Project Objectives
General Objective
The general objective of the project is to investigate the development of students' ability in transformational geometry concepts (translations, reflections and rotations) and the effects of two interactive dynamic resources on this ability. The specific purposes of the study are the following:
1) to investigate the development of 5th and 6th grade elementary school students' ability on transformational geometry concepts (translations, reflections and rotations),
2) to develop activities for teaching transformations with two different interactive dynamic educational resources to elementary school students,
3) to investigate the effect that two different types of interactive dynamic educational resources for teaching transformational geometry have on different types of students,
4) to design tests for measuring students' ability on transformational geometry and spatial abilities, and a self-report questionnaire for assessing their cognitive styles.
Scientific and technological objectives
The scientific objectives of the project are:
(a) to investigate the development of students' ability in transformational geometry (specifically the concepts of translation, reflection and rotation),
(b) to supply the teachers with activities and information about interactive dynamic educational resources for teaching transformational geometry, and
(c) to provide to the teachers and researchers instruments for measuring elementary school students' abilities in transformational geometry.
The technological development of the project is to provide a review of possible characteristics that different types of interactive-dynamic educational resources may have, with examples of software and mathematical applets for teaching transformational geometry. Therefore, a rich database of interactive-dynamic educational resources for teaching Euclidean transformations will be developed, with a description of each resource's characteristics. Additionally, the development of a Website will inform teachers about the program and about transformational geometry concepts and it will provide open access to the database of resources and activities.
Innovation
From the theoretical perspective, we will investigate the development of elementary students' ability in transformational geometry, which has not been investigated in Cyprus. Generally, little attention has been given to the development of transformational geometry concepts and problem-solving strategies. International studies on transformations mainly focus on teaching experiments comparing instruction with technological tools opposed to traditional teaching (e.g. by using manipulatives). As far as we know, there is no study comparing the effects of different types of technological environments in the learning of transformational geometry concepts, and more generally in the area of elementary mathematics, by taking into account the individual differences of students. However, there are suggestions that the effectiveness of dynamic visualizations is not a simple matter, and there is a need to start identifying the complex factors that should be considered in evaluating the effectiveness of such programs.
In the practical aspect, given the emphasis to implement technology in education all over the world, and recently in Cyprus, it is important to be able to identify the characteristics of different types of dynamic environments in mathematics, and their effect on the abilities of different types of learners, and this is the main innovation of the project. Since the implementation of technology is an important aspect of the new Cyprus mathematical curriculum, it is important to know what kind of technologies can be used for supporting the needs of all students.
The project will also develop a set of activities for teaching transformational geometry in elementary school, which is not adequately explored in the current mathematical curriculum of Cyprus. Transformational geometry is one of the topics that has been advocated as an important part of the K-12 geometry curriculum of the National Council of Teachers of Mathematics (NCTM) and helps students develop broad concepts of congruence and similarity. Moreover, geometric transformations are required in many geometrical constructions, and are the basis of much spatial thinking in a variety of other subjects (e.g. art, architecture, geography). Therefore, it is an important and useful mathematical concept, and providing educators in Cyprus with material for its effective teaching will benefit the students.
