The relationship between mathematics education and culture

the relationship between mathematics education and culture

cally to this Special Issue of Educational Studies in Mathematics. There have been two lum and its relationship with the home culture of the child. Mathematics. relationships between culture and mathematical cognition. Their analysis covers two Developmental psychological research into mathematics learning in. This paper presents the results of a series of analyses of educational situations involving cultural issues. Of particular significance are the ideas that all cultural.

Methods of teaching mathematics include the following: Games can motivate students to improve skills that are usually learned by rote. In "Number Bingo," players roll 3 dice, then perform basic mathematical operations on those numbers to get a new number, which they cover on the board trying to cover 4 squares in a row.

Computer-based math an approach based around use of mathematical software as the primary tool of computation. Mobile applications have also been developed to help students learn mathematics.

Starts with arithmetic and is followed by Euclidean geometry and elementary algebra taught concurrently. Requires the instructor to be well informed about elementary mathematicssince didactic and curriculum decisions are often dictated by the logic of the subject rather than pedagogical considerations. Other methods emerge by emphasizing some aspects of this approach. Provides more human interest than the conventional approach. Adopted in the US as a response to the challenge of early Soviet technical superiority in space, it began to be challenged in the late s.

The New Math method was the topic of one of Tom Lehrer 's most popular parody songs, with his introductory remarks to the song: The problems can range from simple word problems to problems from international mathematics competitions such as the International Mathematical Olympiad.

Problem solving is used as a means to build new mathematical knowledge, typically by building on students' prior understandings. Mathematical problems that are fun can motivate students to learn mathematics and can increase enjoyment of mathematics. Uses class topics to solve everyday problems and relates the topic to current events. A derisory term is drill and kill.

In traditional educationrote learning is used to teach multiplication tablesdefinitions, formulas, and other aspects of mathematics. Content and age levels[ edit ] Different levels of mathematics are taught at different ages and in somewhat different sequences in different countries.

Sometimes a class may be taught at an earlier age than typical as a special or honors class. Elementary mathematics in most countries is taught in a similar fashion, though there are differences. In the United States fractions are typically taught starting from 1st grade, whereas in other countries they are usually taught later, since the metric system does not require young children to be familiar with them.

In most of the U. Mathematics in most other countries and in a few U. Students in science-oriented curricula typically study differential calculus and trigonometry at age 16—17 and integral calculuscomplex numbersanalytic geometryexponential and logarithmic functionsand infinite series in their final year of secondary school.

Probability and statistics may be taught in secondary education classes. Science and engineering students in colleges and universities may be required to take multivariable calculusdifferential equationslinear algebra. Applied mathematics is also used in specific majors; for example, civil engineers may be required to study fluid mechanics[12] while "math for computer science" might include graph theorypermutationprobability, and proofs. Standards[ edit ] Throughout most of history, standards for mathematics education were set locally, by individual schools or teachers, depending on the levels of achievement that were relevant to, realistic for, and considered socially appropriate for their pupils.

In modern times, there has been a move towards regional or national standards, usually under the umbrella of a wider standard school curriculum. In Englandfor example, standards for mathematics education are set as part of the National Curriculum for England, [14] while Scotland maintains its own educational system.

Ma summarised the research of others who found, based on nationwide data, that students with higher scores on standardised mathematics tests had taken more mathematics courses in high school. This led some states to require three years of mathematics instead of two. Inthey released Curriculum Focal Points, which recommend the most important mathematical topics for each grade level through grade 8.

However, these standards are enforced as American states and Canadian provinces choose. A US state's adoption of the Common Core State Standards in mathematics is at the discretion of the state, and is not mandated by the Federal Government. The MCTM also offers membership opportunities to teachers and future teachers so they can stay up to date on the changes in math educational standards.

Please help rewrite this section from a descriptive, neutral point of viewand remove advice or instruction. April Learn how and when to remove this template message "Robust, useful theories of classroom teaching do not yet exist".

