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The present work of titulation seeks to encourage the use of strategies for teaching notable products and factorization, the finality is to prevent students of the first of baccalaureate presenting difficulties in the resolution and understanding of exercises related to these issues. It is important incentivize the teacher for the use of strategies when teaching, in this way it provides an alternative path to traditional education, which only generates a student with a memoristic knowledge and without any meaning. On the other hand, with the application of a test and survey of high school students, it was evidenced that they did not acquire the necessary skills during the study of the subjects, it was also identified that the learning was not entirely significant, and that there is a predominance of the use of text and the blackboard when teaching. With the aforementioned, two didactic guides are proposed, one for the teacher and one for the student, in which in addition to the elaborated classes the use of strategies for the teaching of the contents, the use of didactic resources that serve as reinforcement for the consolidation of the contents.

The curricular adjustment carried out in Ecuador in 2016 responds to the constructivist paradigm, the texts that guide the mathematics teacher proposed by the Ministry of Education are also developed according to that vision, and therefore, the teacher should develop an active and reflective class, supported by a series of resources proposed in the curricular adjustment. Education must have all its elements well harmonized so that the student has the appropriate learning results; the objective is to analyze the relationship between three elements: curriculum design, guide text and the teacher. The documentary review methodology is applied to analyze how the curricular adjustment idealizes the relationship between these elements, and then what is the reality. In practice there are some difficulties, one of these is the texts bring excessive amounts of content to be developed, which forces the teacher to “give” classes, without making sure of the students’ learning achievement. Also, the reform has not been sufficiently disseminated to teachers, who still develop their classes in a traditional way, emphasizing the memorization of content and mechanical recipes to solve the exercises.

Although the careers have a curriculum planning, in practice the student takes some additional time to complete his program. In some careers, this delay can be excessive, implying delays and the loss of resources for the student and the institution. This research was carried out with a cohort that began in March 2013 and ended in July 2018, with the aim of longitudinally analyzing the academic progress of the students, and evidencing the gap between the ideal progress and the real progress in each period, and Thus, to define optimization policies for educational management. A faculty was found where its students took 46.6% more than the ideal term; Additionally, those students, whose parents are professionals or who hold high positions, have academic progress that is statistically superior to others., Si bien las carreras cuentan con una planificación de currículo, en la práctica el estudiante demora algún tiempo adicional en cumplir su programa. En algunas carreras esa demora puede ser excesiva, implicando retrasos y la pérdida de recursos para el estudiante y la institución. Esta investigación se realizó con una cohorte que inició en marzo del 2013 y culminó en julio del 2018, con el objetivo de analizar longitudinalmente el progreso académico de los estudiantes, y evidenciar el desfase entre el avance ideal y el avance real en cada período, y así poder definir políticas de optimización de la gestión educativa. Se encontró una facultad donde sus estudiantes demoraron un 46,6% más que el plazo ideal; adicionalmente, aquellos estudiantes, cuyos padres son profesionales o que desempeñan cargos altos, tiene avances académicos estadísticamente superiores a otros.

Early mathematical skills are considered as the basis of the conceptual structures on which the learning of advanced mathematics leans on. Identifying the level of mathematical skills with children begin formal education is essential, this, in order to implement programs focused on strengthening the skills in which children reach low levels and strengthen those that have managed to consolidate. The objective of this paper is to examine the level of performance in the numerical skills of 188 children who start Basic General Education in public and private schools in the city of Cuenca-Ecuador. For this purpose, the Early Mathematical Assessment Test (TEMT) was used as a tool. The applied study, quantitative, exploratory and cross-sectional, reveals that children in public schools obtain a score of 25.5 / 40; compared to the score obtained by children from private schools that reach 32.1 / 40; the difference is statistically significant, with a coefficient of variance of 25% and, p-value less than 5%. The competition, with the highest performance in both public and private schools, is the comparison, while the one with the lowest performance is related to counting. According to the study, it can be concluded that children in private schools achieve better performance in mathematical skills than children in public schools, in addition, it is evident that the level of knowledge in both public and private schools is higher in relational skills than numerical skills

