# The Development of Students Geometrical Thinking through Transformational Processes and Interaction Techniques in a Dynamic Geometry Environment

@article{Patsiomitou2008TheDO, title={The Development of Students Geometrical Thinking through Transformational Processes and Interaction Techniques in a Dynamic Geometry Environment}, author={Stavroula Patsiomitou}, journal={Issues in Informing Science and Information Technology}, year={2008}, volume={5}, pages={353} }

The paper draws on a didactic experiment conducted in a secondary school mathematics classroom in Greece which aimed to explore a) ways in which students develop problem representations, reasoning and problem-solving, making decisions and receiving feedback about their ideas and strategies in a DGS-supported environment b) ways in which students develop rigourous proof through building linking visual active representations and c) ways to develop students’ van Hiele level. The mathematical… Expand

#### Figures and Topics from this paper

#### 20 Citations

Secondary students' 'dynamic reinvention of geometric proof' through the utilization of linking visual active representations

- Mathematics
- 2010

In this paper we describe a twofold teaching experiment carried out in a year 10 mathematics class in Greece which sought to investigate a) how the building and testing of LVAR (Linking Visual Active… Expand

Student's Learning Progression through Instrumental Decoding of Mathematical Ideas

- Computer Science
- 2014

Excerpts are presented from dynamic hypothetical learning paths (DHLP) s and students' learning progression that develop the students' geometrical thinking through the development of their ability to solve real-world problems. Expand

Custom tools and the iteration process as a referent point for the construction of meanings in a DGS environment

- 2008

The paper draws on an experiment conducted in a secondary school mathematics classroom in Greece which aimed to explore ways in which students develop their intuition, their meanings construction and… Expand

DEVELOPING GEOMETRIC THINKING SKILLS THROUGH DYNAMIC DIAGRAM TRANSFORMATIONS

- 2009

The paper draws on an experiment conducted in a secondary school mathematics classroom in Greece which sought to investigate the transformation of students’ skills following the use of the Sketchpad… Expand

Linking Visual Active Representations and the van Hiele model of geometrical thinking

- 2008

The present study presents the different modes of LVAR which can be constructed in Geometer’s Sketchpad v4 dynamic geometry software. The paper posits an explanation of the correlation between the… Expand

Effects of The Geometer’s Sketchpad on Algebraic Reasoning Among Junior Private High School Students

- 2019

Previous studies reported the student’s difficulties in algebraic reasoning for solving problems involving quadratic equations. Mostly full to the agreement of understanding and solving quadratic… Expand

Do geometrical constructions in a Dynamic Geometry environment affect student ’ s algebraic expressions ?

- 2008

The present paper attempts to bridge the world of digital technology and the world Euclid bequeathed us in his "Elements". The role of the design process of activities in an dynamic geometry… Expand

From Vecten’s Theorem to Gamow’s Problem: Building an Empirical Classification Model for Sequential Instructional Problems in Geometry

- Computer Science
- 2019

An empirical classification model of sequential instructional problems in geometry is created, regarded as a process whereby students develop a sequentially deeper understanding and increasingly more coherent reasoning that raises their van Hiele level. Expand

Can a Kite Be a Triangle? Aesthetics and Creative Discourse in an Interactive Geometric Environment

- 2018

In this chapter we will use the lens of aesthetics (Sinclair in Mathematics and beauty: aesthetic approaches to teaching children. Teachers College Press, New York, NY, 2006) to explore mathematical… Expand

A Linking Visual Active Representation DHLP for Student ’ s Cognitive Development

- 2012

In the next sections I shall describe a ‘dynamic’ hypothetical learning path (DHLP) for the learning of the concept of parallelogram in geometry, which helped the students of the experimental team to… Expand

#### References

SHOWING 1-10 OF 109 REFERENCES

The proving process within a dynamic geometry environment

- Computer Science
- 2003

The research findings suggest that proving within a dynamic geometry environment develops as a focusing process, in which the shifts between ascending and descending processes between the spatio-graphical and the theoretical field appear to be key elements for the construction of conjectures and proofs. Expand

Integrating "Geometer's Sketchpad" into a Geometry Course for Secondary Education Mathematics Majors.

- Computer Science
- 1996

Use of Sketchpad in a secondary education math course at the State University of New York (SUNY) at Oswego has allowed geometry to be taught in a dynamic manner, and the paper provides three examples of how Sketchpad is used. Expand

Providing a Foundation for Deductive Reasoning: Students' Interpretations when Using Dynamic Geometry Software and Their Evolving Mathematical Explanations

- Psychology
- 2000

A key issue for mathematics education is howchildren can be supported in shifting from `because it looks right' or`because it works in these cases' to convincing arguments which work ingeneral. In… Expand

Measuring in dynamic geometry environments as a tool for conjecturing and proving

- Computer Science
- Int. J. Comput. Math. Learn.
- 2007

A classification of different modalities of measuring is developed, based on the previous work on dragging, which enables researchers to access students’ cognitive processes and teachers to be aware of the different possible uses and interpretation of measuring, giving them tools to support students when difficulties arise. Expand

Role of interface manipulation style and scaffolding on cognition and concept learning in learnware

- Computer Science
- TCHI
- 2001

This research suggests that some of the educational deficiencies of Direct Manipulation (DM) interfaces are not necessarily caused by their “directness,” but by what they are directed at—in this case directness toward objects rather than embedded educational concepts being learned. Expand

Connecting arguments to actions— Dynamic geometry as means for the attainment of higher van Hiele levels

- Mathematics
- 2005

New technology requires as well as supports the necessity to raise the level of geometric thinking. Freudenthals view of van Hiele's theory corroborates a dynamic multi-level curriculum that offers… Expand

INSTRUMENTATION ISSUES AND THE INTEGRATION OF COMPUTER TECHNOLOGIES INTO SECONDARY MATHEMATICS TEACHING

- 2002

In France, for at least 20 years, the Ministry of Education has been actively supporting the integration of computer technologies into secondary mathematics teaching. Nevertheless, integration… Expand

Characterizing Interaction with Visual Mathematical Representations

- Computer Science
- Int. J. Comput. Math. Learn.
- 2006

A preliminary framework is provided to provide a preliminary framework to help designers of mathematical cognitive tools in their selection and analysis of different interaction techniques as well as to foster the design of more innovative interactive mathematical tools. Expand

An integrated perspective to approach technology in mathematics education

- Engineering
- 2005

This paper concerns a research work developed in an European project. The aim of this work was to produce a document integrating the different theoretical frameworks employed by the project teams.… Expand

Using Dynamic Geometry to Expand Mathematics Teachers' Understanding of Proof.

- Mathematics
- 2004

This paper gives a broad descriptive account of some activities that the author has designed using Sketchpad to develop teachers’ understanding of other functions of proof than just the traditional… Expand