Can a prompt be created for any topic in the mathematics curriculum?

It is undeniable that creating prompts for some parts of the mathematics curriculum can prove more difficult than for other parts. Those topics that do not have close connections to other areas of mathematics are the most problematic. When Caitriona Martin (a maths teacher in Surrey, UK) requested a prompt on constructions, the narrow focus on a discrete skill militated against the design of an open inquiry prompt. However, a closed prompt could start with the end-point of construction. Thus, an inquiry teacher might use a simple diagram combining two constructions of loci. The aim would be to guide students'
questioning and comments back to the initial actions of construction underlying the diagram.

The case of constructions, it could be argued, is similar to bearings. When the prompt on the right was used in the classroom, students suggested measuring the angles, and, on the basis of the results, speculated about the relationship between them. The teacher introduced the context of A and B being two towns and the 
mathematical form of bearings. The class decided to inquire into how to deduce "the bearing of A from B" from "the bearing of B from A". The inquiry ended with a generalisation from different examples drawn by the students and a discussion about the accuracy of their measurements. One conclusion focussed on the importance of ensuring the arrows pointing north are parallel.
The problem with designing a prompt to cover a particular part of the curriculum is that, by definition, its potential is restricted. Lessons based on these types of prompt can easily fall into the trap of investigations in which students are invited to 'discover' what the teacher is thinking. Rather, inquiry maths prompts should have the potential to develop links between different parts of the curriculum in the same inquiry and give students the freedom to explore those links.

For a discussion between Caitriona and Andrew Blair about the openness of inquiries when trying to cover specific content in the curriculum, click here.