Higher order thinking skills can be assessed using tasks which provide opportunities for students to analyse, evaluate or create. Deductive reasoning in geometry requires these types of thinking skills.
Bloom's Revised Taxonomy classifies thinking skills into six levels.
Assessment tasks need to provide clear information about student achievement whilst allowing students to access problems suited to their level of knowledge and experience.
You can read more about thinking skills in Bloom’s Revised Taxonomy (74 KB PDF) of learning domains. This is a particularly helpful organisational and planning tool when designing assessment tasks in geometry.
Listing properties of a given quadrilateral involves recalling knowledge, a low level of thinking. Reversing the direction of the question assesses the same information at a higher level.
The ability to reason logically develops before the skill of writing formal proofs. To assess reasoning, provide students with opportunities to explain their reasoning in their own words.
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Questions which require students to analyse or evaluate can be used to assess deep understanding.
Student thinking is often revealed when playing mathematical games. By observing the decisions and strategies used while playing, student learning can be assessed.