Assessment in secondary mathematics
◄Previous: 3.1 Ideas to enable you to assess your students’ mathematical learning

# 4 Key issue 4: Challenging assumptions about assessment

## Reflection point

What do you see as effective assessment?

Having read this far into this course, you will recognise that assessing students’ learning:

- rarely means using a test or short questions, unless you need to assess their ability to take a test
- is not done towards the end of a topic, as assessment is best used to help your students to improve their learning and they will need time to make those improvements
- means getting to the heart of students’ understanding, and hence requires activities that explore and challenge students
- involves the students themselves, as they are the ones who are doing the learning.

Those who assume that assessing mathematics is straightforward and easy often do not have a broad view of what mathematics is, but see learning mathematics as learning to get simple questions correct and use straightforward procedures. Such an interpretation is likely to be part of the poor view that society has about mathematics and many people’s reluctance to study mathematical or mathematics-related subjects at university level. As more people see mathematics as a way of thinking and modelling the world so that efficient solutions can be found to complex problems, so assessing students’ progress will be seen to be complex and multifaceted.

Formative assessment can take a number of forms, some of which are more formal than others and all of which offer the potential for teachers and students themselves to truly understand where progress is successfully made and what the students’ next steps in learning may be. One big assumption is that it is the teacher that does formative assessment to the students. However, research shows that the more the students themselves are involved in the assessment of their work, the more effective the assessment is in guiding and moving forward their learning.

## Activity 5 Why use self- and peer assessment?

Allow about 90 minutes

Watch Dylan Wiliam’s video about self- and peer assessment, noting down all the benefits he describes of using self- and peer assessment in your classroom. (Alternatively, you can read a transcript.)

Now consider these examples of self- and peer assessment:

1. Asking the students to identify whether or not they feel they have met the objective(s). Asking each student to refer to the objectives and to write about:

   - any difficulties they had
   - what they did to try to overcome them
   - what still puzzles them
   - what they would like to do next to improve that understanding.
2. Asking the students to assess a (fictitious or anonymous) piece of work and deciding if the work demonstrates understanding of the objectives.
3. Asking the students to discuss and resolve situations that relate to standard misconceptions. For example: ‘Does multiplication always make numbers bigger?’

Identify explicitly how the three ideas above are examples of self- and peer assessment. Also, consider how they may offer the benefits that Dylan Wiliam indicates in the video.

## But it’s the teachers’ job!

Many teachers find that their students say they do not like using peer and self-assessment, saying, for instance:

- ‘The student marking my work may not like me and may give me a poor mark out of spite.’
- ‘It is the teacher’s job to do the marking.’
- ‘Only the teacher can know if my work meets the standards or not.’

If your students are making similar remarks, it may be for one of the following reasons:

- The point of what they are being asked to do has not been well explained. One teacher refers to peer marking as ‘seagulling’: her students are asked to go and look at others’ work and identify the good bits (chips) that they can then ‘steal’ to improve their own. Peer assessment is not about marking or grading, but about sharing good ideas and understanding the quality of work required.
- The peer-marking is being done at the wrong time and the students are not being given the time and opportunity to use the knowledge they have gained in the exercise to improve their work.
- The students are being asked to grade another student’s work and they are not qualified to do this.

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