Introduction
As in all other educational fields, usage of technology is relevant in geometry too. This paper deals with the usage of technology in classrooms. It explains about visual applications of geometry that depend on visual effects and technology. It also explains the soft wares that can be used in learning and teaching geometry.
Using technology in teaching Geometry in the classroom
Integration of technology to Geometry makes learning faster and effective. Technology can be used in different ways in learning Geometry. “A new study co-written by a University of Illinois expert in math education suggests that incorporating technology in high school-level geometry classes not only makes the teaching of concepts such as congruency easier, it also empowers students to discover other geometric relationships they wouldn’t ordinarily uncover when more traditional methods of instruction were used” (Adding technology to geometry class improves learning opportunities, 2009, para.1).
Usage of dynamic geometric software makes the job of teachers easier. Instead of manually drawing lines and geometrical figures, they can use drawing soft wares. Besides saving time, these methods of teaching have several other advantages. One main advantage is that many complicated ideas can be conveyed through different options available in dynamic geometric soft wares. When advanced technologies are used in Geometric classrooms, it will not be a mere place to learn about geometric figures. With getting effective knowledge of geometry, the advanced technical environment empowers the confidence in students and teachers.
Internet-based learning of geometry has lots of benefits compared with conventional ways. Usage of www resources and Java tools gives great opportunities for students for interactive learning and creating and sharing new ideas of geometry. One of the main advantages of interactive learning is that it is the best way of motivating the ability of students to make innovative ideas.
Compared with other subjects, the relevance of constructions and demonstrations is very important in teaching Geometry. “Besides the PC-version of dynamic geometry tools like Cabri, Sketchpad or Euklid Java-based constructions sometimes can complete demonstrations and geometric constructions for exploration in the classroom” (Schwarze, n.d., p.4).
There are several additional benefits of using Java-applets in teaching geometry. Geometrical constructions made up of Java-applets can be used with worksheets that are needed for classrooms. Java- applets can be constructed in a way that students can just manipulate it. Sometimes programs designed for original constructions have to be taught. Special features of Java-applet programs avoid the risk of destruction of programs. There will not be similar features in conventional study tools.
There are many areas in Geometry that are difficult to understand for students using conventional ways of explaining things. Now, different kinds of soft wares are available to solve these kinds of problems. Many studies show that usage of technology in learning geometry is both effective and interesting. It would be very difficult for some students to grasp some ideas of geometry. Some students can just learn the theoretical definitions but cannot solve the problems of Geometry. They would struggle to think beyond certain limits. It is very difficult to deal with these kinds of students using the conventional way of explaining things. Studies show that usage of dynamic geometry works in these kinds of students. “After adopting such an exploratory approach, we found that the students can generally master the basic concept better and be able to apply to solve related problems, as reflected from their performance in assignments and final examinations in recent years” (Man & Leung, n.d., p.5).
Several studies have been conducted on the implementation of different kinds of technologies in geometry classrooms. These studies say that the usage of software in geometry would make the subject easier and effective if it is well planned. So, proper understanding about the software and its usages is necessary for teachers to apply it in class rooms. “It has been pointed out that using a construction software may detract students attention to things that teacher has not planned in this lesson. All initial investments in time and distraction should be overcome by utilizing the software in a long time” (Iguchi & Suzuki, 1996, p.2).
