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Archive for the ‘Mathematics’ Category

The society in Spain is traditionally for centuries, with a culture strongly skewed towards its humanistic components. In Spain, culture seems to be synonymous with literature, painting, music … Many of our enlightened people make no bones whatsoever to confess openly their deep ignorance of the basic elements of mathematics and science and even seem to boast Although without any. The pages of most of our newspapers have not yet realized that science, particularly mathematics, and today constitute one of the pillars of human culture. Furthermore, it seems clear that, as Whitehead says, “If civilization continues to advance in the next two thousand years, the new dominant human thought is the domain of intellection math.”

It would be desirable that all members of the scientific mathematical community and we strive very hard to make it clear to society for the influential presence of mathematics and science in culture. A society with a clear understanding of what science is for development will be collectively more sensitive to the problems of education of the youngest in this sense represents.

In the international mathematical community recently has been paying great attention to the appropriate resources to achieve open the eyes of broad sectors of society to the benefit of all the orders that can bring a culture where, in the right way, science and math.

It is safe in our school communities that there are a number of students with intellectual endowment for mathematics truly exceptional. These are talents that would sometimes more or less unnoticed and unattended rather the inability of teachers to devote the personal attention they need. These are people who, at first excited about school, pass a state of boredom, frustration and disinterest that will lead probably to mediocrity and apathy after a period of great suffering possible school.

On the other hand are talents that could pay off outstanding for the common good of our society, if not lost, through his outstanding contribution to the cultural, scientific and technological development. It is a great social responsibility the undoubted loss of talent caused by their neglect. At present no agency, either public or private, continued attention to the task to detect, stimulate and guide the extraordinary talent and early mathematics, nor in any other science. There is, and with much justification, care, support and care with respect to the teaching of underfunded, but I think it has hardly given any attention to the problems of the early talents in the country.

You might think with some justification that the precocious talent in mathematics is easier to detect and stimulate in other sciences. In fact, there has long been successful projects in a number of countries. There are several ways to stem the problem, and among them is non-excessive cost, especially if one takes into account the long-term performance of a well-run performance.

It is possible, judging by the fact that in countries of our Latin American cultural sphere has been the emergence of a few persons of extraordinary ability in the mathematical development of the country, a sustained detection and encouraging mathematical talent could put our country early within a reasonable time at an altitude mathematics and science much higher.

The mathematics of the nineteenth and twentieth century mathematics has been predominantly of the continuum in which the analysis, its power and impact on engineering applications, has played a role.

The advent of computers, with its enormous computing power, with its enormous speed, versatility, power of graphical representation, modeling possibilities for bypassing the mathematical formulation of classical … has opened many different fields, originated not in physics, as the developments of previous centuries, but in many other sciences such as economics, organizational science, biology, … whose problems were opaque, partly because of the enormous mass of information had to be taken up to find valuable mathematical insights that could lead to resolution processes of the difficult problems raised in these fields.

Moreover, the emphasis on discrete algorithms, used in computer science, as well as the modeling of various phenomena by computer has led to a shift of emphasis in the current mathematics to mathematics discreet. Portions of it are sufficiently basic as to be part of a successful initial program of mathematics. The combining classical and modern aspects of it, such as graph theory and combinatorial geometry, could be considered as suitable candidates. The elementary theory of numbers, never to disappear from the programs in some countries could be another.

Attempts have been made to introduce these elements and the like belonging to discrete mathematics in early mathematics education. It happens that this seems only possible at the expense of other portions of mathematics more deeply rooted in not seen how this can be without. Although it seems quite obvious that the flavor of the mathematics of the future will be quite different from today because of the presence of the computer still is not clear how this will be reflected in the contents of primary and secondary schools.

There is now a strong current in mathematics education that strongly supports the need for the learning of mathematics is not done exploring mathematical constructs themselves in different ways that have crystallized over the centuries, but in constant contact with real world situations that gave them and they keep getting their motivation and vitality.

