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Since mathematics is believed to be one of the most difficult fields to learn as it requires both spontaneous and analytic intelligence and the fact that traditional teaching methods place a strong emphasis on lecturing and textual information, the number of people studying mathematics declines each year. Thus, it is becoming increasingly important to encourage students, and present materials in a way that maximizes learning, enjoyment and satisfaction. A more visual, constructivist approach which demonstrates the representation of concepts as well as their practical significance is believed to attract students to the field. And what is better than technology to serve this intention.
Technology continues to impact every aspect of the society, including teaching-learning processes. Traditional approaches to mathematics learning and teaching are being challenged by technology advancements. The infinite opportunities that computers provide have brought new tools and approaches in teaching and learning mathematics. In geometry, Dynamic Geometry Software (DGS) is technological software that provides a range of tools for constructing geometric objects such as points, segments, lines, circlesâ€¦etc. The tools available in the software also include classical constructions (such as midpoint, perpendicular, parallel, perpendicular bisectorâ€¦etc.) as well as transformations (such as reflections, rotations, translationsâ€¦ etc.). Besides, it is important to mention the 'dynamic' aspect of the program; in which the user is able to drag defined objects, such as points, around the screen with the mouse and watch for invariants.
Therefore, computer programs, such as Cabri, can play an important role in giving educators the opportunity to create learning situations that are constructivist, visually attractive, and motivating and thus attract students to this lively field. However, will this integration of the technological tool increase students' achievement? This study aims to find out how Dynamic Geometry Software (DGS), using Cabri-Geometre as a tool, enhance students' achievement by examining their conceptualization of geometric skills, ability to overcome their misconceptions and ability solve geometrical problems on their own.
Purpose of the study
The purpose of this study is to examine if implementing Cabri-Geometer software in a unit on "Quadrilaterals" would improve students' achievement.
Teachers will implement a ready-made lesson plan on "Quadrilaterals" that incorporates the use of Cabri-Geometer. It is important to note that a constructivist approach to learning will be applied in an explorative and interactive format. After this implementation, the aim is to look at how Cabri software will affect the conceptualization of geometric concepts and how will it help students overcome their misconceptions. In addition, it will examine their ability to apply such concepts to solve mathematical problems and on their overall achievement.
This study addresses the following research questions:
Does the use Cabri-Geometer enhance the conceptualization of geometric skills?
Does the use of Geometer help overcome misconceptions?
Does the use of DGS enhance students' overall achievement?
Significance of the study
The National Council of Teachers of Mathematics (NCTM, 2000) has suggested that the mathematical proficiency required for the 21st century workplace develops through conceptual understanding and through the appropriate use of technology. Moreover, in today's evolving world leaders expect students to enter the workplace with a wide range of communication, math, and technology skills. For this reason teachers cannot disregard and are urged to properly implement current technologies. Besides, we are witnessing a trend towards constructivism in the learning method. Students are urged to construct, explore, manipulate and interact with knowledge to form their understanding. Dynamic softwares help serve the intention of teaching through constructivism and in a technological environment. Therefore, the results of this study may be useful for many teachers and educators who are willing to incorporate technology into their constructivist instruction. Furthermore, the study might provide some forms of guidance to researchers that want to practice a similar research in the future.
Definition of terms
In this context, Dynamic Geometry Software refers to the tool used in this study that is Cabri-Geometer software.
Conceptualization is defined as the act of "forming a concept or concepts of, and especially to interpret in a conceptual way", as defined the Free Dictionary.
Misconceptions are defined as "mistaken thoughts, ideas, or notions; a misunderstanding of a concept", as defined by the Free Dictionary.
Review of the literature
DGS has become one of the most widely used pieces of software in schools and colleges all over the world. This is because DGS provide a context where mathematical problems can be done in a different and a more meaningful way. Using Cabri, students construct, explore their constructions and then deduce mathematical properties. A geometrical figure or an equation on the Cabri screen becomes an object to manipulate and interact with rather than a static one. The practicality of DGS programs has attracted several researchers and a number of studies have looked in depth at how students interact with the software. For example, Arzarello and colleagues (2002) have examined what they call ascending and descending processes shown by students using the drag mode. Ascending processes, revealed when students freely explore a situation, occur when students are looking for regularities, invariantsâ€¦ etc. These are moves from drawings to theory. Descending processes are moves from theory to drawings, and involve students validating conjectures, checking geometric propertyâ€¦etc. These movements in the use of dragging are believed to reveal cognitive shifts from the perceptual level to the theoretical one.
