In modern conditions, mathematics is the language of science and technology. With its help, many processes and phenomena occurring in the world, society, and nature are modeled, studied, and predicted, therefore the mathematical training of students is a necessary condition for accelerating technological progress. The scientific, economic, production, and defense potential of the country directly depends on its quality, but not every student wants to devote himself to a profession that is in some way connected with advanced mathematics.
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Mathematics plays an ever-increasing role in the process of learning about reality. Today, there is no field of knowledge in which mathematical concepts and methods are not used to a greater or lesser extent. Problems that were previously considered impossible to solve are being successfully solved through the use of mathematics, thus expanding the possibilities of scientific knowledge. Modern mathematics brings together very different fields of knowledge into a single system, but for many students, it is nothing more than an obstacle to graduation. According to Strauss (2017), although 60 percent of students enrolled at community colleges must take at least one course in math, about eighty percent of students never fulfill the requirement and leave without graduating.
Reasons for Poor Average Performance and Ways of Solving the Problem
Among the possible causes of weak average algebra performance is the lack of student motivation and the lack of professionalism of teachers. The problem of motivation is one of the most critical problems in pedagogy. It is possible to note that “understanding student motivation allows the teacher to design tasks and interventions to improve student learning, especially at the early college level, where students are more likely to give up.” (Nguyen, 2014, p. 14). The educational process in higher education institutions involves young people who continue to develop their personalities. The task is to find methods and means of increasing the motivation of learning, contributing to the maximum development of personal qualities of students necessary for their successful professional activities.
The reasons why students are not motivated to study advanced mathematics vary. Among the reasons that lead to the emergence of intellectual and cognitive motivational barriers is the weakening of interest and the lack of the need to master new knowledge and skills. In the real learning process of mathematics, this can be manifested, in particular, in the form of the intellectual passivity of students. Also, some students may have missed or misunderstood certain parts of the material, and some may have misconceptions. According to Booth, McGinn, Barbieri, and Young (2017), preventing and remediating algebraic misconceptions may be necessary for increasing student success in algebra and, subsequently, more advanced mathematics classes.
The same text presented by a variety of people can have various effects. Different people will absorb different knowledge and impressions from the same lecture. It depends on their level of competence, their attitude to the lecture and their ability to work at the lecture as no skill is formed without a sustained commitment. Cognitive interest is one of the essential factors in activating learning activities. Only in such cases does learning become a personally significant activity in which the learner is interested.
The content of the learning material and the form in which it is presented to learners should be such that the information becomes personally relevant to them. Benson (2015) believes that students should be eager and excited to study mathematics and feel that they are learning skills that will be of great value to them after high school. When the lesson is not engaging, students listen inattentively and learn very little. The duty of a teacher of any discipline is not only to pass on knowledge to students but to develop their ability to think independently and the need for independent efforts to master science. Lecturing in mathematics is particularly challenging due to the nature of mathematics as a deductive discipline.
The Importance of Advanced Mathematics and Mathematics in General in The Modern World, and the Skills That Students Acquire in The Process of Learning
The task of mathematics is to describe a given process with the help of a particular mathematical apparatus, i.e., in a formal and logical way. Speaking about the subject and functions of mathematics, it is evident that the integrative role of mathematics in modern science is becoming more and more noticeable, as it is a general scientific discipline. Functions of mathematics are undoubtedly humanitarian as they are directed on the perfection of the material and mental spheres of the human being. Mathematical knowledge and skills are necessary for many professions, first of all, in those which are connected with natural sciences. Mathematics is the language of science and technology, and therefore the professions of natural scientists and engineers require serious mastery of specialized knowledge based on mathematics. Requiring intellectual and willful efforts, the concentration of attention, the activity of the developed imagination, mathematics develops moral features of the person (persistence, creative activity, independence, purposefulness, diligence) and substantially expands the outlook of students.
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The role of algebra in modern mathematics is extremely significant, and there is a real tendency for further algebraization of mathematics. A typical way to study many mathematical objects, sometimes very far from algebra, is to build algebraic systems that reflect the behavior of the studied objects quite well. Algebraic concepts and methods are widely used in number theory, functional analysis, differential equation theory, geometry, and other mathematical disciplines. Along with the fundamental role in algebra mathematics, it is important to note that algebra has a significant applied role in physics, cybernetics, and economics.
The crucial task of the mathematics course is to develop logical thinking. Like no other subject at school, mathematics has the opportunity to teach logic to students at every step of the way. In the process of mastering mathematical knowledge, the task of developing students’ logical reasoning skills is solved. The ability to find logical consequences from the initial conditions, the ability to abstract, i.e., to distinguish the essence of the question in a specific situation, distracting from the insignificant details, is obtained. While studying mathematics, students master the skills of analyzing the question under consideration, generalizing, selecting necessary and sufficient conditions, defining concepts, making judgments, and finding ways to solve the task. All these factors shape the students’ thinking and contribute to the development of their speech, especially such qualities of thought expression as order, accuracy, clarity, conciseness, and reasonableness.
Algebra, through its specific means, contributes to the solution of a whole range of humanitarian problems and is of great importance in the life of society. The root of the problem of students’ poor academic performance is not the subject itself, but its delivery. Taking into account the internal logical unity of mathematics, the organic interrelation of its parts, the most critical requirement for the organization of its teaching should be consistency and continuity in learning. The goal is to accumulate specialized knowledge, master the methods of formulating and solving mathematical problems, and on their basis to develop the intellect of students, the formation of a culture of thinking, the education of the volitional qualities of the individual, the ability to overcome difficulties.
- Benson, J. (2015). Algebra: Should it be a Graduation Requirement? The Banneker Banner, 29. Web.
- Booth J.L., McGinn K.M., Barbieri C., Young L.K. (2017) Misconceptions and Learning Algebra. In Stewart S. (Eds.) And the Rest is Just Algebra (pp. 63-78). New York, USA: Springer
- Nguyen, G.-N. T. (2014). A Case Study of Students’ Motivation in College Algebra Courses. Community College Journal of Research and Practice, 39(8), 693–707. doi:10.1080/10668926.2013.824394
- Strauss, V. (2017). Of course algebra is important. It’s also a huge problem. The Washington Post. Web.