Abstract
The design of inquiry-based tasks and problem situations for daily mathematics teaching is still a challenge. In this article, we study the implementation of two tasks as part of didactic scenarios for inquiry-based mathematics teaching, examining teachers’ classroom orchestration supported by these scenarios. The context of the study is the Erasmus+ project MERIA – Mathematics Education: Relevant, Interesting and Applicable, which aims to encourage learning activities that are meaningful and inspiring for students by promoting the reinvention of target mathematical concepts. As innovative teaching materials for mathematics education in secondary schools, MERIA scenarios cover specific curriculum topics and were created based on two well-founded theories in mathematics education: realistic mathematics education and the theory of didactical situations. With the common name Conflict Lines (Conflict Lines – Introduction and Conflict Set – Parabola), the scenarios aim to support students’ inquiry about sets in the plane that are equidistant from given geometrical figures: a perpendicular bisector as a line equidistant from two points, and a parabola as a curve equidistant from a point and a line. We examine the results from field trials in the classroom regarding students’ formulation and validation of the new knowledge, and we describe the rich situations teachers may face that encourage them to proceed by building on students’ work. This is a crucial and creative moment for the teacher, creating opportunities and moving between students’ discoveries and the intended target knowledge.
Highlights
In many countries worldwide, today’s curricula promote student-centred teaching approaches and, in the case of mathematics, students’ reinvention of mathematics is at stake
Beliefs are especially important for inquiry-based mathematics teaching (IBMT) because teachers may incorporate their previous experiences and belief systems concerning mathematics into their teaching, which can be a constraint when introducing IBMT into practice
Teaching scenarios designed for the purpose of IBMT within the Erasmus+ project MERIA offer a solid ground for teachers to orchestrate such teaching
Summary
Today’s curricula promote student-centred teaching approaches and, in the case of mathematics, students’ reinvention of mathematics is at stake These ideas are not new in mathematics teaching, their large-scale expansion coincides with the immense expansion of human knowledge in all fields of activity. IBMT supports students’ own inquiry of unstructured problem situations in which they work to researchers by posing questions, experimenting and hypothesising, validating and evaluating These ideas emerged even earlier in science education (Artigue & Blomhøj, 2013), and many projects have been launched that support the development and implementation of inquiry-based science education (IBSE), such as projects promoting relevant school science education at the secondary level (e.g., Holbrook & Rannikmäe, 2014). The design of appropriate tasks or problem situations that have the potential to engage students in inquiry activities is a very important element in this process, since, as the evidence shows, such tasks with teachers’ instructions are often missing (Bruder & Prescott, 2013)
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