This degree work develops a proposal of active strategies and teaching resources in certain topics of spherical trigonometry for the first cycle of the career of Pedagogy of Experimental Sciences. The purpose of the work is to improve the level of abstraction of: formulas, definitions, theorems, three-dimensional figures, etc. that require deeper spatial reasoning and vision. It is important to provide teachers with other ways to explain the subject considering that each student learns differently; for this, the proposal was based on Ausubel's constructivism and significant learning theory, where the student is the generator of his own learnings and relates previous knowledge to new knowledge. In addition, by applying qualitative focus group techniques to students, and interviews with teachers, the problem was highlighted that the subjects had little time load causing them to be seen quickly; leading the student to memorize formulas, concepts, theorems, properties, etc. abstractly losing the relationship of their knowledge with a physical plane and isolating it from the concrete. Therefore, the need to incorporate teaching strategies and resources to improve their understanding and generate more lasting learning is considered. Finally, two texts were developed, one for the teacher and one for students, documents containing eight classes, oriented to the use of a number of strategies such as: inverted classroom, group workshops, forums, exploratory questions, play activities, among others; and, teaching resources such as: software, web tools 2.0, concrete material; pretending to make classes more meaningful, innovative, dynamic and that students develop collaborative and autonomous work.

Traditionally, geometry classes have been difficult, but when these classes are developed mechanically and memoristically, they become even more complex. Teachers who develop theoretical, abstract and difficult to understand topics, which are not related to any practical application and are of little interest, do not contribute to solving this problem. There are new currents of thought that are changing the relationship between teachers and students in the classroom, the teacher designs and applies activities so that the student develops his learning and goes from being a passive receiver to have an active role in the classroom. The action research methodology was used for the theoretical analysis of traditional classes and new geometry class proposals. This article aims to describe an experience with students of the teacher training career in Mathematics and Physics, where creative classes of triangles are developed, with novel themes that describe part of Ecuadorian history, technological resources are used that facilitate understanding and the context problems that are analyzed give practical meaning to geometry and encourage research.

The present titling work has as objective to help to improve the level of abstraction and reasoning of related problems with daily life in the topic of “Solids with curved faces (cylinder, cone and sphere)” for students of the Matemathics and Physics´s career of the University of Cuenca, through a series of methods, resources and teaching strategies that can be used inside or outside of classes. Starting from the aplication of a poll and a test to a sample of the career, it was demonstrated that the learning of these three-dimensional solids in the students was not meaningful, due to that they could not to relate their knowledgewith a contextualized problem. Additionally, these two reaserch techniques helped to get ideas to do a work based on the Constructivism and tthe Meaningful Learning of David Ausubel. With the aforementioned, it is proposed twodidacticalguide, one for the teacher and one for the students, these guides will have eleven classes oriented towards the use of didactical resources as: playful activities, concrete material, inverted class, methodological strategies focused in the team work. With these guides it is intended to generate meaningful experiences with the students in a way that allows to improve the learning of this topic and the most important thing is to offer didactical ideas for their profesionallifes.

There are some criticisms of the access system to the ecuadorian university because many students fail to achieve access to the careers of their preference or vocation; for that reason, an investigation was made to the admission process and leveling course taken by the students who entered the Faculty of Philosophy, Letters and Education Sciences of the University of Cuenca. It is important to demostrate with real values these statements. To achieve this, students were analyzed who were admitted and entered the leveling course between September 2015 and February 2016, through surveys at the beginning and end of the course. Based on the results of the scores of the National Exam for Higher Education -ENES- with which the students entered the careers, it was compared with the careers of preference, and the experience after taking the leveling course in the faculty., Existen críticas al sistema de ingreso a la universidad ecuatoriana debido a que muchos estudiantes no acceden a las carreras de su preferencia o vocación; por eso, se realizó una investigación al proceso de admisión y curso de nivelación que tomaron los estudiantes que ingresaron a la Facultad de Filosofía, Letras y Ciencias de la Educación de la Universidad de Cuenca. Es importante evidenciar con cifras la realidad de estas afirmaciones, para esto se estudió a los estudiantes que fueron admitidos e ingresaron al curso de nivelación entre septiembre del 2015 a febrero del 2016, mediante encuestas al inicio y final del curso. En base a los resultados de las notas del Examen Nacional para la Educación Superior –ENES- con que ingresaron estudiantes a las carreras, se comparó con las carreras de preferencia, y la experiencia luego de tomar el curso de nivelación en la facultad.

