**Any development of something in life implies having to climb levels; in the same way, it happens in the development of analytical abstraction; it becomes necessary to reach the lowest level of analytical abstraction and achieve that successful analytical development that leads us to place ourselves at the highest or superior levels of analytical abstraction**

**We are at the lowest level of analytical abstraction, when we develop the ability to abstract, discern or have understanding of our first academic conceptualization**

**Analytical training at an early age is necessary to reach our first level of development of analytical abstraction faster; educational entities, should have a great methodology and technology that allows establishing that the student has successfully achieved the first level of development of analytical abstraction**

**Lowest level of analytical abstraction**

**Medium levels of analytical abstraction**

**Higher levels of ****analytical ****abstraction**

**It should be noted that in most educational programs, mainly in the primary stage of student training, there is no analytical exercise; since, most of the educational programs are oriented to the descriptive memorization of data; of course, it is important that the student in his primary education knows everything descriptive about the world around us; for example, the description of animals, plants, rivers, lakes; but, today with all the technological advances, so much effort in memorization is not necessary; since any mobile device, in a matter of minutes, illustrates any person about any descriptive data; and furthermore, globally**

**In addition to memorization of descriptive data and basic operational methodologies in mathematics and other sciences; it would be important for educational centers to orient their programs towards analytical training at an early age; and thus, facilitate the student to reach faster the first level of analytical abstraction**

**student**

**Basic memorization and use of technology**

**Operational methodologies in science**

**Introduction to the arts, philosophy and theology**

**Basic analytical exercise**

**Reaching as soon as possible the first level of analytic abstraction should be a basic goal of every student’s life; we are now going to illustrate what it means to be situated at the first level of analytical abstraction; for this purpose, we will consider the exemplification of set theory**

**Developing the academic conceptualization of set theory is something fundamental in the academic life of every professional, regardless of the field of work**

**When we study set theory, we learn a number of set operational methodology, such as set union, intersection, symmetric difference; however, we learn to operate set theory satisfactorily, but we fail to reach the academic conceptualization of what a set is in mathematical set logic**

**We are going to analytically abstract what a set is, the first thing we must establish in the abstract is what is a set? a set does not have a specific form or description, it is simply a group of elements based on definition parameters; ****now ****we must consider two situations that can arise; which are, that it contains elements according to the definition parameters or simply, that it does not have elements**

**If it has no elements, then we call it the empty set.**

**If the set has elements, then we have to analytically infer how it is formed according to the definition parameters; but in addition, the analytical consideration of where we are going to consider the elements that belong to the set is necessary; then, we are going to call the universe, where all the elements are located; remember, that analytically the universe is everything that exists, including the sun, the moon, the planets, the galaxies and all the new stars in formation**

**Developing the analytical capacity to abstract all the elements that should belong to a set under analysis is essential, regardless of the professional field of action**

**3 levels of analytical abstraction well defined, it is necessary to scale**

**Still at the lowest level of analytic abstraction; the exemplification, corresponds to the set conceptualization in set logic; when we successfully, reach that first level of analytical abstraction, we have the analytical capacity to academically conceptualize what a set is and its efficient application**

**Conceptually, a set corresponds to a whole; that whole, must contain all the elements that belong to the set; when, we have not reached that first level of analytical abstraction, it will be common for us to leave elements out of the analysis; that is, we do not have the capacity to be able to abstract all the elements that in reality belong to the set under analysis**

**Regardless of our professional field of action, it is very common to carry out some type of analysis of something in particular; but, if we want to be successful professionals, it is necessary to reach the levels of analytical abstraction that allow us to develop the ability to carry out an analysis and a subsequent successful opinion**

**Suppose we are going to do the analysis and then give the opinion; Regarding the reason, for such low academic performance in the area of mathematics of primary school students in the Americas**

**Let us remember that today, due to technological progress, we can count on all the data from academic tests in the area of mathematics, for all students in the Americas; regardless, of whether they are public or private educational entities**

**Continuing with the exemplification of the analysis of the reason for such low mathematical performance in the Americas of the students of the primary area**

**By using the academic conceptualization of set logic, we realize that we are going to greatly simplify said analysis; without losing, the forcefulness in the analysis**

**We define the root set as the set A which represents the Americas; now, let’s define 4 subsets: A-1 A-2 A-3 A-4 where A-1 is the geographic area of North America, A-2 the geographic area of South America, A-3 the geographic area of Central America and A-4 represents the geographic area of Caribbean America**

**Now for each subset, we are going to define 3 sub-subsets; for exemplification purposes, we are going to focus on the area of Caribbean America; that is, the subset A-4 which we define 3 sub-subsets:**