Mathematics education

The following results are examples of some of the current findings in the field of mathematics education: Important results [19] One of the strongest results in recent research is that the most important feature in effective teaching is giving students "opportunity to learn". Teachers can set expectations, time, kinds of tasks, questions, acceptable answers, and type of discussions that will influence students' opportunity to learn. This must involve both skill efficiency and conceptual understanding.

Conceptual understanding [19] Two of the most important features of teaching in the promotion of conceptual understanding are attending explicitly to concepts and allowing students to struggle with important mathematics. Both of these features have been confirmed through a wide variety of studies.

Explicit attention to concepts involves making connections between facts, procedures and ideas. This is often seen as one of the strong points in mathematics teaching in East Asian countries, where teachers typically devote about half of their time to making connections.

At the other extreme is the U. Deliberate, productive struggle with mathematical ideas refers to the fact that when students exert effort with important mathematical ideas, even if this struggle initially involves confusion and errors, the end result is greater learning.

This has been shown to be true whether the struggle is due to challenging, well-implemented teaching, or due to faulty teaching the students must struggle to make sense of. Formative assessment [21] Formative assessment is both the best and cheapest way to boost student achievement, student engagement and teacher professional satisfaction. Results surpass those of reducing class size or increasing teachers' content knowledge. Effective assessment is based on clarifying what students should know, creating appropriate activities to obtain the evidence needed, giving good feedback, encouraging students to take control of their learning and letting students be resources for one another.

Homework [22] Homework which leads students to practice past lessons or prepare future lessons are more effective than those going over today's lesson. Students benefit from feedback. Students with learning disabilities or low motivation may profit from rewards. That is to say, who transcends the impulse to survive. The actions for transcendence, which always accompany the actions for survival, have their effect on reality, creating new interpretations and uses of natural and artificial reality, modifying it by the introduction of new facts, artifacts and mentifacts.

Knowledge is the producer of knowing, which will be decisive for action. Consequently, it is in the behavior, in the practice, in the doing that one evaluates, redefines and reconstructs knowledge. Among the various dimensions of the acquisition of knowledge we have highlighted four, which are the more recognized and interpreted in the theories of knowledge, namely, the sensorial, the intuitive, the emotional, and the rational.

Granting a point to disciplinary classifications, we could say that religious knowledge is favored by the intuitive and emotional dimensions, whereas scientific knowledge is favored by the rational, and the emotional prevails in the arts.

Naturally, these dimensions cannot be dichotomized or ranked, but they are complementary. So, there is no interruption, no dichotomy between knowing and doing, there is no priorization among them, nor is there any dominance among the several dimension of the process. Everything complements in a whole - the behavior - that has as its result the knowledge. Nobody expresses better this complementarity than the renowned Norwegian mathematician Sophus Lie, cited by Arild Stubhaug: From the individual to the collective The present as an interface between the past and the future manifests itself through action.

The present is thus identified with behavior, it has the same dynamics of behavior, that is, it feeds on the past, it is the result of the history of the individual and of the collective, of prior knowledge, individual and collective, conditioned by the projection of the individual into the future.

All from the information afforded by reality, therefore by the present. Inside reality all past facts are stored that inform the individual. Information is processed by the individual and results in strategies for action, which will originate new facts artifacts or mentifactswhich are incorporated into reality, obviously modifying it, getting stored in the collection of facts and events that constitute it.

Reality is therefore in relentless modification. The past thus projects itself, through the mediation of the individuals, into the future. Rethinking the dimen-sionality of the instant gives life, including here the "instants" of birth and death, a character of continuity, of fusion of past and future in each instant. Thence we recognize that there cannot be a frozen present, just as there cannot be a static action, just as there is no behavior without an instantaneous feedback evaluation that results from its effect.

We can then see behavior as the link between the reality that informs and the action that modifies it. This ability transmits itself, and accumulates horizontally in the relationship with others, contemporaries, through communications, and vertically, from each individual to himself memory and from each generation to the next historical memory. Notice that what we call memory is of the same nature as the information mechanisms associated to the senses, to genetic information, and to emotional mechanisms, and retrieve the experiences lived by an individual in the past.

