Inquiry and online learning
  
During the lockdown, I was adapting the Inquiry Maths workshop I run for teachers to make it suitable for an online session with trainees at a university. In the workshop, the participants and I go through an inquiry - from posing questions about the prompt and noticing its properties to final presentations of the lines of inquiry. The whole process is collapsed into between 30 and 60 minutes depending on the time available, with me 'coming out' of the inquiry on occasions to interject theoretical and practical observations. I wondered if the approach could work online. This set me to thinking about a broader question: What kind of online environment would make inquiry learning in the virtual classroom as effective as it is in the real one?

 
What do we miss online?
In the real classroom, the inquiry teacher learns about how her students think and feel during the inquiry process. She learns about their habits of mind and their strengths and weaknesses as learners. She learns about how they interact with others, how confident they are feeling, how much guidance they might need. In short, she knows her students as individuals and as a collective. At all times in the classroom she is making assessments about students' needs as individual and collective learners: What level of cognitive challenge is appropriate? What amount of emotional support is required? The power of inquiry lies in its child-centred philosophy. With such a wealth of knowledge, the teacher can facilitate deeper learning and engage with more motivated learners than is possible in the traditional instruction-led classroom.
 
However, it is true that a diet of instruction and drill is easier to deliver online than the nuanced practice of the inquiry teacher. In the inquiry classroom, the teacher responds to students by, for example, gently coaxing from a hesitant child the thought that is on the tip of her tongue or skilfully sequencing contributions to build ideas into a coherent concept. This is very difficult to accomplish on an online platform. How do we spot the breakthrough made by a child who is normally content to follow others' directions? How do we reproduce the buzz of excitement as students spontaneously interact to share questions or co-construct conjectures? If we know the class, we can fall back on preconceived notions and invite generally confident individuals to lead online inquiries. However, this seems the antithesis of inquiry teaching.
     
The same is true for adults. I want to replicate the teacher's inquiring disposition during a workshop.Furthermore, I want the participants to be aware of the way I direct or guide the inquiry without appearing to do so. How is 
the inquiry teacher able, in the words of Dewey in the The Child and the Curriculum, “by indirection to direct"? When I ran a workshop in Bratislava, the participants (who were, admittedly, vastly experienced inquiry teachers) commented on how I had achieved my aims for the workshop without seeming to impose them. We reflected on how I had laid emphasis on one contribution or question, which I judged to have greater potential, than on others. I might, for example, have discussed it in greater depth or linked it to another observation and, thereby, influenced a particular line of inquiry. I doubt that an online environment is sensitive enough for an observer to notice the nuanced practices of the inquiry teacher, even if the teacher were able to orchestrate the inquiry in the normal way.
Inquiry as research
Of course, there are different conceptions of inquiry learning. My own conception of mathematical inquiry focuses on interweaving individual and collective exploration with inductive and deductive reasoning. The teacher offers graduated support and guidance depending on the nature of the inquiry and the experience of the individual or class. This is an inquiry process responsive to 30 individuals in which each student can learn from another, join a collective search for examples and counter-examples or set off on their own line of inquiry.
  
Another conception of inquiry is based on research. This form of inquiry is more relevant and authentic to the social sciences than mathematics. Online access for individual students would seem to be a prerequisite for this type of inquiry. Of course the two conceptions are not mutually exclusive. In mathematics, the number line inquiry, which bridges between number and algebra, would be enhanced by research into the origins of algebra in the Arabic world. However, students would not be learning the specific form of mathematical inquiry in this way; rather, they would be learning about the history of mathematics through carrying out an historical inquiry. Using algebra as a mathematical tool (and, thereby, being able to understand the advances made in ninth century Baghdad) requires participation in mathematical inquiry.
  
How could we replicate classroom inquiry online?
The sophisticated interaction, flexible collaboration and immediate feedback (from teacher to student and from student to teacher) of the inquiry classroom are difficult to replicate in the blunt online environment. When lessons went online at the start of lockdown, many teachers had to adapt platforms designed for business meetings in which the highest level of interactivity amounts to sharing a screen or typing a message in a chat box. Even though it is possible to use additional tools alongside the platforms (such as tools that give students the opportunity to interact with a slideshow, type ideas onto a bulletin board and reply to those of their peers or see others' inquiries in progress on a shared document), online environments are generally more conducive to telling about rather than inquiring into
  
That is certainly the case in higher education. The market leading platform promotes the transmission of knowledge and severely limits the possibility of student agency. For example, switching from one breakout group to another, which is one of the very few ways a student could take an independent decision, is contingent on the lecturer setting up breakout groups in the first place and giving permission for students to move from one to another.
 
If the virtual inquiry classroom were to approach the sophistication of the real one, it would give students the opportunity to direct their own learning. They would participate in the design of the online environment by being involved in setting permissions for various functions (although, of course, the teacher would only sanction the settings in light of safeguarding concerns). And one last point: the platform and all its functions would be free. Currently hard-pressed state schools cannot afford to pay for the extra functionality provided by online tools. The social inequality and related educational disadvantages that have been exacerbated in lockdown should not be a reason to deny students remote access to learning through inquiry.
 

Andrew Blair
June 2020