Reflection

If there is one thing that almost all maths education researchers agree on it is the important role of reflection. Some go as far as to imply that if you did not do a reflection at the end of a maths lesson then you did nothing.

Reflection is the third part in the Natural Maths Numeracy Block and it is perhaps the most important part. It is during the reflection that the learning experiences of the middle part of the lesson are consolidated and formalised. It is also the time when students learn from and with each other.

Developing Communities of Learners

Student work samples become the central focus of a discussion in which different strategies are described and compared. Three or four selected students will 'talk to' their work samples, explaining their thinking and any fix-ups they needed (sometimes they may fix up as they explain). Students are expected to listen and follow along during this process, to ask questions and make positive comments about the samples. For example:

A clever teacher can use unfinished, or incorrect work samples skilfully to engage the whole class, for instance an incomplete work sample could lead to questions such as the following:

Usually there will be several suggestions from the floor and we can thank the student whose work we have been using as a springboard for a learning opportunity. This means that even a less able student can have success and have an important role in the community of learners.

The reflection needs to be respectful to the students and rigorous at the same time. There are some reflection questions that can be used in almost all situations and these are:

• Which Strategy that we looked at did you like the most?
• Why? Which strategy was easiest to understand and follow? Why?
• Which method of representation did you think was clearest? Why?
• Which strategy saved most brain space/was most efficient?
• Which strategy do you think was most reliable? Why?
• Which strategy would you like to try next time?
• Which strategies are the same in some way?
• How are they the same?
• What was one thing you learnt today?

Initially students find it hard to answer these questions in terms other than generalisations and we need to prompt them to be more explicit, so instead of accepting "I learnt to add three numbers" we need to prompt with "Exactly what did you learn about adding three numbers?".

It does not take long for students to begin to see that reflection is important and to participate respectfully in a community of learners.