How could the Presentation of a Geometrical Task Influence Student Creativity?

Zoi Geitona,Eleni Deliyianni,Iliada Elia,Athanasios Gagatsis,Panagiotis Gridos

doi:10.31756/jrsmte.514

Abstract

This study aims to investigate high school students’ geometry learning by focusing on mathematical creativity and its relationship with visualisation and geometrical figure apprehension. The presentation of a geometrical task and its influence on students’ mathematical creativity is the main topic investigated. The authors combine theory and research in mathematical creativity, considering Roza Leikin’s research work on Multiple-Solution Tasks with theory and research in visualisation and geometrical figure apprehension, mainly considering Raymond Duval’s work. The relations between creativity, visualization and geometrical figure apprehension are examined through four Geometry Multiple-Solution Tasks given to high school students in Greece. The geometrical tasks are divided into two categories depending on whether their wording is accompanied by the relevant figure or not. The results of the study indicate a multidimensional character of relations among creativity, visualization and geometrical figure apprehension. Didactical implications and future research opportunities are discussed.

Highlights

Creativity has been recognized as one of the most important skills of the 21st century
Most geometrical thinking is based on spatial visualization and reasoning (Dindyal, 2015; Van den Heuvel-Panhuizen & Buys, 2008) and this is the reason why we propose that both the concepts of visualisation and geometrical figure apprehension are closely related to creativity in Geometry
We identify the collective solution space for each Task given to students which is the number of solutions found by the group of students who participated in this research.Leikin (2009) further advanced her research by proposing a scoring scheme for measuring each creativity component as well as total creativity based on student performance in Multiple-Solution Tasks (MSTs)

Summary

Introduction

Creativity has been recognized as one of the most important skills of the 21st century. In the field of Mathematics, creativity has been underlined as a skill which should be taught to students through school curricula (NCTM, 2000). Another important addition to the existing literature came from Kaufman and Beghetto (2009) who stated that creative ability is not a “charisma” of a small group of talented or gifted students but instead, it is an ability which can be fostered to all students through targeted teaching and learning. Ervynck, 1991; Silver, 1997; Stupel & Ben-Chaim, 2017), linking mathematical ideas using multiple approaches for solving problems or proving statements strengthens mathematical reasoning, improves comprehension and increases student creativity in Mathematics As proved by numerous studies (e.g. Ervynck, 1991; Silver, 1997; Stupel & Ben-Chaim, 2017), linking mathematical ideas using multiple approaches for solving problems or proving statements strengthens mathematical reasoning, improves comprehension and increases student creativity in Mathematics

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