Better marking in maths

Author:
Laurie Jacques
Main Subject:
CPD
Subject:
Maths
Date Posted:
09 November 2012

With careful planning, you can provide effective and varied feedback on children’s work without spending every night poring over their books

In its recent report, Mathematics – Made to Measure, Ofsted identified considerable variations in the quality of maths marking in schools they inspected between January 2008 and July 2011. This article explores what marking means in the context of mathematics teaching today and suggests how to give constructive feedback on pupils’ mathematical work.

Marking is a term that has been used for many years in teaching and is traditionally associated with a teacher brandishing a red pen over pupils’ written work. And yet, in recent years, despite a greater emphasis on assessment for learning, marking remains trapped within this time capsule. From this point on I urge you to consider marking in its broadest sense – the act of feeding back about mathematical learning. This process is not one way.

Hodgen and Wiliam (2006) describe three types of feedback that are essential to formative assessment:

pupil to teacher
teacher to pupil
pupil to pupil.

The second is commonly understood, but this can only occur if the remaining two are planned for in lessons.
Typically, lesson plans identify learning objectives, teaching points and activities for pupils; the best will also identify success criteria. Few plans, however, consider how the work will be marked. Whilst this might seem like another onerous task in the planning process, having a clear vision for ensuring that pupils receive useful feedback during, and at the end of, a lesson will ensure the right types of activities are planned in the first place.

 Below is a staged approach to the thinking process a teacher might go through when planning for feedback in a maths lesson.

1 Why feed back to pupils?

 This simple and often overlooked question is worthy of consideration and won’t always generate the same response. How this is answered will depend on the nature of the lesson. If the lesson is the first in a series, feedback about prior learning will be used to reassure pupils they are ready for the next steps. Should the lesson come at the end of a series, feedback will confirm to what extent pupils have achieved what was expected. Also, at the end of every lesson that forms part of a series, feedback will focus on preparing pupils for the following session.

What do I want to feed back to pupils?

The nature and curriculum content of the lesson will determine how this is answered. For example, in a lesson about adding two single digit numbers, feedback may centre around effective mental strategies, rather than whether the answer is correct. For example, “Try putting the larger number first” or “Use your number bonds for 10 as a step towards the answer”.

In a lesson about properties of isosceles triangles, feedback may focus on conceptual understanding, e.g. “Look for two sides that are the same length” or “Can you identify an isosceles triangle when the ‘odd’ side is not the base?” The first of these comments is a prompt to achieve the success criteria. The second might be given to a pupil who has met the success criteria in some cases but is making a common error.

In Mathematics - Made to Measure, Ofsted observed that the “most valuable marking enables pupils to overcome errors or difficulties, and deepen their understanding.” This is the art of skilled mathematics teaching: the ability to anticipate, identify and correct errors in children’s learning, and should form the basis of planning for feeding back.

3 How will pupils feed back and when?

In planning the pupil activity for a lesson, it is necessary to consider how the children’s work will provide feedback to you as a teacher, i.e. what have the pupils learned and understood? Here are some suggestions for how this can be achieved as part of the main body of the lesson (as whole class or group work, or plenaries). Children can:

Sort a set of questions in order of difficulty > Compare different strategies
Take pictures as they work through a problem > Work through a set of problems in a fixed time 
Peer mark and receive peer feedback > Write their own hard question and easy question for the class 
Spot errors in the teacher’s or other pupils’ work > Design a concept or skill poster
Use individual whiteboards – “3,2,1 show me” > Agree? (thumbs up), disagree? (thumbs down), say they are not sure (thumbs to side), and explain why. 
Sort their names on the whiteboard according to which problem (of three) they found most difficult.

4 How will I feed back to pupils?

This will, of course, depend on the type of activity in which pupils have engaged from the list above. Providing written feedback is time consuming, especially if all the work produced by pupils in one lesson is marked in the same way. Instead, pick out a focus group who will receive constructive written feedback in their books, whilst selecting another group to engage in critical dialogue during the
plenary. In the same lesson, you could also spend time listening to and supporting a third group while pupils are working – writing notes in their books as you do this will demonstrate you have seen the work and fed back verbally.

Rotating these marking strategies over the course of a week will enable you to have fed back to pupils in a variety of ways, without having to mark 30 exercise books each day.

5 What will pupils do with the feedback and when?

Pupils need opportunities to reflect on written feedback and verbal feedback. In Mathematics - Made to Measure, Ofsted observed that pupils in effective classrooms were given time during registration or at the beginning of a lesson to look at feedback and then to respond. If verbal feedback was given, then a related mathematical challenge was set at the end of the lesson to be completed the next day, or at home.

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