Організація навчальної діяльності учнів при розв’язуванні нерівностей з параметром та модулем

Abstract

(ua) При вивченні математики розглядаються задачі, для розв’язання яких потрібно не лише знання шкільної програми, а й творче застосування цих знань, зокрема при розв’язуванні задач з параметром. Розв’язування таких задач сприяє інтелектуальному розвитку, розвитку логічного мислення та є гарним матеріалом для відпрацювання навиків. В роботі наведені приклади з детальним описом їх розв’язування, а також увага приділяться методичній стороні їх розв’язання.

(en) Solving equations and inequalities containing a parameter is probably one of the most difficult branches of elementary mathematics. This is due to the fact that the school tries to develop skills and abilities to solve a set of standard problem s, often associated with technical algebraic transformations. Tasks with a parameter are of a different typ e. To solve them requires flexibility of thinking, logic in reasoning, the ability to analyze the situation well and completely.Ability to concisely and transparently write down solutions, go through all possible options and cases, apply graphical interpretations; allow to activate creative activity and thinking: develop skills of research activity as each task with a parameteris a small research. To solve problems with parameters requires a thorough knowledge of the properties of elementary function s, equivalent transformations of equations, inequalities and their systems. Such tasks are offered at the external evaluation as t hey allow to identify promising opportunities for participants to study in universities with a high level of requirements for mathematical training. However, solving them causes some difficulties for students. Difficulties are caused primarily by the fact that in the school course of mathematics they are given little attention, and at the standard level they are not present at a ll. Therefore, it is useless to hope that students who have not been trained in "tasks with parameters" will be able to achieve a positive result in a stressful atmosphere of passing the external evaluation.Experience shows that students who know the meth ods of solving problems with the parameter, successfully cope with other tasks. That is why the tasks with the parameter have diagnostic and prognostic value. In our opinion, the school should organize additional or optional classes for interested students to study the methods and techniques of solving problems with parameters. Experience shows that the greatest effect is given by three-stage training. In the first stage (individual), students try to solve problems on their own. In the second stage (group), during the classes, the achieved results are discussed and full solutions and characteristics of the methods by which these tasks were solved are given. In the third stage (individual-group) students independently come up with similar problems, which are solved using the learned techniques and in the classroom demonstrate their solution with subsequent discussion by the participants.