An important part of the teaching- learning process is the planning. It helps teachers to guide their students due to the educator is able to identify the objectives, skills and evaluation criteria which were proposed in the curriculum and will be addressed according to the subject studied. In addition, the planning shows the best methodological strategies that will be applied, the resources that will be used during the performance of the topic, and the indicators for the performance criteria; it means, the aspects that allow to identify if the students acquired the minimum knowledge that are required and the techniques or instruments to be used in order to evaluate the new knowledge. In the methodological strategies or learning activities space is where five interesting strategies are suggested which have improved the results in the teaching-learning process of the mathematic. These strategies are: the relation, experimentation, application, cooperation and the transference, all of them known as REACT. The implementation of all these strategies in a planning makes the difference between a traditional and constructivist class, being the last one which have the best results in the mathematical education., Parte fundamental del proceso enseñanza-aprendizaje es la planificación, pues permite al docente guiar el aprendizaje de sus estudiantes, identificando los objetivos, destrezas y criterios de evaluación planteados en el currículo que van a ser abordados según el tema tratado, también permite indicar cuales son las estrategias metodológicas a ser aplicadas, los recursos a ser utilizados en el desarrollo del tema, los indicadores de logros de aprendizaje, es decir, aspectos que permiten identificar si los estudiantes adquirieron los conocimientos mínimos requeridos y las técnicas o instrumentos a ser utilizados para evaluar el nuevo conocimiento. Dentro de las estrategias metodológicas o actividades de aprendizaje es en donde se proponen la aplicación de cinco estrategias, que han mejorado los resultados en la enseñanza-aprendizaje de la matemática; dichas estrategias son: relación, experimentación, aplicación, cooperación y la transferencia, más conocidas por sus siglas como la REACT. La implementación de éstas dentro de la planificación marca la diferencia entre aulas tradicionalistas y constructivistas, siendo las últimas las que mejores resultados presentan dentro de la educación matemática.

Math class is in process of evolution, the traditional classes centered on the teacher are losing momentum in Ecuadorian education, giving way to classes that prioritize the student and their learning. Traditionally, the mathematics teacher has had professional training in technical areas and little training in pedagogy and skills to carry out a class based on constructivist paradigms of learning, centered on the student and the quality of their learning. A constructivist class of mathematics involves having a student with a different vision from his or her traditional education, must be motivated to achieve meaningful learning, for this must be able to investigate, analyze, reflect, pose creative solutions, solve situations of the context, formed in values and which contributes to the growth of society., La clase de matemáticas está en un proceso de evolución, las clases tradicionales centradas en el profesor van perdiendo vigencia en la educación ecuatoriana, dando paso a clases que priorizan al estudiante y sus aprendizajes. Tradicionalmente el docente de matemáticas ha tenido formación profesional en áreas técnicas y poca capacitación en aspectos pedagógicos que le den habilidades para llevar adelante una clase fundada en paradigmas constructivistas del aprendizaje, que están centrados en el estudiante y la calidad de sus aprendizajes. Una clase constructivista de matemáticas implica tener un estudiante con una visión diferente a su formación tradicional, debe estar motivado por alcanzar aprendizajes significativos, para esto debe ser capaz de investigar, analizar, reflexionar, plantear soluciones creativas, resolver situaciones del contexto, formado en valores y que aporta al crecimiento de la sociedad.

El presente documento hace un abordaje teórico de lo que implica la evaluación de los aprendizajes, analiza las etapas de un proceso de evaluación, así como las funciones y tipos de evaluación que se presentan en el proceso educativo. Finalmente considerando que el Sistema Nacional de Educación ha experimentado una serie de cambios en su currículo en los últimos años se elabora una propuesta de las diferentes técnicas de evaluación con sus respectivos instrumentos que pueden ser aplicados en la evaluación de los aprendizajes en la asignatura de Matemáticas.