Therefore, they all incorporate into reality and inform that individual in the same way that the other facts of reality do. The individual is not sole. There are billions of other individuals of the same species Homo sapiens sapiens with the same life cycle, and billions of individuals of other species going through a life cycle specific to each species, but essentially similar to the one showed in the figure above.

The process of producing knowledge as action is enriched by the exchange with others immersed in the same process, through what we call communication. The discovery of the other and of others, present or distant, contemporary or from the past, is essential for the phenomenon of life. Everyone is incessantly contributing his or her share to modify reality.

the relationship between mathematics education and culture

Every individual is inserted into a cosmic reality, as a link between a whole history, from the beginning of time and things, that is, from a big bang or the like, and the present moment, the here and now.

All experiences from the past, either recognized and identified or not, constitute reality in its totality and determine the behavior of each individual. His action results from the processing of retrieved information. Those include the experiences of each individual and those lived by others, in their totality. The retrieval of those experiences individual memory, cultural memory, genetic memory constitutes one of the challenges of psychoanalysis, of history and of many other sciences.

It constitutes indeed the basis of certain modes of behavior values and knowledge particularly the arts and religions. In a temporal duality, these same aspects of behavior manifest themselves in the strategies of action that will result in new facts - artifacts and mentifacts - that shall take place in the future, and that, once performed, shall be incorporated into reality. This is the sense of transcendence I referred to above. Although the mechanisms for capturing information and processing it, defining strategies for action, are absolutely individual, and keep themselves as such, they are enriched by the exchange and by communication, which is effectively a pact contract between individuals.

The establishment of this pact is a phenomenon essential for life. In the human species, this pact allows the definition of strategies for common action.

So, through communication new actions can be produced desirable to both, and actions can also be inhibited, that is, in-actions can be produced undesirable to one of the parts or to both. Each individual has these mechanisms and that is what maintains the individuality and identity of each being, although they balance actions and in-actions, which make it possible what we identify as the living together. The knowledge produced by the common interaction resulting from social communication will be a complex of codes and symbols, intellectually and socially organized to constitute what we call culture.

Culture is what will allow life in society. When societies, and therefore cultural systems, meet and are put in mutual contact they are subjected to a dynamics of interaction that produces an intercultural behavior manifested in groups of individuals, in communities, in tribes, and in societies as a whole. Interculturality has been intensifying throughout the history of mankind. The ethnomathematics program The exposition above synthesizes the theoretical fundamentals that serve as basis for a research program on the generation, intellectual organization, social organization, and diffusion of knowledge.

In the academic jargon, we could call it an interdisciplinary program spanning what constitutes the domain of the so-called cognitive sciences, of epistemology, history, sociology, and diffusion. By using, in a true etymological license, the roots "tics", "matema" and "ethno", I originated my conceptualization of Ethnomathematics. Naturally, in all cultures and in all times, knowledge that is generated by the need for an answer to distinct problems and situations is subordinated to a natural, social, and cultural context.

Hence we call what we have described above the Ethnomathematics Program. The name suggests the corpus of knowledge recognized academically as Mathematics. In all cultures we can find manifestations related to and even identified as what we call today mathematics processes of organization, classification, counting, measuring, inferencegenerally merged or hardly distinguishable from other forms, today identified as art, religion, music, techniques, sciences.

They all appear at a first stage of the history of mankind and of the life of each one of us, indistinguishable as forms of knowledge. We live in a period in which the means of capturing information, and the processing of information by each individual are found in the communications and information technology, auxiliary instruments previously unimaginable.

The interaction between individuals also finds in teleinformatics a great potential, still difficult to gauge, for generating actions in common. It can be seen in some cases the predominance of one form over another, sometimes the substitution of one form by another, and even the suppression and total elimination of some form, but in most cases the result is the production of new cultural forms, identified with modernity.

