Prompts are mathematical statements, equations or diagrams stripped back to the bare minimum, while simultaneously loaded with the potential for exploration. In short, a prompt should have "less to it and more in it" as one teacher has said.
(1) A prompt must promote curiosity and questioning in students of the sort "that can't be right" or "I've noticed ...". Prompts should be engaging and ripe for speculation or conjecture.
(2) A prompt must be aimed at students' developing mathematical knowledge, challenging them to decide whether new concepts are required to understand it fully. It must be accessible, yet should stand just beyond the recognition of a class. It should not be designed to intimidate a class; rather, students must feel confident enough to be able to manipulate and change the prompt.
(3) A prompt must be open enough to offer students the opportunity to regulate their own activity. Ideally, it will offer a number of pathways and incorporate different areas of the curriculum at both abstract and concrete levels.
(4) A prompt should provide opportunities for different forms of thinking, including induction (exploration and generalisation) and deduction (logical reasoning and proof).
Five steps to creating an inquiry prompt
Three maths teachers were involved in creating the inquiry prompt that appears at the end of this sequence. Each step shows the prompt becoming progressively more open - literally being stripped back to the essence of the mathematical diagram. Sometimes it is difficult for just one teacher to see the full potential in a prompt, and successive iterations might take the involvement of other inquiry teachers.