First and second year courses in engineering mathematics are primarily used to develop student skills in key mathematical concepts and skills that underpin the study of higher level discipline-specific course modules. However, whilst students often become expert at solving mathematical problems, they are often unable to apply the mathematical concepts that they have learnt to other areas of their studies. This often necessitates lecturers of higher level modules to revisit essential mathematical concepts before moving on to teaching the intended subject matter. A primary cause of this failure is the separation of mathematical theory from engineering application in early-stage engineering course modules. Two papers presented at REES2017 discussed how problem-based learning has enabled two institutions to address this problem, and in this blog I review both papers.
Exploring Differential Equations through Group Projects
In the first paper, entitled Student Engagement in Assessment through Group Work in a Mathematics Course for Bioengineers, Carrere and her colleagues explored the use of group work in enhancing understanding of mathematical concepts in a second year Bioengineering undergraduate course on differential equations.
Carrere and her colleagues redesigned the course on differential equations to include two group projects in which students were expected to explore the application of material covered in the course to the theory and practice of Bioengineering. The course runs over an entire semester, and its content includes topics such as Ordinary Differential Equations (ODEs), Linear and non-linear ODE systems, Fourier series, and partial differential equations (PDEs).
The objectives of the course were to enable students to:
- Identify, formulate and solve problems
- Use technological resources effectively
- Work effectively in teams
- Communicate effectively
- Act with ethics and professional responsibility
- Learn in a continuous and autonomous way, and carry out self-assessment.
Structure and implementation of the Group Projects
Students self-selected themselves into groups of three and were assigned problem sets that required them to use differential equations to model and analyse mechanical and electrical systems that underpin the study and practice of Bioengineering. Students carried out the study over a series of workshops in which lecturers were present to offer guidance and appropriate scaffolding at each stage of the analysis and modelling process.
The teaching team incorporated student peer assessment and self-assessment to identify and discourage non-participation and free-riding. Students were also involved in developing the assessment criteria. In this way students had ownership of the whole learning process.
Assessment of the group project outcomes
In my opinion, this course achieved multiple objectives that are important to the development of engineering education. First, the course succeeded in linking the theory covered in engineering mathematics to engineering-specific courses that are covered in other study modules. Secondly, the team projects gave the students an opportunity to use software to model and simulate the mathematical concepts that were covered in class. In this way, they learnt how to put their knowledge of mathematics into practical use, something that is often difficult for engineering students taught and assessed in traditional ways. Third, the students were actively involved in the design of assessment criteria and in the assessment of their own work through peer assessment and self-assessment. This study suggests that involving students in all aspects of assessment helps them to reflect on the course objectives and encourages them to focus on the key learning goals of the course.
Bridging the gap between first year mathematics and Engineering disciplines
In the second paper, entitled Teaching mathematics in engineering careers: A permanent challenge, Gemignani and her colleagues reported on their efforts to align the teaching of first year mathematics to material covered in higher level discipline-specific courses at the Universidad Tecnológica Nacional, Argentina. In their institution, first year engineering mathematics is covered in two course modules, namely Mathematical Analysis 1 (MA 1) and Algebra and Analytical Geometry (A&AG). Gemignani and her colleagues successfully developed two group projects that drew on material covered in these two modules.
Learning objectives of the two inter-module projects
The learning objectives of these two group projects were to enable first year engineering students to:
- Use their mathematical knowledge to identify and solve problems in the professional context
- Be aware of their own learning process and to develop self-directed learning abilities
- Develop critical thinking skills
- Develop peer assessment and self-assessment skills
- Use contextual applications to motivate and reinforce their knowledge of mathematics
Structure and implementation of the inter-module Group Projects
Lecturers on the two modules collaborated in developing a set of exercises drawn from professional practice. These exercises were deliberately pitched at a level of complexity and difficulty to make it almost impossible for students to solve them simply by applying the manual mathematical processes covered in the two modules. In addition, each individual problem set required students to identify a series of mathematical concepts that they would need to come up with acceptable solutions.
Students also needed to acquire some programming skills in Mathematica to enable them to analyse and model the given problems. These were provided through additional lectures on Mathematica that ran alongside the project timeframe. These lectures covered both Mathematica instructions as well as their application to mathematical problem solving.
To prepare students for these projects, the two modules were redesigned to allow the teaching of both mathematical theory and applications to engineering problems. This was done by ensuring that in both course modules, one lecturer was assigned to teach mathematical theory and another assigned to teach applications of mathematics to engineering.
Assessment evaluated both the overall group performance as well as individual student contribution. Specifically, individual students were evaluated on their ability to generate and propose new ideas throughout the project, their fluency and clarity in communicating these ideas, as well as their team participation and interpersonal communication skills.
Evaluation of the inter-module group projects
In end-of-course surveys, the majority of students found the inter-module projects to be very beneficial to their engineering studies. They especially appreciated the fact that the two inter-module group projects helped them to develop their ability to apply mathematics to solving engineering problems.
Students also appreciated the fact that the group projects gave them the opportunity to solve problematic situations similar to those they may have to face in their future professional lives. It’s noteworthy to observe that in most traditional approaches to engineering education, practical applications are often left out to the latter stages of degree programmes. This often leads to motivational and persistence problems in engineering.
Lecturers of higher level course odules also reported that student cohorts who had done the inter-module group projects had better Mathematica programming skills and they also demonstrated a deeper understanding of mathematics compared to previous cohorts.
Another problem with current undergraduate teaching is that the curriculum is chunked into individual modules. This often leads to students failing to identify the connections between these myriad individual modules, leading to a disjointed student experience. This study shows that this problem can be addressed by introducing module-bridging projects that give the students the opportunity to apply all their learning to the resolution of a given real-life engineering problem.
These two studies suggest that the group project can be a valuable learning construct in engineering mathematics. They also suggest that if engineering mathematics modules are to be effective, then they should not be viewed simply as tools for teaching mathematics theory for its own sake. Rather, academcis in engineering departments should collaboratively work together to develop learning environments where students can experiment and visualise the application of mathematical theory to their own disciplines. As the two studies point out, this helps engineering students to link mathematics theory to studies in their own disciplines, which in turn helps to keep the students motivated, especially in the critical early stages of their degree programmes.
Carrere L Carolina, Ilardo Juan, Ruiz Joaquín V, Iván Lapyckyj, Escher Leandro, Waigandt, Diana (2016). Student Engagement in Assessment through Group Work in a Mathematics Course for Bioengineers. REES 2017: The 7th Research in Engineering Education Symposium 2017 6-8 July 2017, Bogota, Colombia.
Gemignani, María Alicia & Gandulfo, María Itatí (2016). Teaching mathematics in engineering careers: A permanent challenge. REES 2017: The 7th Research in Engineering Education Symposium 2017 6-8 July 2017, Bogota, Colombia.