Nazarian Marina Emilievna,
2 courses of the group 02041860
BELGOROD STATE NATIONAL
RESEARCH UNIVERSITY
FORMATION OF MATHEMATICAL CULTURE OF PUPILS IN SOLVING WORD PROBLEMS CONTAINED IN THE EXAM PROFILE LEVEL
One of the most important tasks of a high school student is to successfully pass the unified state exam. An important component of successful passing the exam is a high level of mathematical culture of students. One of the main tasks of a modern school is to help students develop their potential and develop their mathematical culture. Solving text problems in math lessons helps students not only improve their mathematical culture, but also develop logical and algorithmic thinking. They will also learn to Express their thoughts clearly and clearly, to reason and analyze, and to make their own decisions.
Today, mathematics is considered a natural discipline, the role of which cannot be overestimated in the formation of a person.
Helping a person to form a mathematical culture is a complex and lengthy process that will later make a huge contribution to the formation of a person's worldview.
After analyzing the methodological and psychological - pedagogical literature, we found that there is no single definition of the concept of mathematical culture.
According to N. L. Stefanov, mathematical culture refers to education that includes a system of mathematical knowledge, skills and abilities and is part of the General culture [1].
S. Akmanova considers mathematical culture as a complex, dynamic quality of personality that characterizes the readiness and ability to acquire, use and improve mathematical knowledge, skills and abilities in activities.
Thus, the formation of mathematical culture is very important and has a great influence on the formation of the individual as a whole. Text problems can help improve the quality of a person's mathematical culture.
A mathematical task is a related story in which there are fixed values of certain quantities and it is necessary to find unknown values. The values to be found are dependent on the known data.
Each text task contains two parts:
1. Condition
2. Question
The first part contains information that is known by the condition of the problem, as well as information about unknown values of these values. In the first part, we specify the relationship between these values. The second part specifies what you need to find.
In modern mathematics there are various ways to solve text problems:
• arithmetic,
* algebraic,
* geometric,
* schematic,
• graphic
The solution to any text problem consists of three main points:
1) successful selection of unknown;
2) creating an equation and formalizing what you need to find;
3) solution of the resulting equation.
After analyzing the unified state exam in mathematics of the profile level, we found out that task #11 is dedicated to solving text problems. Let's list the types of tasks that occur in the unified state exam:
1. Problems on percentages, alloys and mixtures
2. Tasks for moving in a straight line.
3. Tasks for moving around a circle.
4. Tasks for moving on water.
5. Tasks to work together.
6. Objectives for progression.
Let's look at some of them [2]:
Task 1.
Two tigers ran out of the same lair simultaneously in opposite directions. The speed of one tiger is 48 km / h, and the other is 54 km / h. What is the distance between the tigers in 3 hours? Decision.
1) 48 * 2 = 96 (km) - one tiger will run for 2 hours.
2) 54 * 2 = 108 (km) - another tiger will run in 2 hours.
3) 96 + 108 = 204 (km) - will be between the tigers in 2 hours.
The answer is: 204 km
Task 2.
How many grams of water should be added to 60 g of a solution containing 5% soda to get a 4% solution?
Decision:
Let x be the amount of water to add. The total amount of the solution is (60 + x) g. Therefore, to find the required amount of soda in the original solution is 60 * 0.05 g. Then, it turns out that to find the amount of soda in the new solution, you need 0.04(60 + x)
Since the amount of soda from the addition of water has not changed, it is the same in the original and new solutions. Get the equation
60* 0,05 = 0,04(60+x),
60* 5 = 4(60 + x),
75 = 60 + x,
X = 15.
Answer: 15 g.
Thus, text problems help to develop mathematical literacy, and arouse great interest in the study of mathematics. To successfully solve text problems, students need to make a short record and a solution plan, complete the solution, and make a check.
References:
1. N. L. Stefanova. Methodology and technology of teaching mathematics. - Moscow: 2007.
2. M. A. Ivanov Mathematics without a tutor. 800 problems with answers and solutions for applicants Textbook. - Moscow: Publishing center, 2002.
© M. E. Nazarian, 2020