Still, dominated by emotional tensions, the relations between individuals from a same culture intracultural and above all between indi-viduals from different cultures intercultural represent the creative potential of the species. Just as biodiversity represents the way to the appearance of new species, in cultural diversity resides the creative potential of mankind. The importance of intercultural relations has been recognized. But unfortunately there is still reluctance to recognize intracultural relations in education.

Children are still placed in series according to age, the same curriculum is still offered for a given series, and one even hears absurd proposals for a national curriculum. And the even greater absurd of evaluating groups of individuals with standardized tests. It is effectively an attempt to pasteurize the new generations!

The plurality of mass communication media, aided by improved transportation, has taken intercultural relations to truly planetary dimensions. A new era thus begins, opening huge possibilities of behavior and planetary knowledge, with unprecedented results for the understanding and harmony of all mankind.

We should say no to the biological or cultural homogenization of the species, but yes to the harmonious living together of the different, through an ethics of mutual respect, of solidarity and cooperation. Of course, there have always been, and now will be more easily noticed, different manners of explanations, of understanding, of dealing with and living with reality, thanks to the new means of communication and transport, which create the need for a behavior that transcends even the new cultural forms.

Occasionally, the cherished free will, intrinsic to being human, will manifest itself in a model of transculturality that will allow each human being to reach his plenitude.

An adequate model to facilitate this new stage in the evolution of our species is the so-called Multicultural Education, which has been growing in education systems around the world. Although I do not intend to discuss Indigenous Education here, the contributions from experts in the area have been very important to understand how education can be an instrument to reinforce the mechanisms of social exclusion.

The concept of knowledge and the practices associated with it in a culture are decisive to the national identity and, therefore, the encounter with other cultures can lead a nation to question its own identity.

Perhaps the most important thing to underline here is the perception of a dichotomy between knowing and doing that prevails in the so-called "civilized" world, and which is typical of the paradigms of modern science, such as created by Descartes, Newton and others. Appearing nearly concomitantly with the age of navigation, with the conquests and colonization, modern science established itself as a form of rational knowledge originated from Mediterranean cultures, and substratum to the efficient and fascinating modern technology.

From the central nations came the definition of conceptualizations structured and dichotomic of knowing knowledge and doing abilities. It is important to remember that practically all countries subscribed to the Declaration of New Delhi 16 Decemberwhich is explicit in recognizing that education is the prime instrument for the promotion of universal human values, of the quality of human resources and of the respect for cultural diversity, and that the contents and methods of education need to be developed to serve the basic learning needs of the individuals and societies, giving them the power to tackle their more urgent problems - the struggle against poverty, increase in productivity, improvement of living standards, and protection of the environment - and allowing them to take up their rightful role in the construction of democratic societies and in the enrichment of their cultural heritage.

Nothing is more explicit in this declaration than the appeal to subordinate programmatic contents to cultural diversity.

Equally, the recognition of a variety of learning styles is implicit in the appeal to the development of new methodologies. In essence, these considerations establish a great flexibility both in the selection of contents and in methodology. Ethnomathematics and mathematics The approach to distinct forms of knowing is the essence of the Ethnomathematics Program.

the relationship between mathematics education and culture

In fact, differently to what the name suggests, Ethnomathematics is not just the study of the "mathematics of various ethnic groups". I have created this word to signify that there are various ways, techniques, abilities tics to explain, understand, deal with and live with matema distinct natural and socioeconomic contexts of reality ethnos. The discipline called mathematics is, in fact, an Ethnomathematics that originated and developed in Mediterranean Europe, having received some contributions from Indian and Islamic civilizations, and which reached its present form in the 16th and 17th centuries, being then taken and imposed in the rest of the world.

Today, this mathematics acquires a character of universality, above all due to the dominance of modern science and technologies, which were developed in Europe from the 17th century. This universalization is an example of the process of globalization that we have witnessed in all activities and areas of knowledge.

