# UNDERSTANDING OF EDUCATIONAL MATERIAL BY STUDENTS IN MATH CLASSES

**DOI: https://doi.org/10.23670/IRJ.2022.120.6.140**

**ПОНИМАНИЕ УЧЕБНОГО МАТЕРИАЛА УЧАЩИМИСЯ НА ЗАНЯТИЯХ ПО МАТЕМАТИКЕ**

Научная статья

**Квашко Л.П. ^{1, }*, Александрова Л.Г.^{2}, Санцевич Я.С.^{3}**

^{1 }ORCID:0000-0002-4803-7297;

^{2 }ORCID: 0000-0003-3591-1333;

^{3 }ORCID: 0000-0002-9566-0508;

^{1, 3 }Приморский институт железнодорожного транспорта − филиал Дальневосточного государственного университета путей сообщения в г. Уссурийске, Уссурийск, Россия;

^{1, 2}Дальневосточный федеральный университет, Владивосток, Россия

* Корреспондирующийавтор (lkvashko [at]mail.ru)

**Аннотация**

*В статье обосновывается необходимость учёта нейрофизиологических особенностей современных подростков и юношей при обучении, выявляются уровни понимания предметно-ориентированной речи преподавателя на занятии. Научная новизна исследования заключается в том, что было получено экспериментальное доказательство того факта, что современные обучаемые не способны усваивать новый учебный материал с первого предъявления на традиционной лекции или на уроке. В результате исследования было установлено, что только третья часть обучаемых понимает речь преподавателя и осознаёт содержание учебного материала непосредственно на лекции. Полученный результат необходимо учитывать в практике преподавания, чтобы модернизировать её с целью удовлетворения образовательных потребностей учеников.*

**Ключевые слова:** понимание учебного материала, консолидация и реконсолидация памяти, обратная связь.

**UNDERSTANDING OF EDUCATIONAL MATERIAL BY STUDENTS IN MATH CLASSES**

Research article

**Kvashko L.P. ^{1, }*, Aleksandrova L.G.^{2}, Santsevich Y.S.^{3}**

^{1 }ORCID: 0000-0002-4803-7297;

^{2 }ORCID: 0000-0003-3591-1333;

^{3 }ORCID: 0000-0002-9566-0508;

^{1, 3 }Primorsky Institute of Railway Transport, a branch of the Far Eastern State Transport University in Ussuriysk, Russia;

^{1, 2 }Far Eastern Federal University, Vladivostok, Russia

* Corresponding author (lkvashko [at]mail.ru)

**Abstract**

*The article substantiates the need to take into account the neurophysiological features of modern adolescents and youth in the learning process, establishes the levels of understanding of the subject-oriented speech of the teacher in the classroom. The scientific novelty of the research lies in the fact that with the help of an experiment, we proved that modern students are not able to master new educational material from the first introduction at a traditional lecture or lesson. As a result of the study, it was stated that only a third of the listeners understand the teacher's speech and are aware of the content of the educational material directly at the lecture. The result obtained should be taken into account in pedagogical practice in order to modernize it and in order to meet the educational needs of students.*

**Keywords**: understanding of educational material, consolidation and reconsolidation of memory, feedback.

**Introduction**

The relevance of the research topic is related to the problems of understanding texts and speech spoken by another person. In philosophy, representatives of hermeneutics [1] evaluate a person's ability to comprehend the meanings inherent in texts. Psychologists study the problem of understanding and comprehension of educational material in the classroom from the point of view of human brain development [2]. Teachers develop didactic and methodological aspects of the educational process, taking into account the functioning of the human brain (neuropedagogy) [3]. Our research contributes to the study of real teaching practice in terms of understanding the teaching material at a lecture at a university or at a lesson at school.

The experience of work with the students convinces us that the new generation of children and youth is more and more different from the previous generations. Individual differences and abilities of today’s trainees are connected with the structure of the brain of modern people [4],[5]. The influence of brain asymmetry on learning activity was studied by many scientists in abroad [6],[7]. In conditions when digital technologies are widely used not only in everyday life, but also in the educational process, it has become especially important to take into account the psychological characteristics of students in the modern educational process.