Math class is in process of evolution, the traditional classes centered on the teacher are losing momentum in Ecuadorian education, giving way to classes that prioritize the student and their learning. Traditionally, the mathematics teacher has had professional training in technical areas and little training in pedagogy and skills to carry out a class based on constructivist paradigms of learning, centered on the student and the quality of their learning. A constructivist class of mathematics involves having a student with a different vision from his or her traditional education, must be motivated to achieve meaningful learning, for this must be able to investigate, analyze, reflect, pose creative solutions, solve situations of the context, formed in values and which contributes to the growth of society., La clase de matemáticas está en un proceso de evolución, las clases tradicionales centradas en el profesor van perdiendo vigencia en la educación ecuatoriana, dando paso a clases que priorizan al estudiante y sus aprendizajes. Tradicionalmente el docente de matemáticas ha tenido formación profesional en áreas técnicas y poca capacitación en aspectos pedagógicos que le den habilidades para llevar adelante una clase fundada en paradigmas constructivistas del aprendizaje, que están centrados en el estudiante y la calidad de sus aprendizajes. Una clase constructivista de matemáticas implica tener un estudiante con una visión diferente a su formación tradicional, debe estar motivado por alcanzar aprendizajes significativos, para esto debe ser capaz de investigar, analizar, reflexionar, plantear soluciones creativas, resolver situaciones del contexto, formado en valores y que aporta al crecimiento de la sociedad.

This research analyzes the causes of desertion that are generated in the development of the leveling course prior to the entry into the first year of the faculties of the technical area of University of Cuenca. Studies show that dropout is a global problem that occurs especially in university admission, cause of waste of time and resources to student and institution. It is important to identify main causes of desertion so that decisions can be taken and actions implemented to reduce dropout rates. For this, the student’s socioeconomic records were analyzed; math tests were applied at the beginning and end of the course; a survey at the beginning of the leveling course and another at the end of the course; also, a survey was carried out on a sample of students who dropped out of leveling, and desertion rates were analyzed for students in the technical area. Results suggest some causes of desertion, such as lack of bases in mathematics, not to enter the career of their preference, high academic requirements in technical careers, a complex evaluation system, lack of economic resources, among other reasons for the desertion. It emphasizes the coincidence of the causes of desertion with other studies, and the concern of the institutions to reduce the rates of desertion.

This study was carried out at the Department of Mathematics and Physics of the School of Philosophy, University of Cuenca. This work is about the challenging understanding of the subject of prisms and straight pyramids in geometry. In order to conduct this study, several techniques like interviews, surveys, and document revision were taken into account. All of them were carefully applied to obtain accurate results. Those results indicate that 54.55% of the students feature low academic performance in in the subject previously mentioned because three-dimensional topics are considered in two dimensions. The objectives is to enhance the students’ understanding of prisms and pyramids by using a handbook for teachers as well as teaching materials with three-dimensional figures, so that the student can see, feel, and use them. Therefore, a teaching handbook was produced for teachers, which is designed with in eight classes in a systematic way.It is necessary the support of teaching materials, experimental practices and the use of technological resources. The teaching handbook is based on the constructivist and cognitivist theories of Bruner, who states that learning is more meaningful and useful when students learn through action; in this way, they can acquire new knowledge from previous learning. Through this approach, the purpose is to persuade the students to participate actively in the teaching-learning process. It is expected that the students can deduce by themselves concepts, procedures, and formulas by organizing them to include them into their cognitive systems with playful activities and problems related to real life.

This search comes from the fact that, during the learning process the student that starts the baccalaureate finds a different reality, which requires interiorized knowledge from their first years of study. Commonly, this does not happen because the lack of conceptualization, techniques applications, study habits and the little use of learning strategies. Because of this, this work’s goal is, determinate the incidence of the learning strategies in the academic performance of the mathematics students of third of baccalaureate form “Guillermo Mensi” High School during the first period of the school year from September 2015 to February 2016. For that, it was used a population of 160 students from third year of baccalaureate, six teachers and one authority. This is a descriptive and correlational search. For the data collection, process was used interviews and surveys. It is important to stand out that there are some student with high knowledge of learning strategies, who actually have a good academic performance. The results demonstrate that the more use of learning strategies the higher academic performance is. Therefore, it is important recommend to the student to use these strategies, which improves their academic performance.