Such a current is fully consistent with the ideas developed earlier and looks like a natural corollary of them. Mathematics, as we have seen, originated as an attempt to explore, in his peculiar way, the various complex structures that lend themselves to it. The creation of the mathematician is performed spontaneously in this attempt to dominate mathematicizable aspects of reality. Mathematics education should aim at main inculturation, trying to incorporate that spirit to the young mathematician of our society.

It seems obvious that if we limit ourselves in our education to a mere presentation of the results are purely theoretical building has developed in such an attempt, apart from its origins in the problems that present reality and its applications for solving such problems we would be hiding a very interesting and substantial of what mathematics really is. Apart from that we would thereby ignoring the great motivating power that modeling and applications have.

Mathematics is an old multipurpose activity. Throughout the centuries has been used with profoundly different objectives. He was instrumental in making predictions, the priests of the Mesopotamian peoples. Was considered as a means of approaching life more deeply, and as a way of approaching the divine, from the Pythagoreans. It was used as an important discipline of thought in the Middle Ages. It was the most versatile and suitable tool for exploring the universe, from the Renaissance. This has been a great guide of philosophical thought, among the thinkers and philosophers of rationalism. He has been instrumental in the creation of artistic beauty, a field of playful exercise, among mathematicians of all time …

Moreover, the mathematics itself is an intensely dynamic and changing science. Quickly and even turbulent in their own content. Yet deep in his own conception, albeit slower. This suggests that, indeed, mathematical activity can not be a simple approach to reality.

The other member of the binomial-mathematics education, is also not so simple. Education has to necessarily refer to the depths of the person, a person still conform to the changing society in which this person has to integrate to the culture in this society develops, the specific ways personal and material at the time one can or wants to have, for the purposes of this education priority is you want to assign, which can be extremely varied, …

The complexity of the mathematics and education suggests that the theoretical mathematics education, and no less than agents of it, must remain constantly alert and open to profound changes in many ways the fast dynamics of the global situation mutant comes calling .

Education, like any complex system, has a strong resistance to change. This is not necessarily bad. A reasonable persistence to changes is characteristic of healthy living organisms. The trouble happens when this is not combined with an ability to adapt to the mutability of environmental circumstances.

In mathematics education at the international level would hardly changes for consideration from the beginning of the century until the 60′s. At the beginning of the century had been a renewal movement in mathematics education, initially through the interest awakened by the prestigious figure of the great German mathematician Felix Klein, with its renovation projects of high school and its famous lectures on Elementary Mathematics from an higher point of view (1908). In our country a great influence from 1927, in the interest of Rey Pastor, who published in the Library Mathematics and its translation into Castilian.

In the 60 emerged a strong movement for innovation. We can say with reason that the push for renewal of that motion, despite any defect that has resulted in the international educational scene, has all the great virtue of drawing attention to the need for constant alertness on the evolution the educational system in mathematics at all levels. Changes in the 60′s have caused tidal against tides along the intermediate stage. Today, we can say with justification that we are still in a stage of profound change.

Elementary algebra is the most basic form of algebra. Unlike arithmetic where using only the numbers and arithmetic operations (like +, -, ×, ÷), algebra, numbers are represented by symbols (usually a, b, c, x, y, z). This is useful because:

* Allows the general formulation of arithmetical laws (such as a + b = b + a).
* Allows numbers refer to “unknown”, formulate equations. and study how to resolve them.
* Allows the formulation of functional relationships.

What are the most commonly used symbols in algebra? Read the rest of this entry »

Mathematics, sciences is one of most beautiful, but over time have become the bogeyman, or a headache for many students, regardless of education level on which it is located. None of this, is further from reality, since the problem is not in mathematics, but on the subject that you study.

Knowing this, we can act on the subject, pointing out the right way forward for the effective understanding of mathematics. This process involves an internalization that will have a period of 15 days is considered sufficient for any student to grasp what is “the essence of mathematics.” Read the rest of this entry »