**A-4-1 A-4-2 A-4-3 being A-4-1 all the professors who teach mathematics in the Caribbean area; being, A-4-2 all students who take courses in the area of mathematics in the Caribbean; and finally, A-4-3 all the methodologies used to teach mathematics knowledge in the Caribbean area; the analysis will be the same for the other subsets**

**Continuing with the exemplification of the analysis of the reason for such low mathematical performance in the Americas of the students of the primary area**

**Since we have defined the subsets; we must proceed, to the determination of the determining analytical factors in the problem of analysis**

**It is important to mention that it is necessary to have developed the necessary level of analytical abstraction; and thus, have the ability to infer the analytical factors to be considered; it becomes necessary, to consider 3 analytical factors:**

**Factor 1: teachers Factor 2: teaching methodology and Factor 3: students**

**Factor 1 teachers**

**Low analytical qualification and low mathematical experience**

**Lack of pedagogical preparation to transmit mathematical teaching**

**Lack of knowledge and updating of technological advances and virtual methodology**

**Factor 2 teaching methodology**

**Mass teaching still predominates through a blackboard and verbal explanation**

**There is no unification of the pedagogical technique to transmit mathematical teaching**

**There is no update; in terms of technological advances, to complement the methodology used to transmit mathematical teaching**

**Factor 3 the students**

**There is no necessary dedication and individual study time, to assimilate and master each mathematical topic**

**There is no classification of students by ability in the area of mathematics; and thus, can develop at a higher level of learning, students who have greater aptitudes****There is no pedagogical feedback and correction techniques; then, from a mathematical evaluation or exam; What predominates, is the low performance of the group mass**

**Part of any analytical abstraction is to develop the ability to analytically infer a favorable opinion; that is, a successful opinion, something that really solves the problem; and make it sustainable; in other words, something very strong and solid in terms of sustainability; the foregoing translates, into finding those key analytical points for the solution of the problem**

**Returning to the exemplification, we have taken the A-4 subset as a critical point, that is, Caribbean America; since, where the problem of low mathematical achievement in primary education is exacerbated, it is where there are not so many technological facilities and there is not a level of development that allows mathematical development in students; Due to the above, we can say that the greatest technological and development facilities are in North America, then in South America and then in Central America.**

**Develop a high capacity for analytical inference; it is power, to develop two analytical visions: the internal analytical vision and the external analytical vision; develop, the internal analytical vision corresponds to how much we can solve the problem, attacking the problem from within the analytical subset and developing the external analytical vision, is to attack the problem from outside the analytical ****subset**

**Subset ****A-4**

**Internal analytical ****view**

**External analytical view**

**Have reached a level of development in analytical abstraction; it implies, having developed the capacity to be able to solve a problem under analysis; helping each other, from the internal analytical vision and from the external analytical vision**

**By analytically inferring from the internal analytical view, we realize that the highest percentage of mathematics teachers receive training in the same educational cycle; we are going to understand, by educational cycle, everything related to the educational requirements in a specific geographical area; that is, how students are trained in educational establishments; which, in the near future, will be giving classes to new students; in other words, if students have low educational achievement, when they become teachers their ability level is relatively low**

**Due to the above, give the internal analytical vision, there is no forceful medicine to successfully solve the problem under analysis; for this reason, we do not see the need to focus all the analytical effort, from the external analytical vision**

**Regarding teachers in the area of mathematics:**

**It is necessary that they receive additional external training and preparation in the area of mathematics; which implies a new reclassification, according to the evaluation and classification carried out by an external committee, made up of high-level professors in the area of mathematics, regardless of their nationality**

**Regarding the methodology of mathematical teaching:**

**Technological updating is necessary in educational establishments; and thus, to be able to implement new teaching methodologies that are backed by technological advances; and thus, to be able to facilitate the assimilation of mathematical teaching**

**Regarding the students:**

**A classification based on analytical capabilities is necessary; and thus, to be able to give a greater knowledge or a greater mathematical preparation to the students who are with the greatest capacity to assimilate more analytical**

**The foregoing implies a classification of mathematics teachers with respect to the students with the highest level of analytical skills; that is, the teachers with the greatest mathematical capacity should be focused on the students with the highest level of capacity to assimilate mathematics**

**As for the rest of the students, they must receive basic mathematical training and they need to be oriented towards teachers with the highest pedagogical level; as well as, the support of all technological advances that facilitate the transmission of mathematical education to those students who do not have the natural abilities to assimilate analytical sciences**

**Now we are going to exemplify the average level of development in analytical abstraction; as mentioned above, the first effort of analytical exercise is to reach the first level of development; at this level, which is the lowest of development, it is possible that we always have quantitative data on the different problems to be solved or points of analysis; however, as we progress in our development of analytical abstraction, we develop the ability to infer analytically with great precision; still, without having any quantitative data; develop that capacity, is to reach a higher level of development of analytical capacity**

