Maths Difficulties and Ways That Students Can Be Supported

Introduction

The development of students within the framework of academic disciplines is a difficult task for both the teacher and the students. The academic discipline, focused primarily on transferring the content of a specific scientific field, has a relatively limited supply of opportunities for developing personality qualities. Therefore, the main factor in the development of students is the methods of educational interaction between students and the teacher. One of these approaches is the method of organizing pedagogical support for students in mastering educational material. Comprehensive support helps students realize the importance of mathematics and gain confidence in their own knowledge and actions.

Understanding Common Maths Difficulties

With great pedagogical potential, mathematical disciplines can influence the development of competencies related to the culture of thinking, the processes of self-development, and ideological activity. However, low motivation to study mathematical disciplines does not allow the effective use of the full potential of disciplines in the educational process. In this regard, the organization of pedagogical support for students experiencing difficulties in studying mathematical disciplines is a critical factor in developing a student’s personality (Ayuwanti et al., 2021). The pedagogical potential of mathematical disciplines lies in the possibilities of the discipline for developing the student’s personality. There is enough material accumulated in the scientific field of Mathematics, the use of which in the educational process will contribute to the formation of various skills of students.

Firstly, it is the development of competencies that characterize a developed culture of thinking. The ability to think rationally is the prerogative of mathematical disciplines. Secondly, in a rapidly changing world, a person must react promptly to various changes and accordingly change themselves (Siregar & Daut Siagian, 2019). The development of metacognitive competence, the ability to manage one’s intellectual resources, and means of mathematical activity, is effective since formalism in mathematics allows people to separate their own thoughts from others. Moreover, in mathematics, as nowhere else, people observe themselves and their thinking processes, as well as work out techniques for overcoming cognitive difficulties.

Thirdly, mathematics is a part of world culture and actively interacts with other sciences in solving ideological problems. Therefore, the development of students’ ideological activity, manifested in the desire to apply mathematical apparatus to analyze and solve practical problems, is also the goal of studying mathematical disciplines (Ayuwanti et al., 2021). The increased emphasis on providing pedagogical support for overcoming difficulties in studying mathematical disciplines will contribute to the development of different competencies. They include the ability to think rationally when making decisions, and the ability to build promising lines of self-development based on metacognitive knowledge. Moreover, it is the ability to see the need for the use of mathematical apparatus, and the ability to understand and apply the mathematical apparatus used in professional activities.

The Essence of the Problem

Modern pedagogical and psychological research makes it possible to define cognitive difficulties as obstacles arising in the course of educational activity in understanding the material. It is reflected in its conscious assimilation, reproduction, and productive use of essential connections and dependency relationships between various studied objects, phenomena, and fragments of knowledge describing them. The higher the individual degree of conscious self-regulation, the easier and more productive the activity is (Yang et al., 2021). Therefore, overcoming cognitive difficulties should be based on solving the problem of developing conscious self-regulation of activity. A subject teacher’s pedagogical role is to consider this problem and organize pedagogical support.

General pedagogical support is aimed at supporting all students, creating an emotional background of goodwill, mutual understanding, and cooperation. Individual and personal support is aimed at organizing operational assistance for each child, considering his personal development characteristics (Bringula et al., 2021). Thus, for the development of students, it is necessary to organize pedagogical support for students in overcoming cognitive difficulties in studying mathematical disciplines (Siregar & Daut Siagian, 2019). The specifics of such pedagogical support will be the activation of metacognitive mechanisms of student activity.

The teacher’s activity on the organization of pedagogical support will be as follows.

1. The difficulties of each student are formulated.
2. Methods of overcoming difficulties are voiced.
3. The possibility of mastering these examples is provided.
4. Such forms, methods, and means of teaching mathematical discipline are used to which every student is allowed to devote time.
5. Promotes a smooth educational process flow; namely, there is no pressure on students and a moderate pace of collective and individual work.
6. The technology of complete assimilation of concepts and skills (Introduction – assimilation – consolidation – reproduction) is used.
7. A variety of control measures are used, which are more aimed at teaching self-control. The advantage is given to control and training activities, in which the student has the opportunity to receive help and advice from a teacher.

Pedagogical support for students experiencing difficulties in studying mathematical disciplines aims to reveal their problems to students and give them a developing character by turning the problem into a specific task.

Methodological Recommendations for Teachers to Organize Pedagogical Support for Students

Recommendation No. 1. Input diagnostic work in mathematics should be carried out at each stage of training.

Diagnostic work can be in different forms: in the form of a questionnaire, in the form of a test paper, in the form of a questionnaire, in the form of an essay (What difficulties did you experience when studying mathematics at school, what are they related to?) (Klang et al., 2021). Questions and tasks should be compiled in such a way as to assess real knowledge of mathematics, emotional attitude to mathematics, and perceived difficulties.

