For self and peer assessment to be good experiences for students, some thought needs to be given to how you will set it up. It’s important, for example, to discuss with students your rationale for the activity and to make clear how the procedure will work. What will happen in the event of a disagreement over feedback or a mark? The assessed task also needs some discussion as well the criteria against which it will be assessed.
Where writing is used as the vehicle of assessment, it's often thought to be good practice to let students know the kinds of criteria that'll be used when marking it. But being explicit is not easy. Simply giving students a list of assessment criteria doesn’t ensure that they know what those criteria mean in practice. For example, saying you will be looking for ‘argument’ in an assignment cannot be assumed to let your students know what the term means to you and how and where you would identify its presence or absence: arguments in texts, after all, are not abstract entities but are intricately tied up with ideas and knowledge, structure and expression. A tick-box approach to assessment, then, is likely to be rather limited in conveying how quality is actually judged.
One better way to develop this understanding is to give students assignments from previous years or similar modules to read, assess and give feedback on. But you might want to consider your aims in doing this: are you aiming for the students to understand what it is you value in assignments of this kind, so that their judgments come close to yours; or are you aiming for them to articulate what it is they value? Or would you like them to recognise that a range of judgments are possible on many pieces of work especially if they are complex and discursive?
The differences between these aims are rather subtle but they’re worth thinking about. In any case it’s generally a good idea to start by allowing students to come up with their own judgments and/or criteria before introducing your own.
Please get in touch if you'd like to talk through these kinds of issue and have some support in trying out self or peer assessment with your students.