Mathematics and AfL

Children understanding their own progress

"...teachers do not create learning; only learners create learning. And yet our classrooms seem to be based on the opposite principle - that if they try really hard, teachers can do the learning for the learners." (Wiliam 2011 p.145)

The more children are part of the whole process of learning the more they become self-regulatory and self-efficacious. When children are part of a classroom that clearly values growth in learning above all other factors (e.g. competition, getting the right answer, guessing what is in teacher's head) they will understand that they have to do the learning and will want to explore how they can learn.

How can children become part of the process? Boekaerts & Corno (2005) say that the environment must be right. A growth environment can be achieved when teachers:

• Share learning objectives and outcomes with the children in a way that can enable them to monitor their own progress
• Promote the belief that ability is incremental (it can grow) rather than fixed (you get what you are born with and no more). When students believe that the more they work at understanding something the smarter they become then there is no reason not to put the effort in. This means encouraging understanding and talking about different ways "to work at it until you have got it".
• Make it difficult for students to compare their criterion based achievement with one another. Each person will have a next step to take in learning; encourage the discourse to relate to how well each pupil is doing with their next step.
• Provide feedback that contains a recipe for future actions rather than a review of previous failures
• Use every opportunity to transfer executive control of the learning from the teacher to the learner to support their development as autonomous learners.

You could:

Use coloured cups: each child has three cups (red, yellow and green). As the teacher explains the children can change cups at any time, providing immediate feedback to the teacher if their explanation is not working for individuals or groups. Deciding which cups should be showing requires the child to be engaged in monitoring their own learning, and the feedback provides contingent feedback on the instruction received both important parts of formative assessment. The children can work in 'cup' groups to ensure that appropriate help is given and those who are showing a green cup can be called on to help others when necessary to ensure optimal learning in the class. Teachers may need to remind the class to 'change cups' often to begin with.

Use learning portfolios: entering into the portfolio the ideas that have been mastered today, in diagram form or in a way that will remind the child about what they can do. This is not a 'latest and best' collection but a reminder of what I can do now. The object is to show growth in learning and thus emphasise that each child is growing their ability to calculate.