The development of research skills by high school students through inequalities’ solution

The scientific research activities of students are actively implemented in the process of studying natural science subjects both in class and in extracurricular activities. One of these subjects is mathematics. The different kinds of activities, such as developing of a project, writing an essay, etc. are widely used for improving the quality of mathematical education. The pupils could form the special type of thinking, the research skills, searching and critical analysis at the lesson of mathematics with help the research activities. They can also show the creative initiative during the explanation difficult mathematic facts to more understandable and interesting form.

There is a special place, which is given to the cycle of topics in the section “Inequality” in the structure of the work program for the academic subject “Mathematics” in high school. Learning of inequalities during all period of training allows to become proficient in wide spectrum of solving problems, to cope with modeling’s methods.

The pilot study to test the effectiveness of research skills of senior students in working with inequalities was organized and conducted on the basis of school Novoshakhtinsk named after the hero of the Soviet Union Mikhail Grigoryevich Yerokhin.

There were 25 students of 10th grade, who took part in the pilot study.

The initial diagnosis was carried out the initial stage in order to determine the initial level of development of research skills among the students of the 10th grade.

According to the diagnostic results it can be noted lacking of students with a high level of research skills’ development. The most have a low level of research skills. The students aren’t able to put the problem fully or partially, formulate a hypothesis, emphasize the main thing in the task, make a logical conclusion.

Only 1/5 students (20%) have an average level. They could solve the mathematics research problem using supporting material or teacher prompts. The average score for the class is 2.44 points out of possible.

These results determine the need to develop a methodology for developing the research skills of high school students. Such methodology should be implemented through solving inequalities, taking into account special pedagogical conditions.

For the solving these problems, it is proposed to organize educational and research activities at the studying of inequalities’ lesson in the form of case-methodologies (the methodologies of specific situations) in the 10th grade.

Students will be offered research assignments on the topic of “Inequality”, where they will need to formulate the problem, propose several solutions and present the most effective solution in the form of detailed analysis and written report.

Besides forming the research skills, the teacher has to increase motivation to mathematics. So it was proposed to carry out such cases using the interactive application LearningApps.

A case study was proposed in the form of a single variable square inequality competition. Students were encouraged to choose multiple players or computers instead of real players.

In addition, let’s present an example of a research case on the equivalence of inequality. Equivalent inequalities are such inequalities which have the same solutions. In a particular case, inequalities that haven’t solutions are also called equivalent. The study proved that one pair of inequalities are equal.

Students must submit a report on the work done after passing the main stages of research cases. They must tell which the task was briefly, the problem, hypothesis were solved and present a sample of solution with a detailed algorithm. All members of the mini-group participate in the protection of the case-tasks.

Thus, in the course of research cases solving on the topic of “Inequality” students were able to learn to highlight the main thing in the task, formulate hypotheses that need to be solved, learn to think critically, make conclusions. This format of classes was very interesting and productive for 10th grade students. Even the most lagging students were active in lessons of this type. The experience was only positive.

The recurrent diagnostic of the level of research skills’ development was carried out among the 10th grade students at the control stage.

Comparing the received results, we can say that the number of students with a high level of research skills after the formative stage was 24%. There weren’t high level students in the initial study. The number of high school students with an average level was 60%, which is 40% more than the primary results. Among the students 80% had a low level of research skills at the ascertaining stage, and only 16% at the control stage. The obtained data confirm the effectiveness of the developed methodology for the formation of research skills of high school students in solving of inequalities in compliance with special pedagogical conditions.

The average grade point increased almost two times and amounted to 4.88 points (out of 8 possible).

Thereby we consider that the goals and objectives of the work have been fully achieved.