3 Key issue 3: Using assessment to enable mathematical learning

There are four important issues for teachers to bear in mind when thinking about assessment as integral to learning:

• Identifying exactly what to assess and then use an activity that will allow those ideas to be assessed: Effective teachers identify what they are trying to achieve in their mathematics classroom in both general and specific terms, then assess how successful their students are in achieving these goals. They assess their students as they work on unfamiliar or extended problems, or as they communicate about their mathematics, whether orally or in writing. They assess not just how well students can perform individual mathematical techniques and skills, but also how well they understand wider concepts and can apply those skills in less familiar contexts.
• Assessing students as individuals: Students learn at different rates; they learn different things from each other; some make quick progress and some develop misconceptions. Students therefore need to be assessed as individuals in order to ensure that teaching is well matched to their particular needs. Assessment will be for a clear purpose, be designed to give the teacher and the student themselves information about the student’s progress.
• Integrating assessment into every lesson: In order to match teaching to individual needs, assessment must be integrated into day-to-day teaching. Therefore, assessment is best when built into lesson planning and the information that is gained from assessment used in planning subsequent activities. In fact, it is only when the evidence from assessment ‘is actually used to adapt the teaching work to meet learning needs’ (Black et al., 2004) that such assessment becomes formative assessment. Remember, it is only formative assessment that evidence shows will make a difference to students’ learning and attainment.
• Assessing their own effectiveness: As well as assessing what students have learned, effective teachers must also assess their own actions. Decisions are made about teaching approaches in every lesson: what approach to use, what resources, which activities, what sort of activity and for how long, and so on. Assessment allows teachers to learn about the effectiveness of each of the decisions that they take and to modify their actions accordingly.