1. Feedback and Next Step Marking
Mathematics

2. Aims of the Session
To clarify the key principles of effective feedback.
To outline the features of next step marking in mathematics.

3. Assessment for Learning
Where anyone is trying to learn, feedback about their efforts has three elements – the desired goal, the evidence about their present
position, and some understanding of a way to close the gap between the two.
This quote is taken from
Sadler, R. (1989). Formative assessment and the design of instructional systems.
It is stated more simply on the next page.

4. Assessment for Learning
Deciding:
where learners are
where they need to go
how best to get there
Recap of key aspects of assessment for learning.

5. Key Elements of AfL Providing effective feedback to children.
Actively involving children in their own learning.
Adjusting teaching to take account of the results of assessment.
Recognising the profound influence assessment has on the motivation and self-esteem of children, both of which are crucial to learning.
Considering the need for children to be able to assess themselves and to understand how to improve.
Key elements of AfL taken from the publication ‘Inside the Black Box’ (Paul Black and Dylan William).
This meeting will concentrate on the element of feedback.

6. Marking and Feedback Oral Written
“To be effective, feedback should cause thinking to take place.”
Shirley Clarke
Feedback has many guises – can be both oral and written and depends where the child is when the marking takes place.
In terms of written feedback, next step marking is desired. Marking which consists of ‘ good’ or ‘ neat’ don’t actually comment on the mathematical achievement or progress within the lesson and therefore do not support children with their learning.
In order to progress and succeed, children need constant and supportive feedback on their learning. Adults working in schools and settings need to give both oral and written feedback that helps children understand how to take ownership and control of their own learning and progress.
Assessment for learning involves creating an ethos in a school or setting where talk and dialogue about learning are central to the day-to-day work of the school. Children will then be more willing to articulate their own successes or areas for improvement, and will also give feedback to teachers and each other more readily.

7. Marking and Feedback
Learners need information and guidance in order to plan the next steps in their learning.
Teachers should:
pinpoint the learner’s strengths and advise on how to develop them;
be clear and constructive about any weaknesses and how they might be addressed;
provide opportunities for learners to improve upon their work.
Whether feedback is oral or written, this is still the case

8. Effective Feedback
The purpose of returning marked work to pupils or of oral feedback is to enable pupils to improve their learning.
However, both teachers and pupils need to be clear about the assessment criteria that will inform marking and feedback.
For instance, if the learning objectives for the work to be marked were not concerned with presentation and neatness, teachers may consider whether comments about those things should be made, particularly if it is the only comment that is made.
In order for feedback to be effective, pupils need to be aware of the assessment criteria.
Research has shown that feedback generally focuses on:
Presentation
Surface features of writing, e.g. capital letters and spelling
Quantity
Effort.
There is an story from Shirley Clarke in which young children have been asked to cut out pictures from a story and stick them in sequence on a page. As the teacher walks round she stops next to one child and praises him for how neatly he has written his name on the page. The other children then think that the lesson is about writing your name neatly and concentrate more on this. The teacher then praises another child for neat cutting out. Again, this reinforces to the children that the focus is on cutting neatly. A third child is then praised for neat sticking. By this point, the children may have forgotten what the original objective and learning of the lesson was supposed to be.

9. Successful Oral Feedback
Oral feedback is regular and interactive. Oral feedback can be direct (targeted to individuals or groups) and indirect (others listen in and reflect on what is said). Works in three directions: - teacher to child - child to teacher - child to child
The teacher can model the language of feedback that children can employ themselves, in discussions and paired peer assessment.

10. Successful Oral Feedback
Oral feedback should be:
positive – recognising the children’s efforts and achievements to date
developmental – offering specific, detailed advice to help children progress
Feedback is for all children, not just those who seem to be struggling. This is often where we tend to focus most of our energies.
These could be during:
Guided sessions
Group work
Plenary
End of unit prior to new unit

11. Successful Written Feedback
Highlights success and improvement against the learning objective.
Asks for small improvement.
Quality marking - once or twice a week - not for every piece of work.
Gives children time to act on it.
Eventually develop shared marking:
teacher and child
child and partner - paired marking
child marks own work.
Identifying elements of success and one or two areas to improve helps children to develop skills and concepts. Over-marking and providing too much written feedback makes the feedback inaccessible to children. It is more effective to have a smaller number of items focused on the success criteria.
Children need classroom time to engage with and respond to feedback. They are unlikely to be able to embed any suggestions for improvement and apply them to later work unless they are given time to respond to feedback. This is particularly necessary for children with special educational needs.
Some children will need to be supported to read the feedback and apply the suggestions for improvement.

12. Effective Feedback
A study by Ruth Butler (1988) analysed pupils’ work marked by one of the following strategies:
- comments and actions for improvement
- grades only
- praise only
no feedback at all
The quality of work of those given only comments and actions for improvement improved substantially from lesson to lesson. Those given praise only, or grades only, did no better than the pupils who were given no feedback at all.
Children need to engage with the work not just because they are being rewarded for it.
Consider Horizon – Who do you want your child to be? programme with research on praise. Findings were that saying to children that they are ‘clever’ is giving praise for an end result and children begin to value the end result, which, if it isn’t arrived at quickly, won’t arrive at all because the children give up too soon. By praising the effort in working towards the end result, children value the time being devoted to the activity and learn to be more persistent.

