in the ME M.Sc. and related interdepartmental tracks.

AEM aims to equip engineering students with understanding and skills related to elementary mathematical concepts and analysis techniques. The course plays a central role in the development of the modeling and analysis capabilities of ME M.Sc. students. The targeted competence level is “understanding” and “applying”. The course attracts a diverse audience, including a significant number (approx. 30%) of international students with miscellaneous backgrounds and equally diverse prior knowledge on the course subjects.

The AEM course is generally perceived of as a complex and abstract course. To enable the students to make the abstract concrete, ample examples and assignments are provided. Part of the assessment comprises two graded midterm take-home assignments. These assignments serve both a formative and a summative assessment purpose, but the emphasis is on formative aspects.

Over the past years, we have experienced that the effectiveness of some of the adopted conventional teaching forms in AEM is limited, while other more effective teaching forms are becoming unmanageable owing to the rapidly expanding student population. In particular, the frontal-style lectures that have been a core means of teaching in AEM are suboptimal, largely because the uniform pace does not cater to the various needs of the heterogeneous student population. On the other hand, the graded take-home assignments, which are essential in the formative-assessment of and corresponding feedback to the students, are becoming unmanageable due to the increasing number of students.

Objectives and expected outcomes of the project

The overarching objective of the A2EM project is to develop digital learning materials for AEM to:

1. Facilitate individualization of the learning process for students;
2. Increase the efficiency (competence development/time) of the educational process;
3. Adapt to the expansion of the student population.

The targeted outcomes are:

1. An increase in the throughput (passes) of the AEM course;
2. An increase in the satisfaction and understanding of the participants of AEM;
3. A reduction in the workload for the lecturers;
4. An enhancement of the sustainability of AEM, by making the efforts of the lecturers essentially independent of the number of course participants;
5. A set of digital tools and guidelines for implementing similar strategies in other courses.

The A2EM project primarily targets the abovementioned educational innovations in the AEM course. However, A2EM will also serve as a template for similar educational innovations in other courses (item 5 above). Experiences and best practices will be disseminated within the TUE organization. To this purpose, ESoE will monitor the development and implementation of the educational innovations in AEM, and the outcomes will be made available in the form of reports, presentations and software tools.

Project design and management

Specifically, the following digital learning materials will be developed:

1. A set of 7 video lectures complemented by pencasts to replace half of the frontal-style lectures: these video lectures and the pencasts enable diverse learners to chart their own course through the learning material and process the material at their personal pace, with the option of repeating and replaying material, either individually or in small teams;
2. An online digital-testing environment (in Cirrus) to automate the assessment of the graded midterm assignments: the digital tests will serve to provide individual formative (and partly summative) assessment to the individual students, without incurring a significant O(n) effort (effort proportional to the number of students) for the lecturers.

The A2EM project is designed as a 2-year project. It is envisaged that the project commences in spring 2019 and runs for 2 full cycles of the AEM course (Q1 2019-2021), ending in spring 2021. The period of Q2 2020-2021 includes the resits. The completion period until spring 2021 serves to process the results of 2020-2021 cycle and report on the outcomes of the project.

The development of the course materials will start immediately after approval of the project. A first batch of 4 video lectures and corresponding pen casts will be recorded before Q1 2019-2020, and will be implemented in the 2019-2020 edition of the AEM course. First versions of the digital tests will also be developed (including beta testing) before Q1 2019-2020. The new course materials will be evaluated during the running of the course and immediately afterwards, so that the modus operandi may be adjusted during the course cycle. Based on the evaluation results, 3 further video lectures and additional pen casts will be recorded.

The development and implementation of the abovementioned learning materials will be supported by Antoine van den Beemt of ESoE, who will advise on effective forms and implementation strategies, assist in the analysis of the effectiveness of the revision, and monitor positive and negative induced effects.

The project is coordinated by the team of lecturers of AEM consisting of the applicants. The principal lecturer of AEM will act as primus inter pares and will act as main coordinator of the project and as point of contact. The team is supported by a TA (PhD student) and an expert from ESoE. It is envisaged that beta testing of the digital-testing environment is conducted by a group of approximately 20 students of the previous generation (2018-2019) of AEM students, under supervision of the TA.

The project coordinator will provide accountability in the requested manner.

Dissemination and sustainability of the project

Sustainability of A2EM is an intrinsic element of the design of the project, as A2EM will result in a set of learning materials, as well as guidelines on their use, that will be utilized as-is in subsequent editions of the AEM course. An enduring effect of the A2EM project is therefore anticipated. Because the project is coordinated by 3 staff members, meta-level insights resulting from the project are consolidated within the TUE organization.

It is anticipated that further spillover effects will be achieved by dissemination of the guidelines and best-practices. An open midterm seminar will be scheduled in spring 2020 to communicate the main insights acquired in the first tranche of the project.

Results and learnings

This project is currently still ongoing