Методична система навчання математичних методів фізики у педагогічних університетах

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Abstract (English)

Podoprygora, N. V. (2016). Methodical system of teaching mathematical methods of physics at pedagogical universities. – Manuscript. Dissertation for the degree of Doctor of Pedagogical Sciences in Specialties 13.00.04 – Theory and Methods of Professional Education; 13.00.02 – Theory and Methods of Teaching (Physics). – National Pedagogical Dragomanov University, Ministry of Education and Science of Ukraine, Kyiv.

Abstract: The thesis carries out a scientific analysis of future school and higher educational establishment teachers' training in Physics. Physical and mathematical training of future physics teachers is determined to be an integral part of their training at the Pedagogical University, forming individual and professional qualities important for future specialists and their readiness for specific types of professional activity. Each discipline in the professional training framework—such as "Mathematical Methods in Physics", "Theoretical Physics", "Physics of Solids", etc.—affects the formation and development of future specialists' professional competence.

It is proved that the formation and development of mathematical competence of future physics teachers in teaching Mathematical Methods in Physics and Theoretical Physics is a multiprocess based on fundamentalization, interdisciplinary integration, contextual, informational, and basic competency approaches, which collectively ensure specialists' readiness and ability to solve educational and subsequent professional tasks.

The concept of mathematical competence in Physics, formed and developed in the process of studying Mathematical Methods in Physics and Theoretical Physics, is defined as an integrated dynamic characteristic of the student's personal qualities, describing readiness and ability to apply academic and professional methods of mathematical modeling of physical systems, phenomena, or processes in terms of the laws or principles of physics within a set theoretical framework.

A four-level structural and functional model of the formation and development of mathematical competence in Physics for future physics teachers during the study of Mathematical Methods in Physics and Theoretical Physics is developed according to the stages of scientific research: the first level provides for the selection of the object and purpose of the study and justifies the theoretical and methodological choices; the second level involves the conceptualization, development, and implementation of the methodical system, accounting for pedagogical, organizational, and methodological conditions; the third level elaborates the targeted, semantic, procedural, and methodological components through diagnostics, goal-setting, planning, structuring, and expectations; the fourth level designs criteria, indexes, and levels of competence formation and development.

The methodical system of teaching mathematical methods in Physics at pedagogical universities is based on an integrated approach providing comprehensive application of fundamentalization, multidisciplinary, contextual (theoretical, applied, professionally oriented), informational (subject-information, information and communication contexts), and competence approaches. The systematizing methodological component is established as a target ensuring the correlation of objectives and learning outcomes of Mathematical Methods in Physics with the formation and development of mathematical competence in Physics.

The study theoretically proves the feasibility of using a comparative-reconciling approach to the targeted formation of mathematical competence in Physics, providing the isolation of an integrative component (physical law or principle paired with a mathematical correlation or equation), comparing it with the content of teaching Mathematical Methods in Physics and Theoretical Physics, and coordinating it with the procedural basis of learning theoretical physics within students' learning activities.

Methodical techniques for developing students' creative abilities in studying Theoretical Physics in terms of the "cyclical principle" are improved; the content, structure, and methods of organizing classes for the discipline "Mathematical Methods in Physics" are oriented toward forming mathematical competence in Physics across defined components: cognitive (knowledge of the professional scientific discipline—Mathematical Physics), activity-based (ability to solve educational problems and situations within Mathematical Methods in Physics), and personal (motivational, value-reflexive, emotional-volitional qualities).

Methodical approaches to teaching Mathematical Methods in Physics are substantiated, providing practical guidance on implementing educational processes via contextual and informational approaches, including the use of educational physical experiments and mathematical information packages. Implementation results confirmed the statistical reliability ofль the methodical system's impact on students' mathematical competence across all components.

Keywords: Mathematical Methods in Physics, Theoretical Physics, mathematical competence in Physics, methodical system of mathematical methods in Physics teaching, integrative approach, future school and higher educational establishment teachers of Physics.