At a recent Inquiry Maths workshop, a teacher suggested that structured inquiry is a contradiction in terms. She defined inquiry as an open process in which students follow their own ideas. Providing an external structure, her comment implied, was incompatible with inquiry. This view, which is not uncommon, has deep roots in educational discourse. It is not only false, but also dangerous.

The idea that classroom inquiry is, by its very nature, open and free has its origins in US progressive schools during the inter-war period. The First World War was a turning point in progressive circles as the doctrine of creative self-expression took hold:

[J]ust as prewar Progressivism had given rise to a new educational outlook, one that cast the school as a lever of social reform, so this postwar protest developed its own characteristic pedagogical argument: the notion that each individual has uniquely creative potentialities and that a school in which children are encouraged freely to develop these potentialities is the best guarantee of a larger society truly devoted to human worth and excellence. (Cremin, 1964, pp. 201-202)

The 'new education', as Dewey called it, defined itself in opposition to traditional classrooms and aimed to be everything they were not. Dewey characterised this as Either-Or thinking. The progressives counterposed the imposition of authority from above to the cultivation of individuality, external discipline to free activity and learning from textbooks to learning through experience. As Cremin observes, "In too many classrooms license began to pass for liberty, planlessness for spontaneity, recalcitrance for individuality, obfuscation for art, and chaos for education - all justified in the rhetoric of expressionism" (p. 207).  

Dewey argued that just because traditional teaching emphasised external control of students' experiences and paid little attention to internal child-centred factors did not mean progressives were justified in their focus on the internal to the exclusion of the external. The traditionalists' violation of the principle of interaction from one side, he claimed, did not mean progressives should violate it from the other:

When external authority is rejected, it does not follow that all authority should be rejected, but rather that there is need to search for a more effective source of authority. Because the older [traditional] education imposed the knowledge, methods, and the rules of conduct of the mature person upon the young, it does not follow, except upon the basis of the extreme Either-Or philosophy, that the knowledge and skill of the mature person has no directive value for the experience of the immature. On the contrary, basing education upon personal experience may mean more multiplied and more intimate contacts between the mature and the immature than ever existed in the traditional school, and consequently more, rather than less, guidance by others. (Dewey, 2015, p. 21, my italics)

Dewey continues that children who escape the control of the traditional teacher have only the illusion of freedom if their actions are then controlled by whim and caprice. He concluded that, "Since freedom resides in the operations of intelligent observation and judgement by which a purpose is developed, guidance given by the teacher to the exercise of the pupils' intelligence is an aid to freedom, not a restriction upon it" (p. 71, my italics). 

For the contemporary teacher, Dewey poses the question of how we can guide students towards open inquiry in a way that does not lead to confusion and disillusionment. In my experience most inquiry teachers would approach this task with a taxonomy of inquiry types, building through the levels towards the final aim. Trevor MacKenzie, for example, lists four types of inquiry in his book Dive into Inquiry (see illustration).