Exploring an innovative approach to teaching mathematics through the use of challenging tasks: a New Zealand perspective
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Exploring an innovative approach to teaching mathematics through the use of challenging tasks: a New Zealand perspective Naomi Ingram 1 & Marilyn Holmes 1 & Chris Linsell 1 & Sharyn Livy 2 & Melody McCormick 2 & Peter Sullivan 2 Received: 14 November 2018 / Revised: 8 April 2019 / Accepted: 22 April 2019 # Mathematics Education Research Group of Australasia, Inc. 2019
Abstract This paper reports on a New Zealand iteration of the Encouraging Persistence, Maintaining Challenge (EPMC) project, which proposes that students learn mathematics best when they build connections between mathematical ideas for themselves. This iteration explores the actions, perceptions and learning of 12 primary teachers and their 281 students during the implementation of a set of challenging tasks related to geometric reasoning. The teachers launched the suggested tasks, ensuring that the challenge was maintained. The students explored these tasks with minimal input from the teacher, and learning was summarised and extended. The teachers were positive about the intervention. The challenging task approach enabled students’ thinking became visible and, at times, the teachers’ prior perceptions of their students’ ability were challenged. A highly significant difference between the students’ pre- and postassessment scores was found. The students were supported to have autonomy in their learning and make mathematical connections themselves. The students became less reliant on their teachers’ help and were positive about their involvement in the project. Keywords Mathematics . Challenging tasks . Persistence . Confusion . Geometry . Lesson
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Introduction A common approach to teaching mathematics assumes that learning is a linear, hierarchical process where concepts are explored through a range of tasks that are presented in micro steps, sequenced from simple to complex. Although the initial
* Naomi Ingram [email protected] Extended author information available on the last page of the article
N. Ingram et al.
simple task may give students a sense of success, students can end lessons feeling like they are unable to solve subsequent, more complex mathematical problems. The Engaging Persistence Maintaining Challenge (EPMC) project1 suggests a different approach wherein learning begins by students working independently on appropriately challenging tasks. The proposition is that students learn mathematics best when engaged in building connections between mathematical ideas for themselves at the start of a sequence of learning, prior to instruction from the teacher. Essentially the notion is for teachers to present problem tasks that the students do not yet know how to solve and to structure lessons that support students in finding a solution for themselves, and move from initial confusion to eventual clarity and understanding. Moving from ‘not knowing’ to ‘knowing’ is the essence of learning (Schroeder and Lester 1989). The purpose of this iteration of the EPMC project was to further explore the potential of teaching challenging m
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