Solving Non-linear Equations Systems through Numerical Methods

This study investigate the contribution assessment methods for solving linear systems of equations and graphical functions by numerical methods to improve school performance. Learning becomes effective only when students actively participate in the learning process: discussions, arguments, investigations, experiments, etc., become sine qua non methods for effective and lasting learning. All the situations, not just the active methods themselves, with which the students are faced and that remove them from their hypostasis of object of training, turning them into active subjects of education involved in their training, are forms of active learning.

The experimental study was based on the following hypothesis: The researcher use traditional teaching-learning strategies combined with the appropriate modern ones, then students will choose to consciously and effectively acquire the methodology for solving exercises and problems, reinforcing the idea that Mathematics, a universe of knowledge and an educational subject, may be understood in a smart, methodical manner, thus facilitating the progressive closeness to her beauty by reasoning and related calculation techniques, disciplinary effort, the logic of intelligently suggested and discovered connections.

Based on this hypothesis, there were established the research objectives, namely: - knowledge of the students’ psychological characteristics and determining their baseline levels; - correct and conscious assimilation of the concepts taught; - building problem-solving and investigation skills; - the optimal integration of evaluation processes during lessons of Mathematics by using effective work tools and techniques; - achieving optimal synchronization between learning and recognition of the learning outcomes, focusing on increasing motivation for learning.

The experiment was conducted at two high-schools, involving three 11th grades from the Pedagogical College “Ștefan cel Mare” from Bacău (60 students) and three 11th grades from the National College “Vasile Alecsandri” from Bacău, (60 students), in the 2014-2015 school year.

Calculating the mean of the two tests (initial and final) and drawing a comparison between the two groups, there may be noticed an increase in the school performance at the experimental group as compared to the control group.

The results obtained by the students confirm the research hypothesis.

In conclusion, the researcher recommends: to achieve high-quality education and obtain the best results, we should combine classical and modern teaching, learning and evaluation methods, different forms of organization and a variety of teaching tools and materials.

In this article we will focus on non-linear systems of equations. The topic is interdisciplinary. It is a combination of two sciences - mathematics and programming. The work is primarily methodological and it is intended for teachers and students.