Geometry depends on visual effects and technology has many visual applications
Today, technology is changing very rapidly; so introduction of the newest technologies in geometry education achieves a successful result from the students. “Computers are an integral part of everyone’s life, and students need to be prepared to use the technology to solve problems and access information as young adults” (Furner & Marinas, 2007, p.83). Computer simulation facilitates better understanding of the subjects. Students find some difficulties in studying the subject like geometry. Implementation of new technologies in geometry helps the students identify recent ideas in this subject. This makes the studying easier and more interesting for the students; moreover, it also makes the coaching of the students easy for the tutors. “Integrating technology in the classroom allows teachers to provide students more opportunities for learning, which gets students thinking about mathematical ideas in a new light” (Adding technology to geometry class improves opportunities to learn, 2009, para.4). A recent study conducted by University of Illinois “suggests that incorporating technology in high school-level geometry classes not only makes the teaching of concepts such as congruency easier, it also empowers students to discover other geometric relationships they wouldn’t ordinarily uncover when more traditional methods of instruction were used” (Technology helps students comprehend geometry, 2009, para.1). There are many hardware and software mechanism to support the technology for doing geometry. This software and hardware facilitates to do geometry in efficient way and also helps increase the practical knowledge of the students. It can create diagram in more specific manner when it is drawn by using the geometric software than it is drawn manually in the paper. Representation of the geometric diagrams in computer provides more visual effects when it is done using computer graphics and more. It can represent three dimensional and two dimensional surface of an object by computer graphics. When the geometric entities like triangle, square etc represent in three dimensions and two dimensions, it helps the students understand the diagram in more precise manner. Through this method, the students can primarily visualize and examine a problem before finding solution for that problem. It is the best method to understand the mathematical ideas in advanced way. The other technique like RKEMS is the latest method for designing and modifying geometry in excellent way. “A new method for representing smooth geometry is using the reproducing kernel element method. Further the formulation provides a simple method to modify geometry that does not require modification of the underlying RKEM mesh” (Geometry representation, modification and iterative design using RKEM, 2007, para.1). Implementing the technologies in education enhance a better future for the students.
Examples of computer programs that’s used in teaching and learning geometry
There are many soft wares that can be used in classrooms for making geometry an easier subject. The Geometric Supposer software is an example for such software. This software helps the users to construct different kinds of geometrical figures and it is very easy to execute all the procedures with this software program. It is possible to take the measurement of those figures created by this software and it can also shift the figures to different positions. There are several tools for supporting the creation of the figures in easy manner. This Geometric Supposer software is appropriate for studying all phases of geometry. Therefore, it is very suitable for the students to study geometry in a simple manner.
Cabri is an important program which can be widely used in geometrical teaching and learning “Rather than repeat the construction, the object constructed can be moved in some sense, so that what is general can be distinguished from what is particular. In the case of the angles of a triangle, a dynamic geometry program such as Cabri allows the user to move the vertices of a triangle at will, all the while repeating the measurement of the angles and the determination of their sum” (Kissane, 1996, para.13). Geometric Supposer and Cabri are just examples for some important soft wares that can be used by Geometric students and teachers.
Geometer’s sketchpad is a computer software program that is used in teaching and learning geometry. It is one of the best software programs for teaching and studying geometry in easy and more understandable way. “The Geometer’s Sketchpad is a dynamic construction, demonstration, and exploration tool that adds a powerful dimension to the study of mathematics” (The geometer’s sketchpad: The geometers sketchpad dynamic geometry software for exploring mathematics, version 4, 2010, para.1). This computer program has been widely used in schools and colleges for studying mathematics in easy and efficient manner. This sketchpad provides visual effect to the mathematical concepts. Therefore, the complex problem becomes simple to the students when it represents visually. Moreover, teachers can make understand the students very easily when it represents mathematical concepts visually. This software helps reduce the effort and strain in studying mathematics. With this software, one can sketch the mathematical diagrams, figures etc faster than drawing on the paper with instruments like compass, scale, and protractor and so on. It is an easy and convenient tool for the students for handling tough mathematical problems. Mathematical calculations can be done easily with this computer software program. Geometric sketchpad provides simplest methods to understand mathematics compared to other geometrical software programs. Therefore, this software program plays an important role in the field of education. One of the main benefits of this software program is that it is possible to do any mathematical concepts or calculation with this software and there is no need of separate software for doing each mathematical concept. Therefore, it is possible to do any complex mathematical problems very fast. This software is “a full set of format tools for mathematical notation and styled text; a more flexible user interface for greater ease of use; built-in web integration; and many, many other enhancements” (Bring maths to life with sketchpad 5, n.d., para.1). As this software provides several tools for drawing and calculation, it makes effortless manipulation of mathematical calculation as well as geometrical figures and diagrams.
All these geometrical soft wares are very powerful techniques for improving the quality of education in students as these soft wares help the students in getting new mathematical concepts. These soft wares also make teaching easier for the tutors. There are several other soft wares which can be used for the same purpose.
Reference
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