Analysis of documents and curricular designs
2. a) After reading the Introduction to the CBC document for Basic General Education, indicate:
- The notion that is used of CBC.
The CBC constitute the definition of the set of relevant knowledge that will integrate the teaching process of the entire country. CBCs are the basic matrix for a national cultural project; matrix from which, each jurisdiction of the Educational System will continue updating its own curricular guidelines or designs and will give way, in turn, to diverse but compatible institutional curricular projects.
- Organization of the document.
The CBC for Basic General Education appear in chapters, which constitute a form of organization of the contents based on their belonging to certain scientific or cultural fields. The chapters are: Language, Mathematics, Natural Sciences, Social Sciences, Technology, Art Education, Physical Education and Ethical and Citizen Training.
Within each chapter, the CBC are presented grouped into blocks, which propose a content organization taking into account the logic of the disciplines. Each block has a name that states the thematic axis around which these contents were organized. These will be: the concepts of each discipline, the procedures, the attitudes and the values linked to this knowledge.
Formally, each chapter of the CBC consists of an “Introduction”, on which the inclusion of the respective CBC is based, a proposal of “Organization”, in which the block structure chosen to present the CBC is reported; a proposal of "Characterization" of those blocks; a proposal of "Scopes" of the CBC per block and per cycle of Basic General Education, and the "Basic Documentation".
The “Characterization” proposal includes for each block: an explanatory synthesis of the contents and their gradualness; the expectations of achievements, which express the competences that students are expected to achieve at the end of Basic General Education, and the links of the block with the other chapters of the CBC.
The proposal of "Scopes" of the CBC per block and per cycle is presented in the form of a table to allow a horizontal reading that relates the contents throughout the three cycles of Basic General Education.
2. b) From the reading of the chapter corresponding to the profile of your training (Mathematics) and that you can dictate in the Third Cycle.
- The chapter appears organized in blocks of content. What elements structure each of these blocks?
The CBC of Mathematics for the EGB have been organized in eight blocks:
Block 1: Number.
Block 2: Operations.
Block 3: Graphic and algebraic language.
Block 4: Geometric Notions.
Block 5: Measurements.
Block 6: Notions of statistics and probability.
Block 7: Procedures related to mathematical tasks.
Block 8: General attitudes related to mathematical tasks.
Blocks 7 (Procedures) and 8 (Attitudes) must be permanently linked to the contents of blocks 1 to 6.
- What does the explanatory synthesis and the achievement expectations express?
By means of the explanatory synthesis, the document establishes ways of approaching the contents of the different blocks, their depth, relationships between the contents of the different blocks, examples of their application, graduability of their deepening throughout the Cycle. The pretensions of learning are established. It emphasizes not only calculation forms or techniques but also an understanding of operations and signs. The most specific procedures related to the theme of each block are detailed.
In the synthesis of each block there are no concepts, since it is not the intention that students be given a course in logic, heuristics or mathematical language, but rather through the implementation of their procedures and the reflection that such practice provokes., the student understands the logical foundations on which they are based.
Procedures are linked to problem solving, reasoning, and communication.
Likewise, a set of latitudinal contents tending to the formation of critical thinking is described. The selected attitudes contents are: Personal Development; Socio-community development; Development of scientific-technological knowledge and Development of expression and communication.
The expectations of achievement express what the students should achieve throughout the Cycle, expressed through terms such as: Recognize and use; understand and know how to use; relate; know; distinguish; know how to operate; organize, process and interpret, express and communicate. Expressing the aspirations that the Educational System has in relation to the competences that the student must achieve throughout the Cycle.
- What are the characteristics of the content scope proposal?
The content scope proposal for the 3rd. Cycle establishes for Blocks 1 to 6 the Conceptual and Procedural Contents for each one of them and for Block 7 it establishes: Procedures linked to the resolution of problems; the Procedures linked to reasoning and the Procedures linked to communication.
3. a) Read and comment on the initial sections of the CBC for teaching at the polymodal level:
- Functions of Polymodal Education.
The education of young people has sought to guarantee three basic functions: citizen training, preparation to pursue higher education, and training to carry out work activities.
Taking these aspects into account, Polymodal Education must fulfill the following functions in an integrated and equivalent way:
Ethical and civic function: to provide students with training that deepens and develops values and competences linked to the elaboration of personal life projects and integration into society as responsible, critical and supportive personnel.
Propedeutic function: to guarantee students a solid formation that allows them to continue any type of higher studies developing permanent learning capacities.
Function of preparation for productive life: to offer students an orientation towards broad fields of the world of work, strengthening the skills that allow them to adapt flexibly to their changes and take advantage of their possibilities.