Recommendation No. 2. The first module in any mathematical discipline should be aimed at updating the necessary knowledge and skills. Actualization is carried out in three directions: generalization of fundamental concepts and ideas, solving key problems of the school mathematics course, methods, and techniques for overcoming cognitive difficulties (Ayuwanti et al., 2021). Generalization of fundamental concepts and ideas is carried out by the teacher at the first review lecture with elements of discussion.

Recommendation No. 3. To teach the process of finding a way to overcome their own cognitive difficulties, the teacher should introduce the student to some basic techniques for overcoming difficulties.

It is worth noting that any idea must be implemented and tested. Often students are not sure of the correctness of their ideas and do not undertake to solve the problem, so the teacher should provide time for the implementation of the solution and the search for errors. Often the discrepancy between the answer received by the student and the real one sharply reduces the student’s activity (Klang et al., 2021). The task of the teacher is to show that the exercise of self-control in solving problems significantly affects the development of the student’s personality (Yang et al., 2021). Regularly emphasize how important self-control and the ability to look for mistakes in all areas of activity are. It is necessary to use emotional stimulation at every stage of overcoming difficulties. The key role in overcoming difficulties is played by the intentional experience of human intelligence because it is in beliefs, preferences, and mindset that the focus on solving problems is reflected. The teacher should recommend students to use a variety of positive attitudes.

Recommendation No. 4. The teacher should be competent in choosing the forms, methods, and means of teaching students who have difficulties in studying mathematical disciplines.

• The development of students’ competencies will be more effective when organizing a personality-oriented interaction between the teacher and students (Klang et al., 2021). Therefore, when designing the educational process, preference should be given to lectures with analysis of specific situations, lectures-consultations, practical classes with individual counseling to overcome students’ difficulties, training to work out a specific mathematical skill, and collective error analysis.
• The main method of presentation of educational material is “quantization”, that is, the division of educational material into parts and the sequential assimilation of each part.
• The teacher should pay attention to the compilation and application of question-and-answer procedures in the study of mathematical disciplines and the occurrence of cognitive difficulties in students so that students are constantly involved in cognitive activity.
• All possible means of pedagogical support should be used, such as questionnaires, questionnaires, group discussions, observation, conversations, and analysis of practical work.
• Control measures should be primarily educational in nature since immersion of students in a state of stress will only increase the problem of cognitive difficulties in the study of mathematical disciplines.

Conclusion

Usually, problems arise as general difficulties in mastering mathematical content in general. Over time, the problems differentiate, deepen, and become more specific, turning out to be directly related to certain mathematical skills and abilities. Thus, if, at the first stage, the role of psychological causes is decisive, then in the future, new difficulties often turn out to be problems of the secondary circle. They include a whole range of both psychological and pedagogical reasons: gaps in knowledge, fear of failure, and misunderstanding of the essence of a mathematical rule. In this case, overcoming difficulties should be of a complex nature, involving both psychological and pedagogical assistance and support.

The task of the learning process is to strive to form a stable interest in the subject among students. It is essential to maintain curiosity, in which the student understands the course’s logic and structure and the methods used to find and prove new knowledge. In his studies, his independent solution of problems and non-standard tasks gives pleasure and captures the process of comprehending new knowledge. The form of organization of educational activities has a significant influence on the formation of the interests of schoolchildren. This process is also influenced by the use of various independent works and creative tasks in the educational process. In addition, essential aspects are a clear statement of the cognitive tasks of the lesson, an evidence-based explanation of the material, the creation of problematic situations, as well as entertaining and visuals. The student’s interest in the subject mainly depends on the quality of the teaching work in the classroom.

References

Ayuwanti, I., Marsigit, M., & Siswoyo, D. (2021). Teacher-student interaction in mathematics learning. International Journal of Evaluation and Research in Education (IJERE), 10(2), 660. Web.

Bringula, R., Reguyal, J. J., Tan, D. D., & Ulfa, S. (2021). Mathematics self-concept and challenges of learners in an online learning environment during COVID-19 pandemic. Smart Learning Environments, 8(1). Web.

Klang, N., Karlsson, N., Kilborn, W., Eriksson, P., & Karlberg, M. (2021). Mathematical problem-solving through cooperative learning – the importance of peer acceptance and friendships. Frontiers in Education, 6. Web.

Siregar, R., & Daut Siagian, M. (2019). Mathematical connection ability: Teacher’s perception and experience in learning. Journal of Physics: Conference Series, 1315(1), 012041. Web.

Yang, Z., Yang, X., Wang, K., Zhang, Y., Pei, G., & Xu, B. (2021). The emergence of mathematical understanding: Connecting to the closest superordinate and convertible concepts. Frontiers in Psychology, 12. Web.