Geometric Representations Built with GeoGebra for Improving the Visualization and Reasoning Cognitive Process

Geometric Representations Built with GeoGebra for Improving the Visualization and Reasoning Cognitive Process

Claudia Orozco (University of Salamanca, Salamanca, Spain) and Erla M. Morales-Morgado (University of Salamanca, Salamanca, Spain)
Copyright: © 2017 |Pages: 20
DOI: 10.4018/JITR.2017010104
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It is well known that Mathematical Software can be an appropriate tool to improve the teaching-learning mathematic process. This Software allows the teacher and student to build certain geometric facts and consequently, to visualize them. This makes possible to concretize certain abstract mathematic concepts and facilitate their comprehension. However, some are expensive and some people do not have access to it. This paper presents the use of geometric configurations built with GeoGebra as a tool for teaching the definition of vector and its operations. These are Open Educational Resources (OERs), and they were built under the Open Knowledge scheme, so everyone to have access to them. The goal is to investigate, in this context, the possible implicit effects that these OERs have as a didactic strategy to improve the visualization and reasoning cognitive processes. The results of the tests performed show that, in this case, the use of the proposal favored the learning of the presented concepts.
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Often, when learning mathematics, certain concepts are not well understood, problem-solving processes and meaningless exercises are memorized, which consequently are easily forgotten (Orozco & Morales-Morgado, 2016). Some concepts, rather than being learned significantly, were acquired through memorization as forms without content, only relations of meaningless symbols, which lack tangible meaning and application necessary for learning.

Soylu (2007) says that the reason of which students have difficulty understanding is because the concepts are difficult to articulate and require a high level of mental activity. Another aspect is that they do not see the importance of the use of the concepts in some area of their interest (Dominguez, García-Planas & Taberna, 2015). So, they are not aware of what the concepts mathematically mean or what applications they have.

In this way, the use of pictorial representations is essential for the teaching-learning process of certain mathematical concepts. However, in an expository class some representations are not as simple to construct. They require too much time for their elaboration, or the error of the human calculation can be performed. These factors may discourage or confuse the student, leading to a lack of interest, wrong learning, or an absence of learning. Mathematical Software in the classroom could help with this situation. The construction, manipulation and reconfiguration of the representations can be executed instantaneously and, consequently, an adequate visualization of the concept is being represented.

On the other hand, the resources created with mathematical Software could be Open Educational Resources (OERs), those “are any type of educational materials that are in the public domain or introduced with an open license. The nature of these open materials means that anyone can legally and freely copy, use, adapt and re-share them” (UNESCO, 2002), and thus contribute to the activities promoted by the Open Educational Movement, which is defined as open access educational activities for training. Some of these are the development and distribution of materials with open licensing, the use of OERs available on the Internet and their selection through repositories, among others (Ramírez & García-Peñalvo, 2015).

According to García-Peñalvo, García de Figuerola & Merlo-Vega (2010) the Open Knowledge is composed of the sum of these four areas: Software + contents + science + innovation. An example of this into educational area is the Learning Object (LO), this concept emerged from the need to access specific digital learning resources that can be reused by users in diverse types of platforms. Morales, García-Peñalvo & Barrón (2007) defined a LO as an “unit with a learning objective, together with digital and independent capabilities containing one or a few related ideas, and accessible through metadata to be reused in different contexts and platforms” p.2. Morales-Morgado, Campos-Ortuño & Pérez-Bonilla (2016b) suggested a methodological design through free LOs built with eXelearning tool to Develop Information Competence in post-graduate Students.

Therefore, this work proposes the use of three OERs for teaching and learning about definition, types and sum of vectors. They were built with GeoGebra. The purpose of these constructions is to help in the understanding of concepts, based on certain cognitive processes that students experience when learning geometry. This topic has been selected because it is fundamental in different undergraduate courses and several problems can be modeled with these concepts to be solved (Dominguez, García-Planas & Taberna, 2015).

Currently, a wide variety of digital educational resources exist for the teaching of mathematics. Some have been created specifically for educational purposes and while others for the development of projects in general, but those that are being used for didactic purposes. For this reason, it is necessary to know the advantages offered by each one, in order to choose the one that most suits the needs of students and teachers.

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