There was much talk about multinationals. Today, the multinationals are global enterprises, for which it is impossible to identify a nation or dominant national group. The idea of globalization begins to appear already in the foundation of Christianism and Islamism. Differently from Judaism, from which those two religions originated, as well as from several other religions in which there is a chosen people, Christianism and Islamism are, essentially, religions for the conversion of the whole mankind to one faith, of the whole planet subordinated to the same Church.

This can be clearly seen in the process of expansion of the christianized Roman Empire and of the Islam. The process of globalization of the Christian faith comes close to its perfection with the age of navigations. The catechism, fundamental element of the conversion, is taken to the whole world.

Just like Christianism is a product of the Roman Empire raised to the character of universality with colonialism, so are mathematics, science and technology. In the process of expansion, Christianism modified, absorbing elements of the subordinated cultures, and producing remarkable variants of the original Christianism of the colonizer.

It should be expected that, likewise, the forms of explaining, knowing, dealing with, living with sociocultural and natural reality, obviously distinct from region to region, and which are the reasons for the existence of mathematics, sciences and technologies, would also go through this process of "acclimatization", a result of a cultural dynamics. However, that did not happen, and it does not happen, and those fields of knowledge have acquired a character of universal absolute.

They do not admit of variations or any kind of relativism. This fact has been incorporated to the level of popular dictums such as "as sure as two and two are four". We do not dispute the fact, but its contextualization in the form of a symbolic construction anchored in a whole cultural past.

Mathematics has been defined as the science of numbers and forms, of the relations and measures, of the inferences, and its features point to precision, rigor, and exactness.

Mathematics big heroes, that is those individuals historically pointed out as responsible for the advancement and consolidation of this science, are identified in Ancient Greece and, later, in the Modern Age, in Central Europe, above all in England, France, Italy, Germany. They are ideas and men from the Mediterranean northwards.

Therefore, to speak of this mathematics in diversified cultural environments, above all when dealing with indigenous peoples or Afro-Americans or other non-Europeans, with workers oppressed and from marginalized classes, in addition to bringing the image of the conqueror, of the pro-slavery, in short, of the dominator, also refers to a form of knowledge that was built by the dominator, and of which he served, and still serves, himself to exercise his domination.

But none of them has, like mathematics, the aura of infallibility, rigor, precision, and of being an essential and powerful instrument in the modern world. This makes it a presence that excludes other forms of thinking. Actually, being rational is identified with mastering mathematics. Mathematics presents itself as the language of a god wiser, more miraculous and more powerful than the deities of other cultural traditions. If that could be identified just as part of a perverse process of acculturation, through which the creativity essential to being human is eliminated, I would say that such schooling is a farce.

But it is worse than that, for in the farce, once the spectacle is finished, everything returns to what is was before. Whereas in education, the real is replaced by a situation devised to satisfy the objectives of the dominator. Nothing returns to the real after finishing the educational experience. The student has his cultural roots, part of his identity, eliminated in the process.

This elimination produces the excluded. This is evidenced in a tragic way in Indigenous Education. The Indian goes through the education process and is no longer an Indian It is probable that the high incidence of suicide among some indigenous populations is associated with that. A natural question can occur after these observations: The question could be rephrased: Naturally, these are false questions, and it would be false and demagogical to answer with a simple yes or no.

These questions can only be formulated and answered within a historical context, trying to understand the irreversible e in? The contextualization is essential to any education program for native and marginalized populations, but no less necessary for the populations of the dominant sectors, if we want to achieve a society with equity and social justice. Contextualizing mathematics is essential to everyone. Or the acquisition of Indo-Arabic numbering system with the flourishing of European mercantilism in the 14th and 15th centuries?

And we cannot understand Newton outside his context. I recall the fundamental work of Boris Hessen Surely, it is possible to repeat a few theorems, memorize multiplication tables, and automate operations, and even calculate some integrals and derivatives, which do not have any relation with anything in the cities, fields or forests.

Some will say that they are worth it as the noblest manifestation of the human thinking and intelligence. We persist with the false assumption that intelligence and rationality are synonyms with mathematics.