The following quantitative research aims to determine if there is a relationship between high school students study habits and their math grades in an educational unit in the city of Cuenca during the 2014-2015 academic year. The research was carried out using the Inventory of study habits completed by Pozar, F. This manual was already used in a research carried out in Spain, but not having chosen the sample at random, the results could not be generalized. The research was formulated with a sample of 300 high school students randomly chosen. To maintain the properties of the population, a classification with two variables was used; grade level and gender. The goal is to determine to what extent the different environmental and physical factors influence math grades, if previous planning exists, the way in which materials as well as other resources are used, and the assimilation of the contents with the grades obtained in mathematics. A comparative analysis between math grades of the Educational Unit where the research was carried out with the local, national and international institutions, describes a not so complex reality, clarifying that the ratings do not always represent programming or knowledge. As a result of the research, it can be mentioned that the biggest weakness of students is their lack of planning, 23% of eighth graders don’t plan ahead, and once they are in tenth this increases to a 45%. Young people are aware that the time they spend studying is not enough to pass the school year; in eighth grade 16%, in ninth grade 26%, and in tenth grade 32% of students have this perception

The following titling work has as purpose to decrease the abstraction of the subject: “Theory of Sets and Mathematical Logic”, in the propositions of algebra unit, in the students of Mathematics and Physics career from University of Cuenca. For this purpose it is proposed didactic strategies for teachers and the developing of teaching materials as a play tool and part of a constructivist teaching. This objective started from a bibliographic study, which searches to consolidate an educational proposal based on constructivism. In addition, through the application of students surveys, the problem of abstraction in the subject is evidenced and the need for teaching materials to improve their understanding and applicability. For this purpose, a didactic guide for teachers which allows to relate the use of circuits with the theory of Propositional Logical through meaningful learning; and with the elaboration of the didactic material of circuits that simulate the logical result of the logical connectives: negation, inclusive and exclusive disjunction, conjunction, conditional and biconditional.

The present research searched to know, through a case study the analysis of all the variables that are structured in the Social Balance, a tool that helped in determining the Social Responsibility of the institution, object of study, of the popular and solidarity economy. It should be mentioned that the type of research used had a qualitative and quantitative approach, besides being supported in a field work. The results indicate that the associative responsibility and the internal social policy of the Institution were rated scalar as good, with significant percentages. However, in terms of the reception channels for information and educational policy and the contribution to community development, the results were not very encouraging, La Responsabilidad Social Corporativa (RSC) evidencia actualmente el compromiso ético que tienen las organizaciones frente a todos sus grupos de interés a través de la rendición de cuentas de su gestión social, en este sentido, la transparencia como elemento de una adecuada RSC asegura un mejor clima laboral, esto sin duda, manifiesta la necesidad que tienen las entidades de involucrar este modelo de gestión como parte de su estrategia empresarial. En este contexto, la RSC toma en consideración las implicaciones sociales y medioambientales de sus actuaciones, además considera como objetivo estratégico la creación de valor para todos sus grupos de interés, entre los que se encuentran sus directivos, socios, trabajadores, clientes, proveedores y sociedad en general. Para la adecuada evaluación de la RSC existe una herramienta de gestión denominada Balance Social (BS), documento público asociado con la información del desempeño social que permite medir y evaluar el nivel alcanzado en un período, por medio de indicadores cualitativos y cuantitativos. La metodología de BS utilizado en esta investigación verifica el cumplimiento de los siete principios cooperativos establecidos por la Alianza Cooperativa Internacional (ACI) y se apoya en los análisis de las Macrodimensiones y Dimensiones tipificados en el modelo de BS de la Superintendencia de Economía Popular y Solidaria.

