Exercices

Exercises are an opportunity for students to put into practise what they have learned. For teachers, exercise sessions can 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, to build fluency in using algorithms or strategies, and to complete calculations and derivations accurately. Exercise sessions can address all of these goals.

Exercises generally happen after a lecture and so students have already heard teachers’ explanations before the exercise starts. What students generally need at that point is opportunities to make the concepts algorithms and skills ‘their own’ by working with them. Typically, therefore, exercise sessions prioritise opportunities for students to work, and ask questions, over re-explaining.

Here are some suggestions which may be helpful in designing effective 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 (the educational principle here is ‘introducing complexity gradually’ to avoid students being overwhelmed).
  • 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 (the educational principle here is called ‘spaced practise’ – people learn better when they engage with material repeatedly over an extended period of time).
  • 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 (the educational principle here is ‘feedback’, which has been found to be a teacher behaviour which is strongly correlated with student learning).
  • 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 (the educational principle here is ‘avoiding accidental complexity’ which can be overwhelming for students). 
  • Students generally like it if the exercises provide them with an opportunity to practise 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 (again, this is linked to ‘feedback’).

In addition to effectively designing exercises, it is also worth thinking about how to teach effectively in exercise sessions.

  • Since the purpose of exercise sessions is for students to make ideas, concepts and algorithms their own by ‘working with them’, it is often a good idea for teachers and assistants to focus on asking questions that enable students to ‘work with’ ideas before giving explanations (see the section on ‘active learning’ for more information on questioning strategies).
  • There is good evidence that students typically learn problem solving better if they are explicitly taught problem-solving methods (see videos ‘Teaching problem solving, below). A common, generalisable problem-solving strategy involves 
    • analysing the problem (which may mean clarifying terms or checking definitions, identifying data which is known and unknown, identifying principles that may apply in a given situation, 
    • making a plan, 
    • carrying out the plan, and 
    • checking solutions and verifying results (which may mean ensuring they’ve answered the question asked in the terms required, verifying units, checking that their solution is plausible etc.).

Students will typically learn problem-solving better if teachers explicitly draw the attention to all 4 stages in the problem-solving process when they are answering student queries. Indeed, often a query arises because a student has not effectively applied one of the stages of the problem-solving strategy (in particular, it seems that student difficulties often arise from jumping straight to trying a solution without adequately analysing the problem). It may be helpful, therefore, if teachers and assistants pay particular attention to making students aware of this when answering their queries. 

  •  Well-structured feedback has been identified as a teacher behaviour that is strongly correlated with student learning. Giving feedback is, therefore, a key teaching strategy in exercise sessions. Not all feedback is equal, however. More effective feedback typically has a number of characteristics: 
    • it clarifies for students what an excellent performance looks like (“If you got a question like this in an exam, you would be expected to be able to…..”)
    • It clarifies where students have met and where they have not met those expectations (“You’ve done what is required here and here, however….”)
    • It helps them see how to improve their performance (“Next time you have a question like this, you might try…”)

For more on effective feedback, see the video and the section on feedback.

In the first year, many exercise sessions in Maths 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).