Elementary students' construction of geometric transformation reasoning in a dynamic animation environment

Nicole Panorkou, Alan Maloney

Research output: Contribution to journalArticle

Abstract

context: Technology has not only changed the way we teach mathematical concepts but also the nature of knowledge, and thus what is possible to learn. While geometric transformations are recognized to be foundational to the formation of students' geometric conceptions, little research has focused on how these notions can be introduced in elementary schooling. > problem: This project addressed the need for development of students' reasoning about and with geometric transformations in elementary school. We investigated the nature of students' understandings of translations, rotations, scaling, and stretching in two dimensions in the context of use of the software application Graphs 'n Glyphs. More specifically, we explored the question "What is the nature of elementary students' reasoning of geometric transformations when instruction exploits the technological tool Graphs 'n Glyphs?" > method: Using a design research perspective, we present the conduct of a teaching experiment with one pair of fourth-graders, studying translation and rotation. The project investigated how and to what extent activity using Graphs 'n Glyphs can elicit students' reasoning about geometric transformations, and explored the constraints and afordances of Graphs 'n Glyphs for thinking-in-change about geometric transformations. > Results: The students proved adept using the software with carefully designed tasks to explore the behavior of two-dimensional shapes, distinguish among transformations, and develop predictions. In relation to varied conditions of transformations, they formed generalizations about the way a shape behaves, including the use of referent points in predicting outcomes of translations, and recognizing the role of the center of rotation. > implications: The generalizations that the students developed are foundational for developing an understanding of the properties of transformations in the later years of schooling. Dynamic technological approaches to geometry may prove as valuable to elementary students' understanding of geometry as it is for older students. > constructivist content: This study contributes to ongoing constructivism/constructionism conversations by concentrating on the transformation of ideas when engaging learners in activity through particular contexts and tools..

Original languageEnglish
Pages (from-to)338-347
Number of pages10
JournalConstructivist Foundations
Volume10
Issue number3
StatePublished - 15 Jul 2015

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Students
student
Mathematical Concepts
Software
mathematics
study contents
Animation
constructivism
scaling
research planning
elementary school
Teaching
Research Design
conversation
instruction
Technology
Graph
experiment
Research

Keywords

  • Constructionist technologies
  • Geometry
  • Transformations

Cite this

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abstract = "context: Technology has not only changed the way we teach mathematical concepts but also the nature of knowledge, and thus what is possible to learn. While geometric transformations are recognized to be foundational to the formation of students' geometric conceptions, little research has focused on how these notions can be introduced in elementary schooling. > problem: This project addressed the need for development of students' reasoning about and with geometric transformations in elementary school. We investigated the nature of students' understandings of translations, rotations, scaling, and stretching in two dimensions in the context of use of the software application Graphs 'n Glyphs. More specifically, we explored the question {"}What is the nature of elementary students' reasoning of geometric transformations when instruction exploits the technological tool Graphs 'n Glyphs?{"} > method: Using a design research perspective, we present the conduct of a teaching experiment with one pair of fourth-graders, studying translation and rotation. The project investigated how and to what extent activity using Graphs 'n Glyphs can elicit students' reasoning about geometric transformations, and explored the constraints and afordances of Graphs 'n Glyphs for thinking-in-change about geometric transformations. > Results: The students proved adept using the software with carefully designed tasks to explore the behavior of two-dimensional shapes, distinguish among transformations, and develop predictions. In relation to varied conditions of transformations, they formed generalizations about the way a shape behaves, including the use of referent points in predicting outcomes of translations, and recognizing the role of the center of rotation. > implications: The generalizations that the students developed are foundational for developing an understanding of the properties of transformations in the later years of schooling. Dynamic technological approaches to geometry may prove as valuable to elementary students' understanding of geometry as it is for older students. > constructivist content: This study contributes to ongoing constructivism/constructionism conversations by concentrating on the transformation of ideas when engaging learners in activity through particular contexts and tools..",
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Elementary students' construction of geometric transformation reasoning in a dynamic animation environment. / Panorkou, Nicole; Maloney, Alan.

In: Constructivist Foundations, Vol. 10, No. 3, 15.07.2015, p. 338-347.

Research output: Contribution to journalArticle

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