The present graduation paper entitle “Plane Geometry Didactic Guide focused on the didactic units of: history, lines, and angles for students of the Mathematics and Physics Major of the University of Cuenca,” is developed from a constructivist perspective, as an additional resource for the Mathematics Laboratory. It aims to be a textbook that is in accordance with the needs of the students of the first semester of this career. This paper consists of three chapters entitled Theoretical Framework, Statistical Framework, and the The Proposal. The first chapter or Theoretical Framework explains the conceptual basis from which the proposal is carried out; it emphasizes the implementation of the constructivist approach in teaching and learning Plane Geometry; lastly, it approaches an issue from which this graduation paper has beenstarted off: the academic performance of students. The second chapter, the statistical section, refers to the field research conducted to gather information to support the development of the proposal; the information obtained by means of a survey is displayed in tables and graphics which are followed by their interpretation. Finally, third chapter in which the didactic guide is elaborated from a constructivist perspective, and making emphases on the three phases of a class lesson: anticipation, building knowledge, and consolidation; these phases are present in every activity of the guide. And these activities aim to reinforce thelearning process, and try to increase the students’ academic performance.

Teaching strategies are the modular axes of classroom activities, explaining and establishing teachers' overall intentions. They allow to identify principles, criteria and procedures which constitue teachers' work and are closely related to outcome indicators, since classroom activities necessarily need to be performed in function and accordance to the expected learning behaviour of students. In this work, the correlation of teaching activities to students' performance in mathematics I curses in the Department of Computer and System Engineering Sciences at the University of Guayaquil was investigated. An ad hoc questionaire was applied to eight teachers identifying the teaching strategies applied: traditional strategies as well as constructivistic strategies focusing on process and knowledge.By means of the one factor ANOVA test, students’ academic performance in different courses was compared. Findings showed that courses of teachers who applied traditional teaching strategies have higher outcome means and those of teachers who applied constructivistic strategies were related to lower outcome means. Traditional strategies, although considered as being passive, are positively related with results in academic performances. Furthermore, process strategies showed to have a higher range in students' failures, whereas knowledge strategies presented an insignificative relation to academic achievements.

The problem in our proposal is the lack of textbooks and guides algebra with constructivist approach, which prepare students in grade exams Bachelor degree. The methods and procedures used to collect data were the statistics, through the survey that allowed us to display data in a way: reliable, tabular, graphical and percentage, where the need of a didactic guide is evidenced by the themes developed algebra issued by the Ministry of Education through INEVAL (National Institute for Educational evaluation). The results show the need for a guide for teachers with constructivist approach to the topics of Algebra exam grade Bachelor degree. This guide is structured as follows: anticipation (graphic organizers, brainstorming, concepts and stories), construction (comparative tables, problems of real life related to the student environment, educational videos, graphics and images), and consolidation of knowledge (recreational activities, quizzes and proposed exercises), thus would reach constructivism and meaningful learning, for better results in the degree examination.

Chapter 1, THEORETICAL is the first partof the project thatpresentsthe theoretical framework,approaching the problem fromthe educational field, allpedagogical trendssurrounding theproposal alsocontextualizationof the electrical partwill be themain theme of thethesis.Asthe main instrumenttic´sin developing the proposal, the various possibilities offered bythe Virtual Classroomaddressed. In Chapter 2, RESEARCH METHODOLOGYIn thischapterall the researchfieldusedto collect information ontheissues surroundingthe proposaldescribed. Usinga questionnaireofclosed questionsto allteachers fromthe areas ofphysics and chemistryis evaluated,to getthe perceptionthat teachers havethe problemsurrounding thesubjectunder study.The useof statistical tablesallows aquantitativeandqualitative interpretationof the weaknessesin students. In Chapter 3, THE PROPOSAL, consists ofa structure based onclassroomplanninggivenby the Ministryof Education,which clearlyshows itsinterest in the developmentof tic´sinthe learning process, with the helpavirtual classroom, the teacheris giventhe possibility to usetechnological means todevelop theirclasses, usingthe various toolsthat has avirtual classroom, for ittook thetopic forthe first block ofElectricitystudythe second year ofhigh schooloverallunified.

