I recently visited Townsville and spoke at the Queensland Association of Mathematics Teachers’ North Queensland conference. The theme was ‘transitions’, which prompted me to think about the transitions between different pedagogical approaches that we all make every day as teachers. One of the contentious debates is around the role of inquiry and the importance of explicit teaching.
The word explicit comes from the Latin words ex (out) and plicare (to fold). To make something explicit therefore literally means ‘to unfold’. This idea of explicitness is completely in line with our view of inquiry, which focuses on unfolding important mathematical ideas by encouraging students to ask questions and seek meaning.
The reSolve resources are carefully designed and structured to help teachers transition between different approaches and lead students to a deep understanding of purposeful mathematics. The Year 4 and Year 9 Algebra resources that Kristen highlights in this newsletter both commence with an accessible problem that involves nothing more than addition. As the lesson progresses the mathematics behind the number of odd numbers required to reach an odd total and the algebraic generalisation of the Addition Chain gradually unfolds under the guidance of the teacher.
Students are not expected to discover the results for themselves, rather at each step of the lesson students learn through the teacher’s active intervention. This includes modelling of the algebra behind the problem, the use of enabling prompts to provide access, attending to misconceptions, and unpacking of alternative strategies.
The mathematical purpose of the lessons becomes clear as students engage with the deeper mathematical ideas behind the results. Students do much more than reproduce an approach demonstrated by the teacher; they understand the mathematical concepts underpinning the method or inquiry, and come to appreciate accuracy and efficiency.
As our Director of Professional Resources, Professor Peter Sullivan says in Professional Module 4 on Challenge, students begin with a problem or context that they do not immediately understand, but one that promotes the desire to know more. As the lesson unfolds they come to understand, and students transition from a state of not knowing to knowing. Peter contrasts this with an approach in which the teacher explains first and students do practice examples. The examples are normally graded to go from easy to harder, so by the end of the lesson almost every student encounters a problem they cannot do. They transition from a state of knowing to not knowing.
This does not mean that teacher modelling and practice examples are not important. But they should always be purposeful and meaningful to students.
When you give us feedback on the resources, whether these are classroom resources, special topics, or professional resources, please let us know how helpful they are in terms of making pedagogical transitions between inquiry and explicit teaching, and about the transitions in student understanding.
Dr Steve Thornton
Executive Director of reSolve: Maths by Inquiry
02 6201 9490
© 2017 Australian Academy of Science