It is believed that this construct of the Mediterranean thinking, taken to its purest form, is the essence of being rational. And thus the fact is justified that individuals, rational because they master mathematics, have treated, and continue to treat, nature as an inexhaustible resource for the satisfaction of their wishes and ambitions. Naturally, there is an important political component in these reflections.

Despite many people saying that this is an outdated slogan of the left, it is obvious that dominant and subordinate classes still exist, in the central countries as well as in the peripheral ones. It makes sense, therefore, to speak of a "dominant mathematics", which is an instrument developed in the central countries, and many times used as an instrument of domination. This mathematics and those that master it present themselves with a position of superiority, with the power to dislodge, and even eliminate, the "everyday mathematics".

The same happens to other forms of culture, particularly with language, as very well discussed by Bernstein And the situations associated to behavior, medicine, art, and religion are well known. All these manifestations are referred to as popular culture.

Naturally, although alive and practiced, popular culture is often ignored, disdained, rejected, repressed, and certainly belittled. This has the effect of discouraging and even eliminating the people as the producer and consumer of culture, and even as a cultural entity.

Mathematics education - Wikipedia

That is no less true of mathematics. In geometry and in arithmetic, particularly, violent contradictions can be seen. For instance, the geometry of people, of the balloons and kites, is colorful. Theoretical geometry, since its Greek origin, has eliminated color. Many readers will be confused at this point. They will be saying: They have everything to do, for they are exactly the first and most notable geometrical experiences.

The reunion of art and geometry cannot be accomplished without the mediator color. In arithmetic, the attribute of number in quantification is essential.

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Two oranges and two horses are distinct "twos". To reach the "two" without qualification, abstract, like reaching geometry without colors, may be the crucial point in the passage to a theoretical mathematics.

Being careful about this passage and about working adequately this moment may synthesize all that is important in the Elementary Mathematics programs.

The rest of the components that make up the programs are a collection of techniques that become less and less interesting and necessary, more efficiently carried out by electronic machines.

One cannot define criteria of superiority between cultural manifestations. Appropriately contextualized, no form can be said superior to another. This is well illustrated by Ferreirap. For example, we learn that the Xavante binary system was replaced, as if by magic, by a "more efficient" base 10 system.

Because it relates to the Xavante context? No, because it relates to the numbering system of the dominator. What happens to the native language is not substantially different. But there is undoubtedly a criterion of efficiency that applies to intercultural relations. Without learning the "arithmetic of the white man", the native will be swindled in his commercial transactions with the white man.

But that happens with all cultures. I have to master the English language if I want to participate in the international academic world. But nobody has ever said, or even suggested, that I should forget Portuguese, and that I should be embarrassed or even ashamed of speaking that language. But that is what is done to peoples, specially the indigenous populations, be it in language, be it in knowledge systems in general, and particularly in mathematics.

Their language is labeled as useless, their religion becomes "fairy tales", their art and rituals are "folklore", their science and medicine are "superstitions", and their mathematics is "imprecise" and "inefficient", when not "nonexistent". Now, that goes on in precisely the same way with the popular classes. But that is exactly what happens to a child or a teenager or even an adult when they approach a school.

Whereas Indians commit suicide, something permitted by their intracultural relations, the form of suicide practiced in other segments of the population is an attitude of disbelief, of alienation, so well depicted in the movie Kids.

the relationship between mathematics education and culture

There is no question about the convenience and even necessity of teaching to the dominated, either Indians or whites, poor or rich, children and adults, the language, mathematics, medicine, and laws of the dominator. We have reached a structure of society and such perverse concepts of culture, nation, and sovereignty that this need imposes itself upon us. What is questioned here is the aggression to the dignity and to the cultural identity of those subordinated to that structure.

The main responsibility of the education theorists is to call attention to the irreversible damages that can be caused to a culture, to a people and to an individual if the process is carried out unconscientiously, many times even with good intention, and make proposals to minimize those damages.

