Text tasks at mathematics lessons can be used for different purposes: to prepare for the introduction of new knowledge, to familiarize with new concepts and properties of concepts, to deepen and expand the formation of mathematical knowledge and skills, to form computational skills, to teach the method and techniques of solving problems at different stages of training.
Consequently: the methodology of work with the task at the lesson should be based, first of all, on the purpose for which this task is included in the lesson. In practice, there is most often no correlation between the method of organizing activity on a problem and the learning goal of including it in the lesson. Pupils work mainly on the task in order to achieve a practical aim: this means to solve the task, i.e. to get an answer to the question posed by the task. At the lessons, the tasks are mostly solved according to the traditional structure and in the process of solving them are distinguished by greater or lesser independence of the children.
When solving problems, to save time, it is more often necessary to use reference schemes for short notes. The time saved should be used in the final analysis of the task, i.e., after the task is solved it is not necessary to hurry to start another task. It is useful to think, try another way of solving the problem, comprehend it, try to find and pay attention to the difficulties in finding a solution to the problem, analyze the incorrectly found solution, identify new and useful information for students.
The mathematics curriculum provides for the use of various techniques of working on a problem. Let’s look at some types of work on a problem in a math class.
The first type: “Problem Solving.” The solution of tasks at the lesson may differ in the form of organization of cognitive activity, the nature and degree of management of the process of solution. The content of the solved tasks, the way of solution. Proceeding from the above, even the solution of a task at different stages of a lesson, in different classes, depending on the purpose of a lesson, can be carried out differently.
Frontal work on the solution of the problem, under the guidance of the teacher. This kind of problem solving, under the guidance of the teacher, can be used to introduce a certain kind of problem. In this case, it should be aimed at having the students memorize the distinctive features of this type of problem and remember the basic steps of the solution. The collective solution, under the guidance of the teacher, is also used to make the children memorize the steps of the solution, get acquainted with some kind of technique, property.
Frontal work on the solution of the problem, under the guidance of students. This type of work can be used most often for mastering the ability of pupils to consistently perform the steps of problem solving. The teacher in this situation only guides the student to the correct solution. The work concludes with a summary and conclusions.
Independent problem solving by students. Independent decision, one of the most widespread types of work on a task at a lesson, however here there are orientations on different purposes: on formation of ability to solve a task by a certain kind; to carry out check and self-check, self-assessment. Depending on the content of the task, the following types of problem solving: solving problems with redundant data, solving problems with missing data, solving problems of a certain type with different classification of types , solving non-standard problems.
The second type: “Execution of part of the solution”. The aim of this type of work is to help students develop the ability to perform a certain stage of solution. For example: make a picture; using the diagram, disassemble the problem from the question to the data; make a plan of solution; given the solution of the problem by actions, write down this solution in an expression. Quite a number of types of additional work on the solution of a part of a problem are considered in the methodological literature. The main goal of this work is to teach the child to find another way to solve the problem, to solve the problem in different ways. The tasks may be: to change the condition of the problem so that the problem is solved by another action; to put all questions which could still be answered by this problem; to compare this problem with another one in terms of content and solution; to change the numerical data so that a new way of solving the problem is found.
Third kind: “Not including an explicit and complete solution to the problem”.Teacher’s goal, to teach how to compare, compare, analyze. To contribute to the development of thinking, increase interest in mathematics. This type of work, will allow the teacher to purposefully form components of the general ability to solve problems.
Types of work: establish correspondence between the content and the schematic drawing and vice versa; selection among tasks the one that corresponds to the given drawing; selection among several solutions of the one that corresponds to the given task; selection of the task, the answer to whose question can be found with the tasks of the sequence of actions.
The fourth type: “pupils composing tasks by themselves”. The goal: to strengthen the ability to solve problems, find different ways of solving them (a certain number of arithmetic ways of solving a problem).
Types of activities: adding missing data to the problem; posing questions to the problem; making a short-word puzzle; composing a similar problem, by solution method, by subject, with the same numerical data but with a different solution. Application of different ways of solution, in the educational process, is very important from the general educational point of view, is one of the main methodological principles of teaching. Systematic use of this type of activity, in mathematics lessons, develops the mental abilities of children. Undoubtedly, not all students can be engaged in this work in full at the lesson, but it is impossible not to teach it to stronger, more capable students. Methods that will help children find different ways of solving a problem: creating a different model of a problem than the one used to solve it in the first way; replacing a given problem with another one, the solution to which can be found the answer to this problem (the equation method).
Consequently, having taught children the ability to solve text problems, the teacher will have a significant impact on the development, training and education of the child, will prepare him for the reception of more complex information in high school.