- Fields in which training at the level is organized: characterization.
Polymodal Education will fulfill the aforementioned functions through two types of training: a General Foundation Training (FGF) that will take up, with higher levels of complexity and depth, the contents of Basic General Education; and a Oriented Training (FO) that will develop, contextualize and specify the contents of the General Foundation Training, attending to different fields of knowledge and social and productive work.
Resuming the contents of the EGB, the General Foundation Training ensures a solid base of common competencies that are required to participate actively, reflectively and critically in the various areas of social life. This training should be conceived as a consolidation and deepening of the set of skills that students have developed during the compulsory cycle of teaching.
Through Oriented Training, students will develop the contents of the General Foundation training, contextualizing them in certain fields of knowledge and social and productive work.
- Modalities adopted by the level: characterization.
The General Foundation Formation and the Oriented Formation give rise to five Modalities:
Natural Sciences modality.
Modality Economy and Management of Organizations.
Humanities and Social Sciences modality.
Modality Production of Goods and Services.
Communication, Arts and Design modality.
These modalities respond to the need to open alternative spaces to contain the varied interests of adolescents and the needs of the social and productive context. Through them, the diversity and complexity of regional and community cultures are contemplated, organizing their problems in fields of knowledge and work defined in a broad sense, which allow the development of multipurpose training.
These fields should not be conceived as closed spaces that differ from each other because all the contents are exclusive to them, although those that are most relevant to the field that defines the identity of the modality are emphasized. In this sense, all the modalities will share an orientation that will be, at the same time, humanistic, social, scientific and technical, although they will organize and develop the contents based on the requirements of the field that differentiates each modality from the others, and the regional and community contexts in which the institutions carry out their activity.
The Oriented Training of the Natural Sciences Modality will focus, integrate and develop the contents of the General Foundation Training, emphasizing from a multidisciplinary perspective, access to content referring to the processes of nature to strengthen students' abilities to understand them, and to interact with them in a responsible way, through different types of activities.
The Oriented Training of the Economy and Management Modality of organizations will focus, integrate and develop the contents of the General Foundation Training, emphasizing from a multidisciplinary perspective, access to content related to socio-economic and organizational processes to strengthen students' abilities to understand them, to participate, intervene and operate in and with them.
The Oriented Training of the Humanities and Social Sciences Modality will focus, integrate and develop the contents of the General Foundation Training, paying special attention to the understanding and interpretation of the processes of personal development and interaction, organization, continuity and transformation of the sociocultural world from a multidisciplinary perspective to strengthen the capacities of participation and reflective intervention in it.
The Oriented Training of the Goods and Services Productions Mode will focus, integrate and develop the contents of the General Foundation Training, paying special attention to knowledge and problem solving in the production processes, to the activities that comprise them - design, transformation, control, management, commercialization, distribution - and to the environmental dimensions and working conditions that they involve.
The Oriented Training of the Communication, Arts and Design Mode will focus, integrate and develop the contents of the General Foundation Training, paying special attention to the understanding of the communicative, expressive and artistic production processes, to the development of aesthetic appreciation capacities, to creative use of the different expressive-communicational languages and mastery of the technical supports involved in them.
3. b) Starting from the reading of the chapter closest to your professional profile (Mathematics), indicate which articulations regarding the expectations of achievement and contents are established between this proposal and that of EGB 3.
The joints observed are:
In the Contents:
- Block 1 Polymodal (Numbers and Functions)
with: Block 1 (Numbers), Block 2 (Operations); Block 3 (Graphic and Algebraic Language); Block 5 (Measurements); Block 7 (Procedures Related to Mathematical Chores) and Block 8 (General Attitudes Related to Mathematical Chores) of the CBC Mathematics for EGB 3.
- Block 2 Polymodal (Algebra and Geometry)
with: Block 2 (Operations); Block 3 (Graphic and Algebraic Language); Block 4 (Geometric Notions); Block 7 (Procedures Related to Mathematical Chores) and Block 8 (General Attitudes Related to Mathematical Chores) of the CBC Mathematics for EGB 3.
- Block 3 Polymodal (Statistics and Probability)
with: Block 2 (Operations); Block 3 (Graphic and Algebraic Language); Block 5 (Measurements); Block 6 (Notions of Statistics and Probability); Block 7 (Procedures Related to Mathematical Chores) and Block 8 (General Attitudes Related to Mathematical Chores) of the CBC Mathematics for EGB 3.
- Block 4 Polymodal (Procedural Contents of the mathematical task)
with: Block 7 (Procedures Related to Mathematical Chores) and Block 8 (General Attitudes Related to Mathematical Chores) of the CBC Mathematics for EGB 3.