Besides, finding of Holzl stated that in the early stages of use, students in general do not use the dragging facility very much. That is because students see dragging as something which distracts especially that they are not used to seeing geometrical objects moving on paper but rather static. However, once they start experimenting they begin to understand the power of the drag mode (2001). Thus, with dragging, students are able to see the invariants that usually hold a theoretical reason. Students, after dragging experiences, are able to discover properties and conclude conjectures (Holzl, 1996). This is believed to enhance their understanding and conceptualization. Moreover, dynamic software programs help students identify detailed characteristics of figures upon transformations. For example, finding the symmetry of a circle with respect to an oblique line on DGS software; in which by dragging a point on the circle and finding its symmetry with respect to that line, considers the notion of viewing objects as set of points rather than wholes (Hollebrands, Laborde & StraÎ²er 2008).
In addition, research has highlighted that the act of constructing diagrams on the use of DGS play an important role in the learning process. In DGS environments, students are more concerned with designing drawings that are unmessable when dragged, and their actions are controlled and assisted by the tool (software). Their construction process therefore, involves theoretical, graphical and spatial properties. Moreover, the communication students have with those tools grant a deeper conceptual knowledge of geometrical properties (Hollebrands, Laborde & StraÎ²er 2008).
However, DGS can also be misleading if not well implemented in the instructional plan by teachers. Teaching activities have to be carefully designed, otherwise, as Hölzl (2001) found, students may avoid mathematical analysis by looking for the practical implementation of a solution and not towards its theoretical aspects and implications. They may also use the tools available in a non-reflective way and try to deviate from the intended task. Healy and Hoyles (2001) tackle some of these problems with carefully designed sequences of tasks. By doing so they found that students could begin to connect between informal explorations and logical-deductive arguments. Hadas (2002) and colleagues demonstrate how appropriate activities can be designed to create situations of contradiction for students, followed by surprise or by uncertainty and that this can lead students to seek for mathematical explanations. Laborde's experience of designing teaching situations based on DGS and integrating them in the regular course of classroom teaching shows that it takes a long time to reach the point where tasks truly take advantage of the computer environment (2001).
A research on quadrilaterals done by Jones, focus on the evolution of students' ability to make use of precise language and to arrive at an understanding of the relationships between the various properties of quadrilaterals. In his research, use of DGS clearly helped students to formulate reasonably precise statements about properties and relationships and to carry out correct deductions (2005).
Therefore, a variety of research shows that interacting with DGS can help students to explore, conjecture, construct and explain geometrical relationships. Indeed, classroom experiments have shown that the software itself does not grant the transition from practical to theoretical. The teacher and the designed activities play a very important role in guiding students to theoretical thinking and to trigger students' analysis. Finding how to manage classroom time well was also something that had to be worked on upon implementing DGS in a mathematical classroom.
Consequently, many researchers have studied the process of interacting with the software and its benefits and little work have been done to examine the direct effect these processes on the achievement of the pupils. How does learning with Cabri enable students' formation of concepts and strategies to solve problems? Especially that geometry tests and assessments are still done on a paper and a pencil format, up until this date. The following study main purpose is to examine the effect of a well implemented lesson with Cabri on students' overall achievement.
The study will take place at a private school located in Mount-Lebanon; it is one of the top schools in the region based on the results of the official exams. The school provides education from nursery to grade 12. The students come from the village where it is situated and belong to average socio-economic class. The implemented curriculum and books are based on the National Lebanese program. Technology is newly introduced in this school however it is barely used.
Sampling and Participants
The sampling procedure is convenience non-randomized. The participants are the students of grade 8. The total number of participating students will be all students of grade 8; 25 students. Their ages range between 13 and 15 years.
Research Design and Method
The study conducted will be an action research where a new method of implementing a DGS into instruction will be administered.
This study will include both qualitative and quantitative methods to collect and analyze data. Qualitative data will be collected through interviews with the participants analyzing their conceptual level of thinking to solve a problem (in the form of oral tests). Quantitative data will be collected through administering achievement tests to the participants and collecting their scores. Initially a pretest will be performed to determine the students' level of conceptualization of geometry skills. Finally a posttest is administered and its scores will be compared to the pretest results in order to determine the effectiveness of the employed approach.
In this study, a geometry unit named "Quadrilaterals" is to be designed based on the constructivist approach and in which technology will be implemented. The aim of this study is to examine the effect of the implementation of Cabri, as a technological tool, on students' achievement. The results of this study will be helpful for many current teachers and educators who are implementing DGS or are willing to implement it into their instruction.