This thesis aims to adapt methods and techniques of study in mathematics area, specifically in the program block number 2 which involves the study of rational numbers to improve the academic performance of students in the eighth year of EGB of the Unidad Educativa Monseñor Leonidas Proaño Extensión Gualaceo, according to new regulations in education area. On the theoretical foundation the current situation of Blended Educational System of Ecuador described, due to the importance of adult education for Ecuadorian society; the importance of the subject of mathematics for the usefulness and necessityfor good social performance of everybody, also are developed the difficulties often have students in the mathematical learning, methods and study skills will be used in the development of the proposal. In the statistical phase the results of two instruments are shown by tables and graphs: Inquiry and Diagnostic Evaluation, whose results allows to know the reasons why learners interrupted their regular studies and the factors that influence an understanding in solving mathematical exercises. In the last chapter on the proposal, classes grounded in a social, pragmatic and constructivist model through the adaptation and application of methods and study to divert and assist teachers in the development of a dynamic class are developed to encourage easy understanding of mathematical content through experimental and thoughtful approach adult learner with the subject matter, applying introductory and evaluation tools to encourage and strengthen knowledge in students activities.

The topic Graphic Organizers to Strengthen the Learning of Physics in Sophomore High School Students emerges from the need of applying a new methodology for the teaching-learning process and assessment of Physics in orderto provide students with interactive classes. In chapter 1, the theoretical foundations will be developed, focusing on topics such as the Modern School, Constructivism, Didactics and its methods and strategies that allow the improvement of the teaching-learning process, highlighting the importance of graphic organizers during the learning process. In chapter 2, a statistical research on sophomore high school students in the province of Azuay was carried out. The intention was to demonstrate the lack of use of graphic organizers by Physics teachers in the class. Also, the lack of graphic organizers in the students’ manuals was proven; employing charts and statistical graphics. In chapter 3, forty graphic organizers related to Physics topics are presented. The organizers are divided into blocks, and a sample exercise is added to every organizer. Furthermore, block lesson plans are included to be a guide for the teacher as to how to employ the graphic organizers during the different stages of a class. Finally, the goal of using graphic organizers in Physics is to furnish students with a learning-study strategy and provide teachers with a new methodology for teaching and assessing Physics.

This paper deals with the graduation Difference academic performance in mathematics between urban and rural students in eighth Year of Basic Education in the canton Azogues. The same is divided into two parts: the first Theoretical Foundations, where concepts freely and rules implemented by the Ministry of Ecuador against different topics is presented, also contains goals to be according to the Design of Good living; The guidance curriculum, knowledge of students, the methodology used by teachers and their qualifications: Diagnosis in the second part, the research was conducted four major aspects. The diagnosis was made in four Azogues Canton Educational establishments, two urban: Luis Roberto Cordero and Rhodes; two rural Ezequiel Cárdenas (Guapán) and Javier Loyola. Studies in each facility allowing several conclusions are then compared.

TEACHING METHODS FOR TEACHING AND DERIVED LIMITS The thesis tries to implement alternative methods of teaching and derived limits is a topic covered in the new unified general baccalaureate (BGU) was implemented in Ecuador. The project consists of three chapters, then detailed each: Chapter 1, PRESENTATION AND DIAGNOSIS OF THE PROBLEM, is part of the project presented the difficulties in teaching these subjects. Displaying statistical tables and graphs that show the problem based on surveys of graduates (2012-2013) and teachers of the subject in the various mid-level institutions (high schools) in the city of Cuenca in which these contents are taught. In Chapter 2 THEORETICAL FOUNDATIONS, brief characteristics described prior knowledge students should have before beginning the study of limits and derivatives. It also presents the theoretical development of pedagogy to guide the project. In Chapter 3, PROPOSAL, comprise the various proposals (teaching materials, methodologies and software such as Derive) applied to it. In turn, this chapter is divided into LIMITS, DERIVATIVE AND APPLICATION OF THE DERIVATIVE. Note that the depth of each subject is compared to the last year of high school. It also highlights traditional activities such as games applied to this topic. Finally, the conclusions and recommendations made which is a personal contribution to this work.