- Block 5 Polymodal (Attitudinal Contents)
with: Block 8 (General Attitudes Related to Mathematical Chores) of the CBC Mathematics for EGB 3.
In Achievement Expectations:
- Block 1 Polymodal (Numbers and Functions)
with: Block 1 (Numbers); Block 2 (Operations); Block 3 (Graphic and Algebraic Language); Block 4 (Geometric Notions); Block 7 (Procedures Related to Mathematical Chores) and Block 8 (Attitudes Related to Mathematical Chores) of the CBC Mathematics for EGB 3.
- Block 2 Polymodal (Algebra and Geometry)
with: Block 3 (Graphic and Algebraic Language); Block 4 (Notions of Geometry); Block 7 (Procedures Related to Mathematical Chores) and Block 8 (Attitudes Related to Mathematical Chores) of the CBC Mathematics for EGB 3.
- Block 3 Polymodal (Statistics and Probability)
with: Block 3 (Graphic and Algebraic Language); Block 6 (Notions of Statistics and Probability); Block 7 (Procedures Related to Mathematical Chores) and Block 8 (Attitudes Related to Mathematical Chores) of the CBC Mathematics for EGB 3.
- Block 4 Polymodal (Procedural Contents of the mathematical task)
with: Block 7 (Procedures Related to Mathematical Chores) and Block 8 (Attitudes Related to Mathematical Chores) of the CBC Mathematics for EGB 3.
- Block 5 Polymodal (Attitudinal Contents)
with: Block 8 (Mathematical Activities Related Attitudes) of the CBC Mathematics for EGB 3.
4. Work on the jurisdictional curricular design for the area (Mathematics) corresponding to your professional profile for the Polymodal level - Modality Production of Goods and Services. Record in writing the result of your boarding:
- What approach do you take for the Level? Justify. Does it contribute something new in relation to the understanding of the field of knowledge itself? What aspects?
The approach adopted is based on the power of Mathematics as a modeling agent of reality, fundamentally through functions, equations, inequalities, Statistics and Probability. It is very important to put the student in contact with the applications of mathematical knowledge, so that they can assess the power of the models, notice their limitations and accept their conclusions and predictions always within a framework of reasonableness. With this approach, the contents do not appear to students “in their pure state”, but rather contextualized and based on real needs, linked whenever possible to the tasks of the modality.
Currently the accent is placed on the meaning and meaning of a notion, and on the importance of its applications.
It is essential for the integration of the youngest members to our society the acquisition of a mathematical training that allows them to pose and solve everyday problems, develop the ability to explore, formulate hypotheses, reason logically, predict, analyze reality, produce ideas and knowledge new, understand situations and information and adapt to changing contexts. In addition to the instrumental value of Mathematics, mathematical knowledge is important in itself, because it constitutes an ideal field for students to exercise thought, thus contributing to their intellectual development.
For this reason, it is convenient to work Mathematics with the students as a process of search, of trials and errors that pursues the foundation of their methods and the construction of meanings through problem solving. The situations must be related to the Modality in which one works.
Thus, it aims at a "comprehensive, comprehensive, cognitive and procedural" Mathematics. In our opinion, this would be the novel aspect regarding the understanding of the field of knowledge itself, hoping that the Professors of the Subject would interpret it as such, in order to really contextualize the knowledge. This would imply that these teachers must know the field of application of Mathematics in the Modality where they work.
We also highlight as something new and necessary the concept that Mathematics Education is necessarily ethical. We cannot think of learning if it is not with, by and for others. All knowledge implies a degree of social commitment from the moment we set ourselves the goal of learning to understand and transform reality.
- Establish content relationships between the Third Cycle and Polimodal. Build a network of key concepts for teaching. Work on the jurisdictional design for EGB 3 and Polimodal and the CBC of the Nation and Province.
In order to simplify the analysis, simple and direct relationships have been established between the contents considered key to teaching, which does not mean that, obviously, a much more complex plot is presented that, due to space, is not established in this document.
