# Mathematical algorithms

Mathematical algorithms . Obtaining algorithms is a basic requirement in the teaching of Mathematics , achieving this requires practical action that establishes the interconnection between contents, calculations and operations of less complexity, giving the teacher the possibility of using them in structuring the steps that make up.

## Summary

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• 1 Concept of algorithm
• 2 Proceed didactically for the formation of algorithms
• 3 Didactic-descriptive guide for the formation of algorithms
• 6 Sources

## Algorithm concept

The algorithm reveals in its constitution a number of operations arranged in an established order, which are promoted in a univocal and rigorously determined way, that is why it is only framed when it completely determines, a certain process, an activity and when it always leads, in the presence of certain essential data of the same type, to the same final results

In this process, students develop under the influence of the teacher who must condition the reduction and generalization of actions; to achieve that they influence the elementality of operations, because these, due to their complexity, must constantly be converted into elementary actions that do not decompose into others.

## Proceed didactic for the formation of algorithms

To achieve an adequate methodological treatment in the formation of mathematical algorithms , the individual historical experience of the students must be explored, the interconnection of the contents and concepts must be established that coherently indicate the interaction that leads to the identification of their steps, so as to motivate and Encourage knowledge, thus creating the necessary unity between the cognitive and the affective, and its various forms of integration that allow the development and solidity of knowledge.

In the joint development of algorithms for solving mathematical exercises, it is necessary to meet three requirements.

1. In the course of the mathematical formation of this process, students should be made aware that rationalizing their application is only possible through the use of procedures, so they must be elaborated and assimilated in the teaching of Mathematics.
2. Learners must assimilate certain steps indicated in the programs.
3. Learners must learn how to proceed in obtaining the operations or steps to perform the calculations.

The algorithms that work in the Mathematics course require the establishment of the links between contents, calculations and operations of less complexity already known by the students, which ensure their interaction, and give the teacher the possibility of using them and synthesizing the ideas, until forming the new procedure that leads to its solution, following the process of analysis-synthesis through which the students’ thinking must pass.

## Didactic-descriptive guide for the formation of algorithms

Numerical fractions. Calculation with fractions. Adding fractions of different denominator. To introduce this content, in correspondence with the highlights, several steps are required:

• Sufficient and necessary links are established to ensure the preconditions and interconnection on the basis of the diagnosisand knowledge that the students possess.

The following fractions are presented ¼; ¾. What do these fractions have in common? How are fractions of the same denominator added? Why is it always possible to add fractions of the same denominator? How do you proceed by adding ¼; ¾?

• Emphasis is placed on the equality of the parts into which the unit is divided as a common element.

It arises as a problem situation. The fraction ½ and 1/3 are represented. Is it possible to add ½ and ⅓? Why?

• At this time, existing ideas are activated from the analysis of what needs to be known.

What type of fraction do they represent? What are their denominators like? Is it possible to find fractions equivalent or equal to these with equal denominators? What studied routes allow to obtain equal fractions? What path studied allows you to achieve fractions of the same denominator?

• It is oriented to find them.
• The result obtained by reducing fractions to a common denominator is emphasized.
• It is insisted that a pair of equivalent fractions is obtained and that they have a common denominator.

The following schemes are analyzed: Equivalents

• What does the scheme represent?
• Why do they represent fractions?
• Which are equivalent? Why?
• It is reiterated in the equality of the shaded area.
• Ideas are synthesized and the procedure is identified.
• Is it now possible to add using the same fractions? Why?
• It is oriented Calculate!
• It is urged to explain the procedure to achieve it.

½ + ⅓ = 3/6 + 2/6 = 5/6 It is required that when the ways of proceeding are declared for the first time, the teacher explicitly highlights in a clear and firm way the step followed for the learners to learn and use independently in a generalized way, that is, they achieve their application in other contexts or mathematical exercises. Therefore, there is a need that they become familiar with the solution procedures and exercise their application through numerous and varied tasks. Success in involving students in obtaining mathematical algorithms requires structuring the indications, questions and impulses given to the students, in correspondence with the three moments represented in the diagram,