Is inquiry age-related?
  
Recently, on social media, Alycia Corey (@corey_alycia) asked if the levels of Inquiry Maths (structured, guided and open) are affected by the age of learners? This is an excellent question.
  
Inquiry Maths was devised for secondary school classrooms. Unless children have been through an inquiry-based curriculum (such as the PYP programme), there is little opportunity for them to learn how to inquire into academic domains. In consequence, structure is often necessary for secondary students to inquire constructively. Yet, at the other end of schooling, young children's inquiry might be inhibited by structure. They inquire naturally through play. Paradoxically, we might characterise early years as a time of open inquiry and secondary school as one of structured inquiry.
  
The development from structured to open inquiry established in the hierarchical levels of Inquiry Maths appears to be reversed. This is the situation in most school systems. As children are institutionalised into the culture of traditional classrooms, they either learn to conform and comply, as is the case with the majority, or become the subject of ‘behaviour interventions’. Either way, inquiry processes disappear from formal schooling. A teacher wishing to introduce inquiry at secondary level faces obstacles created by conventional classroom practices and power relations.
   
In most schools, then, the levels of inquiry are linked to the students’ prior experience of inquiry and the extent to which they demonstrate initiative and independence. These considerations are not related to age.
  
That is not to say, however, that inquiry is not age-related. Four years ago when advising a new 4-19 school about inquiry learning at different stages of schooling, I drew up a diagram of how the nature of mathematical inquiry changes. The diagram (right) assumed children are involved in open inquiry processes across the age ranges.

  
The changes that occur in the three phases do not relate to inquiry processes per se, but rather to the consciousness children have of those processes in relation to the object of inquiry. While curiosity, noticing and questioning underlie all phases of inquiry, their content and form develop as children learn to direct inquiry at higher levels of subject knowledge. Firstly, children become more able to regulate their activity in a manner consistent with the domain-specific method of inquiry. Secondly, the object of inquiry changes: immediate perceptions in early years, experience of surroundings in primary and de-contextualised stimuli in secondary. In mathematics, for example, students learn increasingly complex (and abstract) concepts, while simultaneously developing a more sophisticated understanding of the mathematical form of inquiry.
  
Reflecting now on the diagram, it implies a rigidity between the age groups that is not warranted. The idea of play, for example, endures in the exploratory phases of later inquiries. Similarly, applications of abstract mathematics can be studied in practical projects at secondary level; just as prompts that focus on a mathematical object can be used at primary level when supported by concrete apparatus.
  
Even if the phases of inquiry do not fit into neat categories, it is the case that open inquiry is age-related; self-consciousness develops and the object of inquiry changes as children grow older. However, the levels of Inquiry Maths are not related to age because they are designed for classrooms in which students do not normally have prior experience of inquiry processes.

Andrew Blair
April 2017