The zone between knowing and not knowing
Part 1: Slowing down
During a recent Inquiry Maths workshop, I was asked how I could expect students to request instruction when they "don't know what they don't know". The questioner found it impossible to conceive of how my claim that students in Inquiry Maths classrooms use regulatory cards to signal a need for new knowledge could work in practice. Yet, for me, this is precisely the distinguishing feature of inquiry. The teacher and students are continually working in the zone between what is known and what is not known. Inquiry is all about unearthing what ex-US Secretary of Defense Donald Rumsfeld called the "unknown unknowns".
I was reminded of the question when I read this article by Andy Hargreaves. He describes his experience with a class of 7- and 8-year-old pupils who were trying to guess his identity:
Much more interesting and engaging [than having the knowledge] for them had been that magical moment before they had the knowledge – the wonderful moment of ignorance. We should cherish this kind of ignorance. It’s not the ignorance that refutes knowledge and expertise. It’s not prejudice or stupidity. It is simply the absence of knowing that invites and anticipates the knowledge that is to come.
The article was brought to my attention in a tweet by Kath Murdoch, the international expert on inquiry learning. Kath commented that the article valued the "inquiry-filled space between not knowing and knowing". She continued that the space "connects to slowing down and tuning in more carefully to students and our own thinking. And nurturing wonder."
For Kath, then, there are five aspects to learning in the zone between knowing and not knowing:
(1) Valuing the space
(2) Slowing down
(3) Tuning in to students
(4) Tuning in, as teachers, to our own thinking
(5) Nurturing wonder.
For me, showing that we value the space, tuning in and nurturing wonder are all predicated on slowing down. If teachers make the time, then they can achieve the other aspects.
However, slowing down is often the hardest to achieve. In inquiry classrooms, students are excited to explore their questions, observations and conjectures and enthusiastic to follow up on their insights and ideas. Even in workshops with teachers and educators, I have found myself asking participants to stop 'doing the maths' and step back to think about how our inquiry will develop and why we plan to develop it in that way. The regulatory cards play the key role in the Inquiry Maths model of slowing down participants by requiring them to consider the direction of the inquiry.
There are relentless pressures on teachers not to slow down. Curricula are full of content objectives that have to be 'covered' and education departments and boards in many jurisdictions value 'pace' in lessons. Galina Zuckerman, the Russian educationalist and researcher, gives a compelling explanation of why slowing down at the start of inquiry is essential. After creating "a high-potential field" that energises students’ imagination, arouses their curiosity and evokes questions, the teacher must slow down the "sparks of imagination" so that they are registered by other students. The whole class can then become involved in the process of inquiry by reformulating the original naive questions into aims. What's more, the slowdown is necessary to ensure the ultimate success of the inquiry:
Like thermal neutrons in a nuclear pile, this slowdown must provide for a self-perpetuating chain reaction of interactions in the class, propagating new questions that lead from the initial chaotic question to hypotheses that can be verified.
During the slowdown, the teacher and students co-construct the foundations that will lead to a self-perpetuating inquiry based on a class-wide understanding of the central questions and aims.
As students enter the zone between knowing and not knowing, the inquiry must proceed slowly. Students have to have time to understand and reflect upon the questions, observations and ideas of their peers. The teacher has to have time to support the process in which the initial aims and direction of the inquiry develop out of the students' contributions. Once the slowdown has served its purpose, inquiry classrooms see an explosion of directed and purposeful activity. Importantly for those jurisdictions that value 'pace', the students' activity, built on high levels of motivation and excitement, moves so rapidly that it easily 'makes up for' the slow down at the start of the inquiry.
We leave the last word to one student who gave her feedback about a series of Inquiry Maths lessons: "Inquiry lessons make us slow down and think about it." Exactly!
Andrew Blair, March 2018