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The purpose of this degree work is to help the teacher in his teaching-learning work in which the students of Unified General High School will directly benefit; that is, first, second and third of Unified General High School since this new methodology is directly related with the use of Information and Communication Technologies (ICT) and is also linked to the subjects that correspond to the Geometry Block, specifically on the subject of conics and their graphs. It is evident that there are drawbacks in the teaching-learning process of these subjects since it is linked to the creation, interpretation and analysis of graphs; therefore, the teacher takes valuable time for their work who seeks different methodologies to achieve a full understanding in their students and to adapt with the time that limits him in each class. It is necessary to mention that the use of technological tools for education is limited for these subjects. With the aforementioned we infer that the teacher is looking for innovative ideas to bring them to their students in order to make their classes interactive, with this in mind, I seek to make a proposal for a virtual course for the teacher that can develop, polish and improve their skills in the use of technological tools related to education; specifically, in the educational software GeoGebra, in order for the teacher to achieve said skills and use them in their work, the aim is to know how to reach their students and achieve a meaningful learning linked to new technologies. To develop this work, two research techniques have been implemented: interview and survey, teachers and students of the Cesar Davila Andrade Educational Unit based in the Cuenca canton were interviewed and surveyed. In response to this need, the author opts for a degree project that includes a virtual course and video tutorials for teaching- learning the subject of conics at Unified General High School.

The teaching-learning of Physics must start from the student's own knowledge, as well as from the analysis of real physical phenomena, so that they could build their own knowledge and relate reality to scientific content. The theory of didactic situations allows to develop this form of teaching when posing sequences, where students face individually and in groups to different activities. For this reason, this teaching work proposes didactic situations for the teaching-learning of linear kinematics, applying the “Tracker” software with the aim of supporting and improving the study and analysis of kinematic concepts and graphics. Allowing the students to be related to real events in order to solve the difficulties that they present in their interpretation. It was a problem which was evidenced in the Mathematics and Physics Career of the University of Cuenca while obtaining the results of the application of the TUG-K test. In addition, as a complement, a bibliographical study was made about the problem, the theory of didactic situations, Vygotsky's constructivism and the importance of the implementation of ICT, specifically the Free Tracker software in the teaching-learning of Physics.

The present research was carried out with the objective of promoting the significant learning of factorization cases with linear and quadratic terms, in students of the tenth year of Basic Education, using the magnetized algebraic tokens as a methodological strategy. This quantitative study of pre-after quasi-experimental design was in the students of the 10th year of Basic Education of the Baccalaureate school Dr. Modesto Chávez Franco of the city of Santa Rosa, El Oro. Two groups of students: 27 control and 31 intervened. For the collection of information, 4 instruments were used: a questionnaire of 93 items on a Likert scale, designed Ad hoc for this research and validated by experts in the area of mathematics teaching. The survey showed that the teacher is most often using pre-instructional and instructional strategies in factorization teaching. In addition, two tests were applied with 13 questions; A pre-test and a post-test to determine the level of knowledge of the students before the beginning and the end of the implementation of the didactic proposal. The data obtained were organized into tables of frequency distribution, the comparison was in percentages because they were groups of unequal sizes and. After the intervention was evidenced. That the students of both groups improved their average, their average by 10%, although the quantitative level reached was unsatisfactory, while those of control did it in an average point. However, the students in the intervention group showed a greater degree of understanding of concepts and algorithms, greater motivation and performance during the development of the whole proposal. Finally the impact of the whole intervention was evaluated through a survey, resulting novel, dynamic and interactive for the students.

The proposal of educational innovation, aims to encourage methodological strategies to facilitate the resolution of mathematical problems in the sixth year of Basic General Education. For the development of the proposal, it began with a diagnosis of the problem situation in which was used different techniques such as: interview with the teachers and students, direct observation of mathematics classes and the FODA carried out by the teacher. The theoretical framework of the proposal, has as a basis the mathematical context Education Document, which proposes as an approach to teaching five strategies that they have been grouped under the name of "Strategy REACT" which according to the order of the letters are: Relationship, experimentation, implementation, cooperation and transfer. The guide of the proposal is divided into three sections: Teaching Guide; tab of the student; Answer Key.