**At the middle level of analytical abstraction development, we develop the ability to infer analytically; even when, we do not have quantitative data in sight; we are going to consider, the relative movements of everything that exists in the universe; we start analytically, that everything that exists in the universe is in constant motion**

**The first thing that we are going to infer analytically is the rotational movement of the planet earth; as a consequence, of that relative movement; we can infer, day and night; in other words, by being aware that day and night exist continuously; then we infer, that the planet earth has a rotation movement on its own axis**

**It is possible to see day and night**

**Now we are going to infer analytically, the movement of the planet earth around the sun; then we infer, the seasons of the year and we realize that summer appears, then winter; as well as, the heat is stronger as the planet is closer to the sun and the greatest cold occurs when the planet is further from the sun in its elliptical path around it continuously**

**It is possible to see summer and winter**

**Now we infer analytically, that the entire solar system; that is, the sun, the nine planets and other celestial bodies that make it up, also follow an elliptical path around the milky way; that is, the galaxy to which our solar system belongs; analytical inference, leads us to predict that any change in generational time is linked to the trajectory of the solar system around the milky way; for this reason, in future times we live something very similar to what our generational ancestors lived**

**It is no longer possible to count on something face-to-face or seen, everything is analytical**

**The most interesting of the above is that some ancient civilizations had this high degree of development of analytical abstraction; achieving, calculate with great precision, the time it takes for the solar system to go around the center of attraction of the milky way; that is, our galaxy**

**If we infer analytically, that everything in the universe is in constant motion; then, it is also possible to affirm that both the milky way; just as, all the other galaxies also follow an elliptical trajectory, about some center of attraction in the universe; the foregoing leads us to conclude that the dimensions of the universe are superlatively infinite, which exceeds all human rational capacity**

**It ****is time to analytically infer at the higher levels of development of analytical abstraction; reach, a higher level of analytical abstraction; It will be, the result of a great analytical exercise throughout our successful academic and work life; from academic analytical problems, solved in the basic sciences such as mathematics, physics, chemistry; as well as, all the analytical exercise in the resolution of academic problems in the superior sciences; such as, differential and integral mathematical calculation, descriptive geometry, statics and analysis of resistance of materials, dynamics, thermodynamics, hydraulics and others; and above all, the different working analytical problems and other analytical inferences**

**To exemplify the most analytical and abstract level of development, we are going to infer analytically about the dimensional worlds; let us remember, that everything that exists in the universe is subject to a volume; therefore, only the 3D dimensional world is where it is and we can see with the sense of sight everything that exists or as far as we can see in the universe; still, using all the existing technological advances**

**We start by inferring a 1D dimensional world in which we associate a dimension to geometric shapes; but, that at the moment of being in 1D they will only appear as a point or a set of analytical points, defining straight lines and analytical vectors in unison; that is, only one at a time; since, the 1D dimensional world does not exist the space or what we call the areas**

**1D is associated with analytical line**

**Now we analytically infer the 2D dimensional world in which the two dimensions are associated with the formation of analytical spaces; where, specific analytic geometric areas begin to appear; let’s remember, both in 1D and 2D everything is analytical; since, to be able to see something we necessarily need the sense of sight; which, is only in 3D**

**2D is associated with analytical areas**

**To analytically infer the 3D dimensional world is simply to observe everything that surrounds us; since, the entire universe is immersed in a 3D dimensional world**

**We are now going to infer the more analytical dimensional worlds; we associate, the 4D dimensional world with time; only, human persons are aware of time; since, as time passes, the person ages and in the end dies; it is that moment, it ceases to be associated with a 4D dimensional world since time only exists, as long as there is life**

**4D is associated with analytical time**

**The 5D dimensional world can only be inferred when there exists in a male and female couple, the perfect complement between the masculine and the feminine; this is, only achieved by living true love or authentic love; that, privileged and superlative feeling that is enduring, never fades; moreover, it grows day by day and never stops growing and becoming stronger; then, we infer that the only thing that exists in the 5D dimensional world is true happiness or authentic happiness which is a privilege for the couple man and woman who live true love; in other words, in 5D only eternally in love couples are associated; it is not possible, that someone individual can be aware of the 5D dimensional world**

**5D is associated with happiness**

**Now the most analytical and abstract corresponds to the 6D dimensional world, this dimensional world is reserved only for people who live the true faith or the authentic spiritual faith; which, entails a totally harmonious relationship between the created being and the supreme being, that is, the only creator of everything that exists; we infer, that the only thing that exists in 6D is eternal glory; that is, to live and develop authentic spiritual faith is to achieve ****eternity**

**6D = eternity**