Article 3 (paragraph 7) of the Federal Law “On Education in the Russian Federation” dated December 29, 2012 No. 273-FL (with amendments and additions dated December 30, 2021), establishes the need to “create conditions for the self-realization of each person, the free development of his abilities”. Therefore, the establishment of the fact of understanding or misunderstanding of the educational material in mathematics lessons is necessary to create comfortable pedagogical learning conditions. It cannot be said that such a study is being conducted for the first time. Our predecessors [8],[9],[10] also studied comprehension issues in math lessons. Such a study was conducted for the first time at the Primorsky Institute of Railway Transport, a branch of the Far Eastern University of Railways in Ussuriysk. This is due to the fact that the practice of teaching mathematics has accumulated didactic and methodological problems that are insufficiently studied and not covered in the pedagogical literature. This research contributes to solving the problem of successful mastering by students of technical and natural sciences disciplines.

This article suggests that the readers should get acquainted with our research, which was first conducted two years ago [11] and has been worked on up to the present time. Students and schoolchildren are changing, but one thing remains unchanged: their low level of understanding of the teacher’s scientific speech. In this study, we obtained the same data as in the previous one.

Having been teaching mathematics to schoolchildren and students for many years, it was noticed that over the years the learning process becomes more and more complex. The number of children with good and excellent math skills is decreasing. When teaching children individually, we began to notice a growing trend of deterioration of children's mathematical knowledge, poor memorization of information. The *goal* was to establish the degree of understanding or misunderstanding of the educational material in mathematics classes.

To achieve the purpose of the study, the following *tasks* were solved:

1) to study the pedagogical and psychological literature on the subject of the study;

2) to develop a survey technology and questionnaire to diagnose the subjective state of understanding of educational material by students and schoolchildren in the classroom;

3) determine the number of students and schoolchildren to conduct the study;

4) analyze the data obtained using point statistics and draw conclusions based on these results.

To conduct this research, the following methods were used: contextual analysis of philosophical, psychological and pedagogical literature, questioning of students and schoolchildren, statistical analysis of the results.

The theoretical basis of the research was the main provisions of hermeneutical theory [1] and a personality-oriented approach to teaching mathematics to students and schoolchildren [12]. As well as research in the field of neuropsychology (A.R. Luria, Y.M. Mikadze, L.S. Tsvetkova), neuropedagogics (V.A. Moskvin, N.V. Moskvina, T.P. Khrizman), neurodidactics (the term was introduced into scientific circulation by G. Price; O.V. Kulikova, A.S. Potapov, A.L. Sirotyuk).

The state of the brain of modern children differs from the brain of their parents [5]. According to the scientist, the brain of modern children works slower, but more efficiently. There is an uneven, with “interruptions”, functioning of the brain, which leads to the fact that the child has difficulties with the implementation of the school curriculum. The brain of our children develops not only slowly, but also in two directions at once: in the left and right hemispheres. In such a situation, learning becomes easier, more and more information is assimilated, which is structured “at the behest” of both hemispheres.

Taking into account the bilateral brain development of a new generation of children and youth requires teachers to build a presentation of new educational material fragmentarily, limiting the amount of information on one slide, linking the new part with the already known and with the practice of the field of application. In addition, rigorous mathematical reasoning should be accompanied by vivid images and associations. This will allow you to use both hemispheres in the learning process.

The processes of assimilation of scientific knowledge are associated not only with the psychological characteristics of modern students and schoolchildren, but also with the peculiarities of the functioning of the processes of memorization and reproduction of scientific information.

As a criterion for assessing the fact of misunderstanding of educational material when teaching mathematics, the subjective state of students' understanding of educational material in mathematics lessons and the time during which this state was observed was chosen.

**Results and discussions**

The study involved 22 secondary school students and 59 first and second year students of the technical University. The math lesson for schoolchildren lasted 45 minutes, the lesson with university students lasted 90 minutes.

To assess the subjective state of students’ comprehending the educational material, we chose the time of the class, during which they experienced this situation. The technology of the survey was the following: during the class, the students were constantly asked a question: “Who understands what I am talking about?” They raised their hands, and we fixed this number. At the end of the class, we asked each student to indicate in writing what part of the time (in percentage or points) he felt a state of understanding and awareness of what was said in the class.

The results of the observations and the survey were compared and ranked for further analysis and assessment of the current state. We have chosen the following percentage scale to assess this current state and the corresponding point scale (see: Table 1).

