School of Mathematics Teaching

Feedback

Purpose of feedback and formative versus summative feedback.

Feedback

Feedback encompasses any mechanism by which learners get information on their performance, whether this is from the teacher or from fellow students and it could include model solutions and marked work with comments.

Prompt and useful feedback is important in learning. The importance of promptness suggests that often quick but rough feedback such as analysis from fellow students is as important as measured careful feedback from academics if the latter takes days or weeks.   

Feedforward

The idea of feedforward is that the real value of feedback is only realised if the learner later gets to use the feedback to improve an attempt at some related task. For example, a project at the end of a course may be of little value.

Within a course, feedforward is often realised when feedback on (usually low-stakes) formative assessment will enable the learner to perform better in later summative assessment.

Feedback is not just marking

One very traditional activity that provides feedback is setting work (assessed or not) and marking it. It can obviously be useful to students, but if it is just ticks and crosses it may not be as useful as we think. A "model solution" may help to suggest why we did not give full marks and comments on the students' work may do more. But even with all those things, we may only be addressing a fraction of the things that students may find helpful. If the marking is not so detailed, the student may feel that they have not had feedback at all: they have just been assessed.

The University's Enhancing Feedback Website has an extensive discussion of feedback, references to the teaching literature and subject-specific suggestions. You will find a huge range of ideas there as to how feedback can operate.

University's Enhancing Feedback website 

Formative versus summative 

There are type types of marked work:

  • Summative - its main purpose is assessing the students’ performance as part or all of the final grade that they will be awarded.

  • Formative - its main purpose is to provide feedback to the student on how they are progressing, or whether their methods and results are correct. 

The main point of feedback from the formative assessment is that it should feed forward; it should enable the student to perform better on something similar next time. Think of somebody learning to play tennis or golf with a coach: they try a shot once or twice, then a coach will explain how they can improve it (feedback) and then the learner tries again (feed forward) until they have mastered it. Ideally, there should be a feedback cycle of attempt - feedback - try again, and this is a good way of thinking about things but it can be hard to achieve in a University course. 

Purpose 

In our courses, students are normally asked to hand in regular written work which is marked and returned to them. We often give credit for this (typically 5-15% of the total mark for the course) to nudge students towards completing it but its main purpose is formative. For this to work well, it is essential that work is marked in a way that helps and encourages the learning process.  

Feedback guidelines

Ticks, crosses and total marks at the bottom of a question do not provide much useful feedback. Please observe the following guidelines. 

  • Indicate clearly (if possible) where precisely the student has gone wrong.  If the error they made was obvious to the student, they probably would not have made it!  
  • Where possible, explain a little more about why the thing you have identified is a mistake, and indicate if appropriate what would have been a better way of proceeding. (but you only have time for a few words - don't write whole essays.) 
  • Be sympathetic: read what students have written and try and understand what they are trying to say. Remember that learning is a slow uncertain process and coursework marking is meant to help it rather than judge it. 
  • Keep your comments objective: comment on the mathematics, not on the student. 
  • Write ‘Please ask about this’ if you think it is necessary. This puts the responsibility on the student to seek help from you, or from MathsBase, etc. This can be particularly helpful if you think the student has a serious misunderstanding. 
  • Add positive comments as well as criticisms.
  • Do pass information on common mistakes or misconceptions to the Lecturer. 
  • Try and give some helpful feedback even on correct or nearly correct answers. There is usually something we could suggest that would improve the student's work.  
  • In all this, exercise some judgment on what to comment on so that students get a sensible amount of feedback. Clumsy wording that you should remark on in an excellent piece of work might sensibly be ignored in one where more serious errors are being made. 

Considering the above, returning a piece of work to a student with no written feedback is unacceptable except for occasional cases where all the students' answers are 100% correct and very professionally presented.

Returning and collecting work 

Pay attention to any class rules about accepting hand-ins directly when they are supposed to be collected at a lecture or accepting them after a deadline.  A sympathetic attitude is good, but students will be aggrieved if some tutors are following the rules strictly and others are not. 

Students sometimes report having not gone to workshops because they were embarrassed to hand in partial work or worried about getting back something with a very low mark. Be thoughtful about these issues. Here are some suggestions: 

  • Put the final mark on the bottom of the last page rather than on the top. That way it will not get publicly displayed with the work on the table. (And students often put away work as soon as they have seen the mark rather than studying the feedback, so hiding it at the back has an added benefit.) 
  • If a student has done poorly, ask to have a quick chat with them at the end of the workshop. End the chat on a positive, optimistic note. 
  • Avoid anything that might be regarded by a sensitive student as a public humiliation. 
  • Keep it impersonal: it is the work that is bad, not the person.