The need for a slow start to inquiry
Recently, during a workshop at the British Congress of Mathematics Education, I was asked more than once about a lack of pace at the start of an inquiry. This is a common concern of UK teachers and an indictment of the current educational system that demands demonstrable progress at all times.
My reply to the questions at the workshop was that pace is necessarily slow at the start of an inquiry so that all students are clear about its content and aims. This process has been referred to as 'zooming in', although I prefer to describe this phase as one of orientation. (Zooming in suggests that the class narrows its options when we might decide to follow multiple pathways.)
At the conference, I suggested that the inquiry teacher should deliberately slow down the start by stopping students 'doing the maths'. In this way, they can consider the inquiry at a metacognitive level: Where is the inquiry heading? What are we going to do to get there? How do we know when we have arrived?
In a discussion after the workshop, Dominic Penney (a maths teacher in Sale, UK) described the start of an inquiry like this: “We are all on the same platform and then we jump off together." Preparing for the jump takes time, but invariably leads to a fast-moving inquiry carried out by committed and motivated students. The considered start is essential for a successful inquiry.
Since the congress, I have re-read a research paper* about the use of inquiry in two state elementary schools in Moscow (pupils aged between seven and eleven). The authors provide such a compelling description of the opening phases of an inquiry that it deserves to be quoted in full:
1. To evoke students’ questions, the teacher must create a high-potential field that energises students’ imagination by presenting new and breathtaking phenomena that are already within the students’ zone of proximal development, that is, within the child’s ability to recognise the new elements in these phenomena and to relate these new elements to the context and structure of existing background knowledge. A child’s curiosity and imagination are aroused when sparks of the first questions – however sporadic, naive, and chaotic – appear. During this phase, rational discourse based on accepted rules and evidence is blended with intuitive and often irrational assumptions.
2. Now the teacher must “slow down” these sparks of imagination so that (a) they are registered and identified by other children, and other students become involved in the process of inquiry; and (b) the original inquirers and other children can reformulate the original naive question into a presumption that is channelled toward the problem under discussion.
3. 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.
What a wonderful passage! The teacher must slow down the initial sparks to generate a self-perpetuating chain reaction of inquiry.
Andrew Blair, April 2014
* Zuckerman, G. A., Chudinova, E. V. and Khavkin, E. E. (1998). Inquiry as a Pivotal Element of Knowledge Acquisition within the Vygotskian Paradigm: Building a Science Curriculum for the Elementary School. Cognition and Instruction, 16(2), 201-233.
The research paper compares the learning in inquiry classrooms, which are based on students’ creativity, to traditional classrooms. Traditional, in this case, is defined as textbook-based lessons in which students might answer a teacher’s closed questions. The statistical analysis of post-tests shows a significant difference in the ability of children in the two types of classrooms to reason conceptually. The control groups taught in a traditional way used object-based descriptions to answer questions in the post-test, whereas the inquiry classes used predominantly concept-based descriptions.