Analytical method of reasoning for mathematical tasks and games solving

Abstract

The purpose of the research is to review the analytical method of reasoning in the process of solving of mathematical logic tasks and games. The research tasks include: - Analysis of theoretical concepts related to different methodologies for solving of mathematical tasks; -Introduction of fundamental theoretical concepts related to the analytical methodology of reasoning; -Presentation of task for which the analytical methodology of reasoning is applied. The report reflects the point of view of the researchers Mr. Portev and Mr. Nikolov regarding the two groups of methodologies for solving of mathematical tasks - the general logic approach and the specific mathematical approach. The research presents in greater details the general logic methodologies for task solving that reflect the analysis and the synthesis in the process of seeking the solution of the task, and namely: 1. Analytical methodology of reasoning and its two variations - the ascending (or perfect analysis, diagram of Papp) and the descending (or imperfect analysis, diagram of Euclid); 2. Synthetic methodology of reasoning and analytic-synthetic methodology of reasoning (reasoning at both ends). This methodology is a combination between the synthetic methodology and one of the analytical methodologies of reasoning. The advantages of the analytical methodology are very important. The following specifics of this methodology that lead to effective task solving are presented in the research: -The analytical diagrams provide high repeatability and have control function in comparison with other diagrams. Even more, it seems that they have primary position to the others thus having a generating function. Something else which is of extreme importance is that after the conscious absorption of the knowledge, the control over the diagrams is performed with high degree of awareness. -The diagrams for analysis and synthesis are anteriorly connected mostly with knowledge regarding the general logic methodologies and the heuristic rules. They are sooner strategies for seeking of task solutions and are transversal through different ages and activities. -The diagrams are suitable to determine the stages of the solution of the mathematical task - to determine its components and to synthesize the information related to the main terminology that has got a descriptive and control function towards the rest of the components of the task. This leads to operability and heuristics of the analytical methodology of reasoning. -The logical foundation of the analytical methodology and the high level of verbalization of its applicable diagrams show that the students can take part in the process of methodology building up.