Using AfL in Mathematics. Lynne Startin

To develop a better understanding of effective formative assessment in maths (AfL) To consider practical strategies which support AfL in maths

Discuss with a partner what AfL techniques you use in your classroom. List any you use.

AfL in Mathematics. What does it involve? Learning objectives? Success criteria? Marking ladders? No hands up? Talking partners? 2 stars and a wish? Traffic lights?

Formative assessment – a definition. An assessment functions formatively to the extent that evidence about student achievement elicited by the assessment is interpreted and used to make decisions about the next steps in instruction that are likely to be better, or better founded, than the decisions that would have been taken in the absence of that evidence. Dylan Wiliam, 2009, (Co author with Jeremy Hodgen of Mathematics Inside the Black Box.)

Their project promoted four key elements of practice: a focus on the learning (clarity about and sharing of learning intentions and what counts as success); effective questioning (significance of questioning to improve learning); formative feedback (feedback that moves learning forward); scaffolding reflection (developing self-critical, reflective learners).

Unpicking formative assessment: Key processes –Establish where the learners are in their learning. Recognise that pupils need to reconstruct their ideas, not merely add to them an overlay of new ideas. –Establish where they are going. Only by understanding of what counts as good quality work and where they stand in relation to the target, can pupils steer their work in the right direction. –Working out how to get there. Feedback should encourage pupils they can do better by trying, and can learn from mistakes and failures. Participants –Teachers –Peers –Learners D Wiliams

The benefits of AfL

AfL in Mathematics. Pupils will:- Be involved in and responsible for their own learning Be able to explain what they are learning and what a successful outcome looks like Contribute to developing success criteria and use to identify next steps, possibly reflecting ‘must’, ‘should’ and ‘could’ progression Identify aspects that are easy/difficult possibly through mini-plenaries, referring to success criteria Think, learn and talk about how they learn and what helps them to learn Use feedback to make improvements in their own work

What are success criteria? ‘… success criteria summarise the key steps or ingredients the student needs in order to fulfil the learning intention – the main things to do, include or focus on.’ - Shirley Clarke

Why Are Success Criteria Important?  Improve understanding  Empower pupils  Encourage independent learning  Enable accurate feedback

Effective Success Criteria…  are linked to the learning objective  are specific to an activity  are discussed and agreed with pupils prior to undertaking the activity  provide a scaffold and focus for pupils while engaged in the activity  are used as the basis for feedback and peer/self-assessment

Learning Objectives ‘What’ and ‘Why’ Success Criteria ‘How to recognise success’

Success Criteria: 1.Outcome based success criteria 2.Process success criteria

Outcome based E.g. Learning Objective: –To be able to round two-digit numbers to the nearest 10. Outcome based success criteria –I can round two-digit numbers to the nearest 10.

Process based E.g. Learning Objective: –To be able to round two-digit numbers to the nearest 10. Process success criteria: –Find the number on the number line –Identify the multiple of 10 at either side of the number –Count the jumps to the multiple of 10 before –Count the jumps to the multiple of 10 after –Round the number to whichever is nearest –If the last digit is 5, round the number up to the next multiple of 10

Possible drawbacks of success criteria? Unhelpful in some areas of maths? Concepts –E.g. to visualise a 3-D shape from a 2-D drawing Remembering key facts Pupils become over reliant on them?

Possible drawbacks Restricts progress of more able pupils? –‘It is not useful for me because I know it.’ –Some “more able” pupils may find it difficult to verbalise, as the steps are ingrained but they cannot transfer these orally. –It restricts the pupils’ own strategies.

For Whom is it Most Effective? Process success criteria is most effective when used to support the learning of those children who are working slightly below age-appropriate expectations and those who are less confident. The reasons for this are: - It gives children the confidence to ‘have a go’ at mathematics within a defined and structured framework. - Because they have access to a list of steps they become less dependent on an adult to guide them individually through each step in the process. - It encourages children to be more self-evaluative and able to identify exactly where they are stuck.

It is especially useful for: aspects of place value, ordering and rounding, e.g. multiplying or dividing by 10/100/1000 many aspects of calculation, including written methods areas of the measures curriculum, such as measuring angles using a protractor, using a ruler, calculating area and perimeter and reading a scale aspects of shape such as reading and plotting coordinates constructing graphs and diagrams, including Venn and Carroll diagrams solving word problems, i.e. carrying out the calculation once it has been identified For Which Mathematics is it Most Effective?

For Which Mathematics is it Least Effective? It is less helpful for: exploring properties of number or shape interpreting data solving word problems, i.e. identifying the operation

A good rule of thumb when deciding whether the use of process success criteria is helpful is to identify whether the area of mathematics is based around a sequence of steps. If this is the case then it would be more appropriate. This works mainly when the barrier to children’s learning is remembering the steps, not the understanding of the concept. The use of process success criteria does not support children in understanding mathematical concepts or remembering key facts. How to Decide?

Learning Intention Success Criteria We are learning how to draw a line graph. Draw the axes. Decide the biggest amount needed on both axes. Work out the intervals needed on both axes. Plot the points, and join them accurately.

Impact on Pupils Gains in confidence through being able to identify small areas of difficulty. Children become more independent. Self and peer marking is a more robust process. Identifying steps to learning helps with booster classes as it meant that the session foci can be more tailored to the children’s own needs.

Marking is more effective. Clarifies the progression of learning in the mind of the teacher. Expectations are more focused and therefore potentially higher. It enables teachers to pinpoint more precisely those areas which needed to be consolidated or reviewed. Better dialogue with teaching assistants. Impact on Teachers

It is important not to become too rigid when using process success criteria. It may turn some of the children off learning if they have to follow each step of the process, especially more able children. Some children may become over reliant on them, and therefore unable to function when not given a set of process success criteria. It does not lend itself to all areas of mathematics, so trying to impose it in every lesson would be counter productive Teachers need to have good subject knowledge to be able to identify the steps in learning. Barriers

Summary If the use of process success criteria is to work, assessment for learning needs to be well established in school. The end goal is about the learning and the links in learning, so children need to understand that ultimately they need to work independently without relying on the steps in place. If higher ability children don’t need to use process success criteria, teachers should ensure that they are still able to explain methods and strategies, which promotes the use of vocabulary.

Summary Teachers should not agonise over putting the process success criteria in place in every unit/ topic. Some, like aspects of shape, just don’t lend themselves to the process. If it’s not going to enhance the children’s learning, don’t do it! It is particularly useful when working with methods of written calculation. Schools should have a written calculations policy in place that is being followed by all staff for the use of process success criteria to be successful.

Summary The implementation of the use of process success criteria in maths should be supported by the senior leadership of the school. This will ensure that time is given to allow the mathematics subject leader to discuss with and support other teachers. There is no one fixed model to implementing the use of process success criteria in mathematics. Schools should apply the elements flexibly and develop them to fit their school situation. Each school should agree on certain ‘non- negotiable’ elements, e.g. format, name etc to promote and ensure consistency.