This project consisted in a field investigation in which I developed the statistical analysis of the use of Information Communication and Technologies (ICT), in order to diagnose how it is being implemented in the teaching - learning process by teachers of Secondary Level. To achieve this goal, I used the digital bases of Ministry of Education Coordination Zone 6 and I collected information of educational institutions, teachers and students from the high school level, which were in the South District (01D02) of the city of Cuenca during the school year 2014-2015. With this information, a sample was delimited. The techniques of the survey and the interview were applied. A descriptive analysis of the perceptions, opinions and experiences with teachers and students regarding the use of technology in their everyday educational activities was carried out. Moreover, additional available resources in participating institutions, the access that people may have, and use that the main actors in the educational process are given to them, were investigated. In this research a literature study on the use of ICT and what its integration in education implies is presented. Besides, a discussion about how ICT is incorporated into the city's classrooms is also held.

The main objective of this work is to give a new methodological alternative for the teaching – learning process regarding the subject Differential Calculus, in the Engineering careers at Salesian Polytechnic University. The main purpose of this work is to diminish repetition and desertion in this subject. As an starting point, it was necessary to make a diagnose of the learning environment, analyzing aspects, such as quality of the students who get into the University, scientific and pedagogical preparations of the professors, student perception, classroom equipment, and use of technology; these aspects helped us to determine the absence of a different methodology from the traditional one. The new proposal considers as philosophical base the critical theory of mathematics education, and as pedagogical base, the social cognitive theory. To ensure a minimal quality regarding this proposal, it has been taken as a reference, the directives of the Superior Education Law (LOES), and the general and specific competences for the Industrial Engineering careers declared by the Spanish National Agency of Evaluation and Accreditation ANECA, belonging to the European Space of Superior Education EEES. Aside from that, the Theory of Didactic Analysis Content has been considered as a procedure for the design, practice and evaluation of the activities in the teaching learning process of mathematics. All the mentioned above, helped us to get the final products of this work, and to constitute the new micro curricular design and a modern learning guide for the topic Function Analysis, they both coherent with the educational model proposed.

The process of teaching – learning for a long time was based on repetition and memorization, currently seeks out of this situation, causing the student to construct their own knowledge, with the help of diverse didactic resources. This research work was applied in the third year of “Manuel J. Calle High School” as a model of intervention through the implementation of concrete teaching materials and the educational software Geogebra, presenting itself as an alternative solution to the problem that causes the lack of visualization of the figures, for the resolution of the problems of the conics. For the purposes of this research , the idea of constructivist learning was used , which with the help of teaching materials, the student can build their own concept of the treated cone , while the software Geogebra by applying the process to resolve the Van Hiele proposed problems of conics. The methodology is supported on an exploratory and descriptive research, using the technique of observation .The implementation of these two elements, with the aid of an instruction manual has improved the teaching - learning process, the area of mathematics, and the institution.

This work is a proposal of dynamic methodological strategies to reinforce the Mathematics learning in the 9th grade of Primary School. It aims to provide ideas to solve the several difficulties the teachers face at the moment of reinforcing the studied topics in the Mathematics subject. In order to elaborate this project, Jean Piaget’s theories related with the cooperative learning have been considered, as well as Castellanos and Gutiérrez’ specific definitions about dynamic strategies as a group of processes, actions and activities that the students can develop intentionally in order to improve their learning. Personal experiences have been considered within a long teaching career, as well as other teaching experiences from other fellow teachers exposed during certain moments of pedagogic socialization. Reading of texts about this subject, the approaches covered in the Master’s classroom, institutional reality and other influential factors in the students’ learning have been considered as well. This work will cover five chapters. The first chapter provides an explanation about the problem, its justification, and the objectives on which this work will be based. The second chapter addresses the theoretical framework which covers the following aspects: dynamic methodological strategies, motivation, cooperative learning, resources, educative reinforcement, and games. The third chapter provides the work methodology, and the statistical analysis of the information obtained from surveys. Thus, further decisions and proposals will be made based on their results in order to improve students’ academic performance. The forth chapter covers the most important part of this work. In this section the teachers will find precise ideas about what, how and why, of each dynamic methodological strategy, which in practice will allow teachers to motivate young learners, and thus improve their academic performance in the Mathematics subject. The proposed strategies are dynamic activities

This present work is a field investigation and it is a descriptive type, in which was made a comparison between students of physic-mathematics and science bachelors, about their perceptions of their academic preparation received in high school and their accomplishment, once they became Engineering and Architecture Faculty students from Cuenca University in school year 2011 – 2012; contrasting then with the academic efficiency obtained into the first year of their universitary career. For that case was made an analysis of the studies plan structure of these two specialties, surveys were applied to students and professors and results were analyzed from obtained evaluations for these students in their first universitary year.