Mathematical Competence Model of a Technology Teacher

The purpose of the article is to define the structure and build a model of the mathematical competence of a teacher of technological education, develop methods for its parametric identification, analyze the results of the testing of the proposed methods of measuring mathematical competence. The conducted research was based on theoretical methods of system analysis, pedagogical modeling, as well as experimental methods of sample research, methods of statistical analysis of experimental data, in particular, descriptive statistics and correlation analysis. As a result of the study, a reasonable definition of the mathematical competence of a teacher of technological education is given, its components are highlighted: operational-arithmetic (arithmetic), geometric, mathematical modeling, analytical-statistical, which determine the functions of mathematical activity of a teacher of technological education. A hierarchical structure of the content of mathematical competence has been built, it is justified that it should contain three levels: basic, medium, high. It is shown that a basic level of mathematical competence is sufficient to ensure the main work of a teacher in the technological education field. A structural model of the mathematical competence of a teacher of the technological educational field was built, in which information connections between the subject-professional activity of a teacher of the technological educational field, his/her scientific and analytical activity, components of mathematical competence and the system of forming its content are reflected. The value of the index of the basic level of mathematical competence was evaluated as the probability of coping with a randomly selected task from the population of tasks related to the teacher's work functions, the average value of which is 0.63. It is estimated that approximately 70% of technology education teachers can solve more than half of the basic level problems. The correlational dependence between the results from the mathematical modeling components and the arithmetic component was revealed. The main problematic mathematical questions for teachers of technological education are also revealed. The practical significance of the study is that the obtained results allow to improve the system of training future teachers of the technological educational field, in particular their mathematical training, as well as to adjust the content of postgraduate pedagogical education of teachers. The main conclusions of the study include that it is the basic level of mathematical competence that is necessary for the realization of the functions of a teacher of the technological educational field, and also that at least 30% of the teachers of the technological educational field need the development of mathematical competence. