Active learning in mathematics courses for engineering students (Project Innovation Mathematics Education (PRIME))

Blended learning in mathematics education: Prepare, participate and practise for best results!

Short description

This innovation concerns the bachelor mathematics courses for non-math students, designed by the Delft Institute of Applied Mathematics at TU Delft, as part of PRIME (Project Innovation Mathematics Education). Currently motivation and activity of these students is low. Therefore it was decided to redesign the course. 

The aim of the redesign of the current math courses for non-math students into a blended learning cycle is to:

  • improve study results
  • improve connection between mathematics and engineering
  • increase students active participation and motivation. 

This innovation was first applied to Calculus 1 and 2, Linear Algebra (all first year courses) and Probability & Statistics (first or second year course). In the future courses like Differential Equations and Calculus 3 in certain programs will also be innovated.

Bachelor programs with courses in PRIME are Aerospace Engineering, Computer Science, Electrical Engineering, Civil Engineering and Mechanical Engineering.

Objective

The aim of this innovation is to redesign the current math courses for non-math students to a blended learning cycle design intended to:

  • improve study results,
  • improve connection between mathematics and engineering
  • increase students active participation and motivation

The structure of a blended course (typically 9 weeks duration) with focus on preparation, participation and practise is:

Pre-lecture (prepare): watch an online video where new material is introduced, do online exercises to practise conceptual understanding of the subject, together with book exercises . During the subsequent in class activities (participate) of 90 minutes the knowledge is assessed, if needed explained again, new theory explained and problems solved under supervision. The lecturers use a standard slide pack including workflow of the lecture, learning goals, definitions, theorems, contextual examples*, interactive quiz questions.

After the lecture the students process their new knowledge by doing exercises using the on-line tool with direct feedback as mentioned earlier (practise).

All the material for the course is presented to the students in a well-organized page on Brightspace, the collaborative learning environment in use at TU Delft.   

Strong points

We were able to achieve this redesign by using a project management approach: a core team consisting of six dedicated lectures from the Delft Institute of Applied Mathematics (DIAM), one e-learning developer, an educational advisor and a project leader, and a steering committee consisting of representatives (deans, directors) from different faculties and from the executive board, students affairs & education and students. By this the project was well embedded into the organisation thereby securing support. For such a large project (all 1st and 2nd year students in Delft are involved (3000 students)) this is key for buy-in and final delivery. 

*In each course the contextual examples are tailored to each individual program, to illustrated the use of mathematics in the field at hand. Therefore the courses are no exact copies, but most of the content is exchangeable.

  • Evaluation of the course needs to take place. However preliminary results indicate that students like the new approach, they are more actively engaged, more interaction and better results.
  • All students get the same content and knowledge on the topic. No differences between lectures anymore in that respect.
  • Assessment results can now be linked to a specific lecturer and improvement activities can be defined.
  • Lecturers are frequently invited to discuss the course and improvements needed. This peer to peer discussion provides new insights and improves the quality of the content of the lectures.
  • Meaningful examples taken from the engineering faculty where the students are studying, show students what role mathematics play in their field of interest. This also helps them to develop their skills in mathematical modelling.
  • The lecturers spend less time on preparation and all have the same slides. The content is streamlined and all students get the same offer.
  • Embed the change in the organisation by involving the lecturers, make sure you work as a team and create wide buy-in. Support and buy-in is essential for final delivery. Positive feedback is also essential: people should start talking about the benefits of the project. Basically this project was similar to a change project. Enthusiastic lectures are needed to get the project running. Bear in mind that implementing the course takes at least 3 years.
  • A burning platform is needed to start this large project: low pass rated, no motivation and low feedback on the original course. This really needed a drastic change in course design.
  • This blended approach can be applied to other courses and will increase student activity. The basis can be used and adapted to other faculties.
  • Train the lectures on this new way of working. What to do if students do not do the pre-work, what if you have problems with a few slides. All lectures should provide the same information to the students in their own way.
  • To improve the quality of the in class sessions, video coaching will be introduced to observe the reaction of the students to the behaviour of the lecturer and vice versa. External video coach is hired to evaluate, in an intervision session with several lecturers, the recording and recommend improvements

More information

Visit the PRIME website
Read a Dutch article on 'PRIME: Eerste hulp bij de worsteling met wiskunde'