Math Problems And Their Classification
Task-concept and the broadest sense, means something that requires execution of the decision. Sometimes under the challenge understand exercise, you want to perform or solved by reasoning, calculation, building, etc.
Each task sets the set of data-condition tasks and issue, indicating the search, claiming a task.
There are various classification tasks.
On the relationship between the condition and the conclusion of tasks are subdivided as follows: 1) defined; 2) uncertain; 3) redefined.
If the data in the provided task is not sufficient to answer the question, the task is called indefinite. If the provided task data is enough, and after discarding one of the conditions is uncertain, this task is called a. If the provided task also contains sufficient data and any data yet, the task is called an override.
In relation to the various sections of mathematics objectives subdivide on arithmetic, algebra, geometry, trigonometry, etc.
For didactic purposes tasks fall into educational, training, educational. Cognitive tasks are mainly to obtain new knowledge and especially widely used in lower grades for the introduction of new concepts, knowledge. Training tasks designed to develop strong skills in solving problems, examples, applications of knowledge. Educational objectives serve to promote creative thinking.
By type of thinking tasks fall into algorithmic and heuristic.
When learning mathematics tasks have large and multilateral significance.
Educational value of mathematical problems. Solving the math problem, a person learns a lot: meets with the new situation, described in the task, using the mathematical theory to solve it, learns a new method of solution or new theoretical sections of mathematics required to solve the problem, and so on. In other words, when solving mathematical problems the person acquires the mathematical knowledge, improves their math education. When mastering solution method of a class of tasks a person formed the ability to carry out such tasks, and with sufficient training and skill, that too increases the level of mathematical education.
You must select multiple kinds of tasks on their teaching role.
1) tasks to learn mathematical concepts. It is known that the formation of mathematical concepts good passes, subject to careful and painstaking work on concepts and their definitions and properties. To master the concept in math problem solver, it is not enough to learn its definition, you must understand the meaning of each word in the definition clearly know the properties of target concepts. Such knowledge is achieved, first and foremost, in solving problems and exercises.
2) Task to master the mathematical symbols. One of the purposes of teaching mathematics is mastering mathematical language and consequently mathematical symbols. The simplest symbols introduced back in primary school and classes IV-V (signs of action, equation solver, equality and inequality signs, brackets, angle and its size, parallelism, etc.). The correct one should teach the characters studied consumption, revealing in their role and purpose.
3) tasks to teach evidence. Learning evidence-one of the most important goals of teaching mathematics.
4) tasks to generate mathematical skills.
5) Teaching role and tasks and treats exploring new mathematical facts, concentrating the attention of the students to the newly studied the ideas, concepts and methods of mathematics, tasks, through which introduces new concepts and methods, tasks, creating problem situation with a view to acquiring new knowledge by students. Here you should consider and tasks with which renders complex for students of the proof of the theorem.
The practical significance of mathematical problems. When solving mathematical problems pupil learns to apply mathematical knowledge to practical needs, prepares for future action, to meet the challenges put forward by practice of everyday life. Almost all design calculations must solve math problems based on queries practice. The study and description of the processes and their properties is impossible without the involvement of the mathematical apparatus, i.e. without solving mathematical problems. Math problems are solved in physics, chemistry, biology, materials, electrical resistance and help, especially in their theoretical bases, etc.
This means that math students should offer tasks associated with related disciplines (physics, chemistry, geography, etc.), as well as with technical and practical life.
The value of mathematical problems in development thinking. Solving mathematical tasks accustoms to allocate parcels and opinions, data and search, find the total, and especially in the data, compare and contrast the facts. When solving mathematical problems, brought up thinking, first and foremost, students become accustomed to full reasoning. The task must be fully substantiated, i.e. not allowed illegal synthesis, unsubstantiated analogy, the requirement of completeness of disjunction (consideration of all cases given in the problem situation), observed the completeness and consistency of classification. When solving mathematical tasks students formed 1) style of thinking; 2) ability to succinctly express their thoughts; 3) skill is clearly fragmented progress of thinking; 4) accuracy of symbolism.
Educational value of mathematical problems. First of all, the task of raising its plot, textual content.
Educates not only plot tasks, educates the whole learning process solution of mathematical problems. Training delivered correctly solve math problems educates students honesty and truthfulness, perseverance in overcoming difficulties.
Consider the basic methods for solving problems in school mathematics course.