Many educators are not aware of that. Various examples, such as the transport in boats, balancing a bank account, and others show that the Indians master what is essential to their practices and to the elaborate arguments with the white man about the things that interest them, usually dealing with transports, commerce, and use of the land. So, mathematics is contextualized as one more resource to solve new problems that, having originated in another culture, have arrived demanding the intellectual tools of that culture.

The ethnomathematics of the Indian can do the job, it is efficient and adequate to many - really important - things, and there is no reason to replace it. The ethnomathematics of the white man is good for other things, equally important, and it cannot be ignored. To say that one is more efficient, more rigorous, in short, better than the other is, if removed from a context, a false and falsifying issue.

The mastery of two ethnomathematics, and possibly of others, obviously offers greater possibilities of explanations, understandings, of handling new situations and solving problems.

But that is exactly what is done in mathematical research - and in fact in any other field of knowledge. The access to a greater number of intellectual instruments and techniques gives, when these are appropriately contextualized, a much larger capacity to deal with situations and to solve new problems, of modeling adequately a real situation to reach, with the use of those instruments, a possible solution or course of action.

This is learning par excellence, that is, the ability to explain, learn and understand, to critically face new situations. Learning is not the mere command of techniques, abilities, nor is it the memorizing of a few explanations and theories.

Formal education is based on the mere transmission of explanations and theories theory-based teaching and expository classeson the training in techniques and abilities practice-based teaching with repetitive exercises. From the viewpoint of the most recent advances in our understanding of the cognitive processes, both methods are completely flawed. Cognitive abilities cannot be assessed outside their cultural contexts.

There are cognitive styles that must be recognized in different cultures, in an intercultural context, and also within the same culture, in an intracultural context. Naturally, each individual organizes his intellectual process throughout his life history, collecting and processing information, as discussed above.

Metacognition offers a good theoretical apparatus to understand this process.

Society, culture, mathematics and its teaching

The risk of the more common education practices is, when trying to match the intellectual organizations of different individuals, and thereby create a highly acceptable social scheme, to threaten the authenticity and individuality of each participant in the process. The frailty of this pedagogical structuralism, anchored in what we call the myths of current education, is evident when we reflect on the dizzying fall of the results of the education grounded on these myths around the world.

The big challenge faced in education is precisely that of being capable of interpreting the abilities and the cognitive action itself in the non-linear, stable, and continuous way that characterizes the more current educational practices.

the relationship between mathematics education and culture

The alternative is to recognize that the individual is a whole, integral and integrated, and that his cognitive and organizing practices are not unrelated with the historical context in which the process takes place, a context that remains in permanent evolution. That is clear in the dynamics that prevails in the education for everyone and in multicultural education. We are in search of an education that encourages the development of an open creativity, leading to new forms of intercultural relationships.

These relationships characterize mass education and afford adequate space for the preservation of diversity and elimination of inequalities, bringing forth a new organization of society. Throughout history, the curriculum has reflected a conception of education and of its importance in society, which is very different from the academic importance of each discipline. The Romans have bequeathed us an institutional model that persists to this day, in particular in education.

What would correspond to fundamental education was organized in the Roman world as the trivium grammar, rhetoric, and dialecticsand the main motivator of this curriculum was the consolidation of the Roman Empire.

With the expansion of Christianism in the Middle Ages, other educational needs were created, which reflected in what would be upper schooling, organized as the quadrivium arithmetic, music, geometry, and astronomy. The extensive advances in the styles of explanation of the natural facts and in economy that characterized the European thought since the 16th century created a demand for new goals for education. The main goal was to create a school accessible to everyone, and following a new social and economic order.

Already in Comenius said: If therefore we want well ordered and flourishing Churches and States and good administrations, first of all let us order schools and let us make them flourish, so that they be true and live workshops of men, and ecclesiastical, political and economic nurseries.

Steps to an ecology of mind. Class, codes and control: The Free Press, Interdisciplinaria, Buenos Aires, v. Summus Editorial,p.