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# Pen and paper

It is very helpful to collect samples of student work to assess individual progress and diagnose areas of misunderstanding. Samples should be collected regularly and annotated with written feedback. Further discussion of helpful feedback can be found in *What is Wrong with this Proof?* Return the samples promptly so that students derive maximum benefit from your feedback.

This process informs the teaching-learning cycle and reveals individual or class misunderstandings.

Although not the most effective measure of student understanding, summative tasks in geometry are frequently in the style of a pen-and-paper test.

When designing a pen-and-paper test in geometry it is advisable to:

- arrange the questions so that 'easier' concepts are addressed first
- include some questions which require
- values only
- formal reasons

- pose some questions which allow students to explain reasoning in their own words
- ask some questions which
- probe for knowledge
- require the application of knowledge

- provide a challenge question at the end
- ensure that there is ample time for the students to respond.

Deductive thinking requires far more time for students than teachers often allow, so be generous in the time allowed.

## Congruence and similarity test

This pen-and-paper test is a thorough examination of congruence and similarity. Students are required to communicate their understanding in a variety of ways.