Numerical sequences , is part of the subjects received in mathematics , and which allows you to plan the teaching of this complex.
Summary
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- 1 Introduction
- 2 What are successions?
- 3 Teaching Mathematics in Basic Secondary
- 4 References
- 5 Sources
Introduction
The training of the graduate in the specialty of Mathematics-Physics , has among its purposes that they acquire knowledge, skills and abilities on different branches of knowledge of Mathematics , based on the theoretical aspects of the process, which allows them to direct it with a comprehensive approach and interdisciplinary and with a practical meaning of Mathematics for life.
That is why, from the initial training of the Mathematical-Physics teacher, prepare to learn to learn and learn to do . It means that you acquire basic mathematical knowledge and power that can be expanded and used to understand intra-mathematical and extra-mathematical problems, enhancing logical thinking, not only in the teaching process, but also in the learning process.
What are successions?
Sequences are as old as natural numbers in the evolution and development of Mathematics . For example, the ordering of the days of the year, the ordering of the siblings of a family from oldest to youngest.
For the Pythagoreans, passionate about natural numbers, they must have been the first to be interested in the construction of infinite sequences. They considered in particular, sequences of numbers originated by playing with stones (calculations), when placing them in the form of polygons; in this way they were building sequences of triangular, square, pentagonal numbers, etc. [one]
Galileo Galilei observed and wrote down the space, that every second, a ball travels when falling down an inclined plane.
In practice in filling a swimming pool, the water level is recorded every hour and a succession of numbers is achieved. The Pythagoreans considered pairs of numbers that were obtained by quotient, these approaching default or excess alternatively, constituting this the first example for recurrence and limit for Infinitesimal Mathematics.
A set whose elements are numbered, that is, put in simple correspondence (one-to-one one-to-one) with the natural numbers, so that in the set there is a first element, a second, a third, etc. [2]
Sequences can be finite and infinite. What do successions solve? They are used to study, represent and predict phenomena that occur over time intermittently.
For example: if you start recording the maximum temperatures for each day, you can predict the behavior of the temperature on successive days.
A sequence is a function that makes each natural number correspond to a real number. The transformer of a number n is designated by any is named the most enesimo (nth) term of the sequence.
Teaching Mathematics in Basic Secondary
Mathematics teaching takes advantage of algorithmic and heuristic procedures. Taking into account that heuristic instruction is a powerful instrument for the achievement of the cognitive independence of students, it favors the development of intellectual skills such as: analyzing, synthesizing, comparing, classifying, as well as the formation of mental abilities, among which they find intuition, originality and creativity.
The heuristic principles of recurrence and induction should be studied by teachers in training in the Mathematical-Physical career , for use in solving exercises and problems that lead to successions and progressions. In general the term an = an -1 + n this expression is called the general term of the sequence. Then the general term of the successions that meet these conditions is:
Prepare the teacher how to direct the teaching-learning process of Mathematics in such a way that students acquire mathematical thought, capable of solving the problems that may be faced in their daily life, using the determination of terms of a succession of arithmetic or geometric, as well as the regularity that this sequence represents.