Table 1 – Criteria for assessing the subjective state comprehension of educational material in mathematics classes

The percentage scale of assessment, % of the total time of the class | The scoring scale, conventional unit | Meaning description of the scoring |

0-20 | 1 | did not understand anything |

21-40 | 2 | understood something |

41-60 | 3 | most often did not understand than understood |

61-80 | 4 | most often understood than did not understand |

81-100 | 5 | understood the training material during the whole class or during the greater part of it |

This scale is well correlated with the Russian system of assessing the achievements of schoolchildren and did not cause difficulties for the respondents. At this stage of the experiment, the error in obtaining objective data was also minimal.

It should be noted that while receiving the initial data, the educational material that was studied in the classroom corresponded to the existing school and university programs and textbooks, and did not undergo any changes. The training method also was not changed in relation to previous periods of teaching. The students of five groups of the first and second courses of three different specialties of a technical university, in which the authors of the study worked, were selected for the survey.

We conducted survey procedures with students of different ages. They were united by the fact that they all have difficulties in learning mathematics. Teaching mathematics, we had the opportunity to set the amount of time for certain when a student was included in the learning process and learned the material, and when it did not happen.

Our experiment was aimed at establishing the subjective state of students’ understanding of educational material in mathematics. We calculated the average grade for all groups in order to have an idea about the general picture of the subjective state of students’ comprehending educational material in mathematics classes and got the following result: Then we found the variation of each grade of a student xi around the average: σ =1,10. We also obtained the average point X for all groups:

The mean square deviation, in addition to its purely mathematical meaning, also has pedagogical significance. The indicator σ indicates how far each of the individual data obtained is from the average and how close the respondents' opinions are to each other. The difference between the average index and the spread around the average gives us a statistical index X - the average score, which can be compared in further research.

Having received such an index as an averaged point, we can state that the students of the reference group are in the situation “Something was understood” during the semester. In some cases they are in the situation “Most often I did not understand than understood”. Returning to the original meaning of this index - the time during which the trainees were in a situation of understanding the educational material, it can be stated that 40-60% of the time the students “understood something”.

In addition to students, we interviewed schoolchildren and got the following result: and . This indicator is not much different from students.

As among students, the average score of schoolchildren indicates that they are most often in a situation of “I understood something”, in some cases they are in a situation of “Most often I did not understand, then I understood». This gives us the right to say that, like students, schoolchildren “understood something” for 40-60% of the time.

The final data show that the subjective state of students' understanding of the teaching material in mathematics worsened after entering the university. This is indicated by the following data. The average score for this sample of students, which was 3,07, is 0,11 less than that of schoolchildren (3,18). The spread around the average score of students is 0,22 higher. This suggests that schoolchildren are more unanimous in their assessments than students.

Assessing the subjective state of students and schoolchildren’s comprehending of the educational material in mathematics classes and analyzing the results, we can draw the following conclusions:

- 5% of the surveyed students understand the study material during 60-100% of the study time.
- 3% of the surveyed schoolchildren understand the educational material 60-100% of the lesson time.
- The situation with the understanding of educational material in mathematics lessons for both schoolchildren and students is equally bad. As a result of the research, the fact of having difficulties in understanding of the educational material by the students of a technical university and the students of secondary schools was established. Two-thirds of the total number of subjects, both the schoolchildren and the students, were in the state of “I don’t understand anything” or “I understand something” throughout the whole period of learning. And only one third of the testees understood the training material.

**Conclusion**

The difficult understanding of new educational material in math classes has been explained in studies by neuroscientists and psychologists, who claim that the brain of the generation born after 2000 is arranged differently. This means that the work of teachers in the field of education should be based on these features. In this study, the goal was to test the level of understanding of educational material in the classroom during lectures. It was found out that a third of both students and schoolchildren understand the educational material from the first presentation and experience a state of satisfaction with the learning process. The practical significance of the research lies in the fact that teachers of natural sciences can take into account the results of our research when teaching students of engineering and technical areas of training. Therefore, a methodical recommendation for teachers can be a “clip” introduction of new educational material, presented in the form of a presentation with a minimum number of slides and text on them, and the organization of regular feedback. This topic requires further research related to didactics and methods of teaching natural sciences, as well as neuropedagogy.

Конфликт интересов
Не указан. |
Conflict of Interest
None declared. |

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