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SCIENCE AND EDUCATION IN THE MODERN WORLD



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SCIENCE AND EDUCATION IN THE MODERN WORLD: 
CHALLENGES OF THE XXI CENTURY"
 
ASTANA, KAZAKHSTAN, FEBRUARY 2023 
43 
- Development of "applied" probabilistic-statistical thinking skills in conducting calculations on 
the probability theory and mathematical statistics course. 
- Framework for the preparation' mathematical skills including the use of probability theory
The matter of probability theory is being taught not only in Kazakhstan but also in other 
countries too, demonstrates how important understanding is in modern society. In terms of 
significance, PISA survey involves questions regarding probabilistic and statistical knowledge 
implementation dates back to 2003. 
It should be noted that teaching students about the close ties that exist among the various 
regions of the world has historically been the primary goal of education in Kazakhstan. While it 
is not necessary for everyone, mathematics in the school curriculum has a reputation for being a 
conservative discipline that places a strong emphasis on math education, which is not needed by 
many students. The drawbacks of isolating the demands of society from the educational program 
are made more clear every year. Probability theory is a subject that is taught in other nations as 
well, demonstrating how crucial it is to understand things in the contemporary world. The PISA 
survey asks students about their understanding of probability and statistical principles, which is 
significant information. 
Analyzing and sole theory learning shouldn't be the main emphasis, as was already 
mentioned. Instead, teachers must demand that students have a solid understanding of the 
fundamental concepts such as models of variability, averages, dispersion, sample studies
random variables, etc. Students learn a lot of ideas and information from an experiment, 
excluding formulas and logical conclusions. After completing statistics and probability courses, 
students are expected to critically analyze, debate, and reflect in order to develop a framework of 
guiding principles and intuition. As a result, educators place a high value on tasks and 
circumstances that invite subjectivity and speculation but do not offer a definitive solution. 
In order to successfully transition from introducing abstract facts to discussing real-world 
applications of mathematics, math teachers must first have a thorough understanding of and be 
conversant with the ordinary perception of statistics and probability. The fact that practice-
oriented tasks for calculating change, choosing an alternative, and calculating travel time were 
published in textbooks and found to be subjectively more difficult to complete than working with 
logarithmic expressions. The existing issues that occur in teaching probability are primarily due 
to the formal and frequently aimless teaching of probability at schools, as well as the 
insufficiency and poor quality of teaching materials. All of this is due to the lack of school 
policies for teaching probability and statistics. As the method is refined and users gain 
experience, these problems will gradually disappear, making way for the ensuing ones. The most 
crucial time in the development of a new school subject should be viewed as the eighth to tenth 
grades. After this, new teachers who started their studies in middle school do not think the 
subject is novel or too difficult. 
Three key terms in probability theory are "event," "probability," and "random".The idea 
of an "event" in probability theory is closely related to the idea of a theoretical set. Students 
should therefore be familiar with the fundamentals of set theory and probability theory in order 
to give a precise definition of this concept.Since set theory education is not a part of the standard 
school curriculum, it takes a highly skilled teacher to approach this problem in the right 
way.Using an experimental math course in elementary school is one approach to solving this 
issue. In elementary school, the idea of a set is taken for granted, and operations on sets and their 
properties are explained using an illustrative (visual) method.
Simple probability models are first taken into consideration when the concept of "event" 
is being formed. If we take coin flipping,its "heads" or "tails" is facing up when there is an event. 
Similarly, the concept of "elementary experiences" is formed intuitively by actions like rolling 
the dice, grabbing a ball out of an urn, and shooting at a target. Students learn from these 




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