PRIME: First aid for students struggling with maths
How can we transform maths teaching so that it better connects to the world as experienced by the students? How can we activate them, and what role can IT play in this process? Annoesjka Cabo, Director of Studies Interfaculty Education, talks about ‘PRoject Innovation Mathematics Education’ (PRIME): an innovation project for teaching mathematics to engineers.
Can you explain why maths teaching needed an overhaul in the first place?
Mathematics is at the heart of all engineering courses. It teaches students how to think analytically. They learn to formulate, to reason and to abstract. It’s part of their academic education.
Mathematics is also a fantastic tool that students can use to really get to grips with the material covered in their engineering courses; it’s something that they can really count on and use. Because that’s what engineers do: they translate a problem into a mathematical model to be able to solve it. Then they translate it back to the original situation to continue working on it and interpret the results.
But the pace at university is much faster than at secondary school. Students who walked through pre-university education without having to try very hard are now falling flat on their face. Due to the binding recommendation concerning the continuation of studies, they don’t have any time to loose.
So we’re seeing that students are really struggling with maths. They prefer to dive straight into the engineering courses. But both we and their study programmes want them to spend more time focusing on maths; it’s all about practice, practice, practice! We want them to really work on it so they have a solid foundation. Because only then they will be sufficiently familiar with it and able to apply it. And that’s why PRIME was introduced.
What are the objectives of the project?
First of all, we want to review and renew the teaching method. IT opens a lot of doors and we want to use new technologies in a more structured way so that we can offer more interactive education. Secondly, we want to put mathematics in an engineering context. That way, students can see why and how it’s relevant. Finally, we want to activate and motivate students. We want students to work on their mathematics courses right from the start of their degree programmes, thereby improving the pass rates. This puts the responsibility for passing partly with the students.
PRIME was introduced around two years ago. Can you tell us about the successes you’ve had so far?
Of course! The introduction of the prepare-participate-practice cycle has significantly transformed the teaching method: we combine face-to-face lessons with online teaching. This method works as follows:
- Prepare: students watch a video at home to prepare for their lectures. Then they complete a task to see if they have understood the material.
- Participate: the lecture starts with an interactive quiz. To test students’ understanding; it gives the lecturer an idea of how well the students have understood the material. The quiz is followed by an explanation of new material. Students can ask questions and do exercises. This way, we make it easier for students to start doing maths.
- Practice: at home they practice the material using an online homework system. They receive feedback on their exercises and can ask for hints.
It’s great to see that this method is actually working. Students tell us that they think it’s a good way of teaching, although they have to get used to actively preparing for a lesson.
So you have already achieved results in terms of the first objective. And the other goals?
To put mathematics in an engineering context, we ask the different programmes and senior students where and when they use mathematics. In aerospace engineering, for example, you use a differential equation to describe airplane wing vibrations. By using examples, we can show students that mathematics is relevant for their studies. That seems to work, students are explicitly asking for it.
It is difficult for lecturers to develop those examples, because engineering is completely different from mathematics. And the classes are taught by mathematicians, not engineers. That’s because you really have to have mastered the material to be able to explain it properly. In addition, it’s important to be able to present the material without using potential applications, and to teach the students to learn to think in an abstract way. This is essential, because they need to be able to solve problems in real-life situations later on in their career. We therefore want to achieve the final objective of improving students’ foundation in mathematics by introducing a stimulating teaching method and by calling upon mathematicians to explain and teach mathematical concepts to the students. We are seeing that students are becoming more activated and motivated. However, there is still room for improvement when it comes to examinations.
Every course which uses this method is evaluated by students and lecturers. We then use this feedback to improve the teaching material. It’s a continuous process. This innovation project is gradually being rolled out across the university.
What motivates you to work so hard on this project?
DIAM offers 123 mathematics courses to non-maths students at TU Delft. You need maths in all engineering programmes. That versatility is wonderful, but you see that it helps if engineers and mathematicians develop alongside each other. Mathematicians are taught to think about abstract mathematical concepts and to prove new theorems with those. In applied mathematics, you then learn to create good mathematical models. Engineers, on the other hand, apply mathematics. Sometimes, a result is enough. Their main goal is not to prove the material used, although this can help them understand the overall concept better.
Mathematicians realise that not managing to prove everything doesn’t detract from the level of mathematics. You have to teach students to think about what they are doing and not to just give answers. Students learn to translate a situation into abstract mathematics and then translate that back to the application. Learning to think about definitions and formulas - also in a physical sense - is a challenge for everyone; mathematicians can use their background to make an important contribution here.
I think it’s interesting to try to establish a bridge between these two fields. That’s what motivates me. It results in good-quality education, provided by inspired lecturers. The interesting question for the near future that I want us all to think about is: "How can we design our assessments so that the set of learning objectives are actually achieved and that students can successfully apply what they have learned in mathematics courses in their own degree programme and throughout their career?”
Text: Maartje Roozeboom | Photo: Mark Prins | January 2018