13. Improving Marking & Feedback
In marking pupils’ work, teachers can consider:
how well the pupil has understood the task;
what the pupil knows and does not know;
what the pupil needs to do next to improve;
how the pupil will be informed of this;
how they can encourage pupils to review their work critically and constructively.
Teachers who use a range of effective techniques for assessment, marking and feedback are more likely to be successful in raising standards.
This is through questioning, oral and written feedback.
Handout 1 - AfL self evaluation sheet with focus on feedback (p5 of self-evaluation grid handout)

14. Effective Feedback Outcome of piece of work Correct Incorrect
Correct, with thorough understanding
Correct, inefficient methods
Incorrect, inefficient methods
Incorrect in part of process
Lack of prior knowledge/
understanding
Identify next steps/
challenge
Model efficient method with task set
Highlight errors/model efficient method with task set
Identify
error in process
address appropriately
Identify gap and address appropriately
Only show the first click of this slide with the bottom section missing. It is also absent on the handout slides.
Essentially these are the most common outcomes of a piece of work. Give out Handout 2 - can the teachers identify what the feedback might be for each.

15. 30  6
 2
20  4 = 24
80  9
 3
40  6 = 46
70  1
 7
30  6 = 36
50  2
 6
30  4 = 34
What is happening here?
Questioning at the first level would have indicated that this child has a problem as they would have explained it as subtracting the smaller number from the larger. This is not apparent if the only examples given are ones where the larger number is always at the top. This has stored up problems for later stages.
Children should be encouraged to self correct as we discussed earlier. If they cannot self correct, they may not understand what has been taught.
Give out Handout 3 – Examples of work. What feedback and next steps would these involve? Work in pairs / groups on all of them (approximately 10 minutes) and then take feedback.

16. Child A Go through responses.
Example 1 - Incorrect in part of the process
Feedback could be - Child does not understand what to do when the numbers add to a 2-digit number.
Next steps could be - Move back to expanded calculation as this will not occur and discuss what happens in each column.

17. Child B Example 2 - Correct but use of an inefficient strategy
Feedback could be – Comments about how the answer is correct, but could they solve this in a ‘quicker’ way.
Next steps could be - Model multiplication strategy and set similar problem

18. Child C
Example 3 - Incorrect due to lack of prior knowledge. The process is there and the child knows how to solve these types of problems, but does not understand the meaning of the inequality signs.
Feedback could be – Oral feedback, explaining one to one with the child (or group if problem with more than one child) and modelling the use of the inequality signs using practical equipment.
Next steps could be - Address lack of understanding through revisiting concept or intervention if appropriate.

19. Child D Example 4 – Incorrect due to inefficient method.
Feedback could be - Model method in line with school policy and set question to reinforce.
Next steps could be - Reinforce tables with class.
- Model checking when copying down from question.

20. Child E Show the reflection of shape A in the line of symmetry A
Example 5 - Lack of prior knowledge/understanding (lack of understanding of key principles of reflection).
Feedback could be - Explain one to one with the child or the group if there is a problem with more than one child.
Next steps could be - Address and revisit using practical materials and physically reflecting objects.

21. Child F
Example 6 - Incorrect in part of the process, child has missed the second part of the 2-step problem.
Feedback could be - Prompt as to whether this question has been completed.
Next steps could be - Use second example to model and identify.

22. Child G
Example 7 - Lack of prior knowledge/understanding. The child has completed the question with annotations as would be expected, but believes that hexagons have 5 sides.
Feedback could be - Need a memory jogging way of remembering the number of sides a hexagon has, e.g. Hexagon and six.
Next steps could be - Revisit – homework or in starter session if group issue.

23. Child H
Example 8 - Incorrect in part of process/misunderstanding. Calculation is not the issue here, it is the understanding that time comes in intervals of 60 mins.
Feedback could be - Model use of number lines to help support.
Next steps could be - Revisit in mental sessions counting in minutes, e.g. 10, 20, 30, 40, 50, 1 hour, 1 hour 10, 1hour 20 etc; revisit using number lines to model hours and minutes.

24. Child I
Example 9 - Lack of understanding. The child does not understand the concept of the ‘universal set’, the area inside the rectangle which is the set that contains all elements being discussed, e.g. Numbers, numbers to 30 etc.
Feedback could be – where does number 7 go? Suggesting other numbers that could not be placed in either circle.
Next steps could be - Revisit Venn diagrams and ensure that teaching involves numbers that go into this set.

25. Key Messages
When AfL is truly embedded, there will be a range of evidence:
- pupils know what they are learning
- next step marking will be in place
- opportunities to reflect upon learning are
provided
- assessment informs practice.
The aim is not to add to the workload, the aim is to make lessons more efficient by engaging on a deeper level with the children's learning and enabling them to do the same.
This is not for every piece of work, nor is it on a specific timescale, e.g. one piece per child per week, it is down to professional judgement and when it will support a child in moving on.