Exercises are an opportunity for students to put into practice what they have learned. For teachers, exercise sessions provide immediate feedback on students’ level of understanding of the subject.
In EPFL, students need to be able to understand scientific concepts, but they also need to be able to apply them, to model them in mathematical terms, and to complete calculations and derivations accurately. Exercise sessions can address all of these goals.
Ideally, what sort of activities should students do in exercises?
- Because repetition is crucial to developing fluency and memory, they should repeat the skills and approaches which have been demonstrated in class.
- As students become more fluent in using techniques, they can be asked to develop their abilities by applying them to more complex questions or to previously unseen situations.
Here are some suggestions which may help to improve student learning in exercises:
- Include some easier exercises at the start before moving to more complex or challenging ones. Students will find it easier to face complex problems, if they have had a chance to develop some fluency with the techniques first. In fact, there is some evidence that students complete exercises quicker and more successfully, when the complexity of the exercises is graduated, even if that means there are more exercises for them to complete.
- Give exercises on material covered in the previous week’s lectures (i.e. give exercises in week 3 on material covered in week 2, and so on). Although students may find it challenging to go back to the previous week’s material, the repetition over time will increase their chance of remembering the material long-term.
- Make sure that students have some way of checking their answers, such as by getting worked out solutions. These can be provided a few days after the exercises, if you want to ensure that students have a chance to attempt the exercises before going to the solution.
- Avoid typos or errors in exercises or corrections. Remember that while the error may be obvious to you, students do not have your level of expertise and consequently may waste lots of time trying to “figure out” where the “new” formula came from.
- Students generally like it if the exercises provide them with an opportunity to practice the kind of skills they will be assessed on. In other words, they appreciate it if some exercise questions have the same format and level of difficulty as the exam.
In the first year, many exercise sessions in Math and Physics are organised as “tutorial” sessions (“tutorat”). Here students work in small groups of about 8, alongside a more experienced tutor (typically a master’s student), who can guide their thinking. Ideally the tutor will try to avoid directly pointing out their errors to the students, but will instead help them to develop their problem-solving and error-checking abilities by guiding them with questions. Students in tutorat are also encouraged to help each other, because such peer-teaching has been found to be very beneficial for both the peer-teacher and the peer-learner (for more information, you can go here).
These same ideas can be applied in other exercise sessions also:
- Supervision of exercises can be seen as a process of guiding students to a solution, without providing the solution but by scaffolding them towards the acquisition of efficient problem solving strategies by asking questions that direct their attention.
- Similar group-work practices can be utilised in other exercise sessions even in the absence of a dedicated tutor. Simply organise students into teams of three and arrange that they should ask each other in the case of a problem before asking for help from the person supervising the session.