- Make the objectives of the lesson explicit
Share the objectives with students and from time to time ask students to produce evidence that they can achieve these objectives.
“Make up an example to show me that you know and understand Pythagoras’ theorem.”
“This lesson was about you deciding what methods to use. Show me where you did this.”
Students may find it difficult to appreciate that some lessons are concerned with understanding concepts, while others are more concerned with developing inquiry-based processes.
Making objectives explicit doesn’t mean writing them on the board at the beginning of the lesson, but rather referring to them explicitly while students are working. If the objectives are to develop inquiry-based processes then in plenary sessions, ask students to share and compare approaches, rather than answers.
- Assess groups as well as individual students
Group activities allow many opportunities to observe, listen, and question students. They help to externalise reasoning and allow the teacher to see quickly where difficulties have arisen. Moreover, working in groups helps students to peer-assess and function as instructional resources for each other.
- Watch and listen before intervening
Before intervening in a group discussion, wait and listen. Try to follow the line of reasoning that students are taking. When you do intervene, begin by asking them to explain something. If they are unsuccessful then ask another student to help.
- Use divergent assessment methods (“Show me what you know about …”)
Convergent assessment strategies are characterised by tick lists and can-do statements. The teacher asks closed questions in order to ascertain whether or not the student knows, understands or can do a predetermined thing. This is the type of assessment most used in written tests.
Divergent assessment, in contrast, involves asking open questions that allow students opportunities to describe and explain their thinking and reasoning. These questions allow students to surprise us – the outcome is not predetermined.
- Give constructive, useful feedback
Research shows that responding to students’ work with marks or levels is ineffective and may even obstruct learning. Quantitative feedback of this type results in students comparing marks or levels and detracts from the mathematics itself.
Instead, use qualitative oral and written comments that help students recognise what they can do, what they need to be able to do and how they might narrow the gap.
- Change teaching to take account of assessment
As well as providing feedback to students, good assessment feeds forward into teaching. Be flexible and prepared to change your teaching plans in mid course as a result of what you discover.
These principles are adapted from: Improving Learning in Mathematics, Department for Educational and Skills, 2005