### 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 language | English |
---|---|

Pages (from-to) | 338-347 |

Number of pages | 10 |

Journal | Constructivist Foundations |

Volume | 10 |

Issue number | 3 |

State | Published - 1 Jan 2015 |

### Fingerprint

### Keywords

- Constructionist technologies
- Geometry
- Transformations

### Cite this

*Constructivist Foundations*,

*10*(3), 338-347.

}

*Constructivist Foundations*, vol. 10, no. 3, pp. 338-347.

**Elementary students' construction of geometric transformation reasoning in a dynamic animation environment.** / Panorkou, Nicole; Maloney, Alan.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Elementary students' construction of geometric transformation reasoning in a dynamic animation environment

AU - Panorkou, Nicole

AU - Maloney, Alan

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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..

AB - 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..

KW - Constructionist technologies

KW - Geometry

KW - Transformations

UR - http://www.scopus.com/inward/record.url?scp=84937027688&partnerID=8YFLogxK

M3 - Article

VL - 10

SP - 338

EP - 347

JO - Constructivist Foundations

JF - Constructivist Foundations

SN - 1782-348X

IS - 3

ER -