There are three purposes for assessment:
- to evaluate student knowledge
- to provide students with opportunities for deeper learning
- to provide the teacher with direction for future instruction.
Assessment is not simply a single event which occurs at the end of a topic. At each stage of the learning cycle, gather information about the knowledge already acquired and then develop strategies to help your students progress to the next stage.
The van Hiele model claims that students develop geometric reasoning by progressing through five levels of understanding:
- informal deduction
- formal deduction
and that these levels are not based on age, but on experience.
The teacher's responsibility is to provide tasks and formative assessment procedures that enhance student learning appropriate to their level of understanding.
The Australian Association of Mathematics Teachers provides a more detailed discussion of good practice in assessment in their Position Paper on the Practice of Assessing Mathematics Learning, available on the AAMT website.
Assessment in geometry is most effective when it includes different types of activities and incorporates both individual and group work. It can be formative (throughout the learning sequence) or summative (at the end of the learning sequence).
Assessment tasks in geometrical reasoning can be designed around a hierarchy of thinking skills.