| EGB 3 content | |
| 01 | Numbers: Scientific Notation. Rational numbers. Irrational numbers. Identification of equivalent forms of writing of a number. Approximation of Real Numbers. Rational numbers |
| 02 | Operations: Rational Numbers. Power. Proportionality. Trigonometric Ratios. |
| 03 | Graphic and Algebraic Language: Algebraic Expressions. Formulas, equalities and equations. Numerical functions. Systems of Equations: Meaning, Graphic and Analytical Resolution. |
| 04 | Geometric notions. Reference Systems for the location of points. Figures. Bodies. Vectors. |
| 05 | Measurements: Area. Volume. Units The Trigonometric Reasons and the Pythagorean Theorem and its Application. Estimation, measurement and operations with quantities of different magnitudes. Use of measuring and geometry instruments. |
| 06 | Notions of Statistics and Probability: Elementary notions of statistics. Probability. |
| 07 | Procedures: Search for reliable sources of information. Generalization of solutions and results. Use of appropriate arithmetic, geometric, algebraic and statistical vocabulary. |
| Polymodal Contents | Relate to the numbers assigned to the EGB 3 content |
| Numbers: Real Numbers: Operations. Decimal approximation. Rounding and truncation techniques. Complex Numbers: binomial and trigonometric form. | 01 and 02 |
| Functions: Operations. Polynomial functions. Trigonometric functions. Limit of functions. Derivatives. Integral | 02 and 05 |
| Algebra and Geometry: Equations and Inequalities: Forms of Resolution. Vectors in the plane and in the space. Operations. Flat Curves. | 03 and 04 |
| Statistics and Probabilities: Statistical data: Collection, classification, analysis and representation. Probabilities: Conditional probability and independence. Probability Distributions. | 03; 04; 05 and 06 |
| Procedural Contents: Development of notation and vocabulary, elaboration of definitions. Relationships, generalizations, particularizations and applications of results. Use of appropriate vocabulary and notation. Description of procedures and results. | 05 |
As a complement to this work, we elaborated a reflection referring to the text “Curriculum: Crisis, Myth and Perspectives” by Alicia de Alba.
In the brief but comprehensive pages of the regency work, we can see that the subject of the curriculum goes far beyond a technical educational problem, that in reality in this field of confrontation what is at stake is the destiny of the entire society. This led to controversy within the study group and the following reflections and comments emerged.
One of the aspects that we found most interesting when dealing with the question of the curriculum is the difference between the structural-formal aspects and the procedural-practical aspects. Although resistance actions, through negotiation and struggle, lead to the inclusion in the curriculum of some values of non-hegemonic groups, they do so as subordinates. We believe that the true battlefront is in the institutional sphere and more specifically in the classroom. This is where the curriculum is put into practice and generates resistance attitudes, both by teachers and students. It is here that some, instead of passively following the candlelight, extinguish it.
The collapse of the socialist world and the lack of utopias, has led some authors to speak of the end of history. We do not believe that this is so, it may have ended a type of military political confrontation for world domination, but we are far from having reached peace. Capitalism has not solved man's problems either, and today more than half of humanity struggles in poverty, even if the euphemism of calling these nations emerging or developing countries is used, as if the first world were waiting to share a common destiny. The gap between rich and poor, be they countries or social classes the terms of the comparison, widens more and more, making the future of both uncertain.
These social problems, together with the environmental and ecological ones, make the struggles of the 21st century more important than the great wars fought in the last century. Not the confrontation for the domination of the planet by a block of countries, it is the fight for the salvation of our world, for the survival of all humanity. That is why it is essential to include environmental and social aspects in the curriculum with an ecumenical idea: we are one single people on a small planet that we are determined to destroy. In these circumstances, no one can save himself, it is useless to throw others out of the boat, the only alternative is to save everyone.
This is the new utopia that those who have become aware of must fight for, and this we consider to be the fundamental fight that must take place around the curriculum. Today more than ever, it is utopia that we must turn into reality, or what will become reality are the words of the poet for whom life without utopia is only an essay for death.
Another aspect of great importance, and which is related to what has been said so far, is that of diversity, in all its senses, personally, ethnically, culturally. Of course, here the resistance to include these issues in the curriculum is from the ruling classes, who are the ones who define normality, which of course is them, the rest, be they social class or nations, are the different. Much is said in the discourses of equality, integration, native peoples, but little is what is concretized in practice. And in this we consider it necessary to banish the word tolerance, very fashionable nowadays and which is given a positive meaning that we think does not have it. Whoever says to tolerate is in fact implicitly marking the other's annoying presence. It is essential to create the ecumenical sense that we were talking about,give a priority place within the curriculum to these topics.
From what has been said so far, the importance of the participation of all the social actors in curricular determination can be deduced, in order to introduce into the curriculum the values of that majority, silent or silenced, that normally cannot be heard. It is necessary that this social subject, through its grassroots organizations, manifests itself to introduce into the discussion on education the quota of reality so necessary for a correct formulation of the curriculum. What we normally see is a controversy between the dominant groups and the intellectual groups considered progressive, but both are very far from the daily reality that the vast majority of our peoples live, or rather suffer.
So far these reflections, which more than a comment on educational issues, are a plea for a better world.
