# 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={355-393} }

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…

## 21 Citations

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

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### Student's Learning Progression through Instrumental Decoding of Mathematical Ideas

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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.

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

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Both the bridging of empirical and traditional methods by presenting the proofs using dynamic means and aesthetic development through the computer software enhance the user’s interaction, instilling a ‘digital proof’ impulse.

### DEVELOPING GEOMETRIC THINKING SKILLS THROUGH DYNAMIC DIAGRAM TRANSFORMATIONS

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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…

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

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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…

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

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

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

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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.

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

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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…

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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 raise their van Hiele levels.

## References

SHOWING 1-10 OF 86 REFERENCES

### The proving process within a dynamic geometry environment

- Education
- 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.

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

- Computer Science
- 2000

The research suggests that the students' explanations can evolve from imprecise, `everyday' expressions, through reasoning that is isovertly mediated by the software environment, to mathematical explanations of the geometric situation that transcend the particular tool being used.

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

- Computer ScienceInt. 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.

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

- Computer ScienceTCHI
- 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.

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

- Philosophy
- 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…

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

- Education
- 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…

### Characterizing Interaction with Visual Mathematical Representations

- Computer ScienceInt. 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.

### An integrated perspective to approach technology in mathematics education

- Education
- 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.…

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

- Education
- 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…

### Changing how and what children learn in school with computer-based technologies.

- EducationThe Future of children
- 2000

It is concluded that further research is needed to identify the uses that most effectively support learning and the conditions required for successful implementation of these uses.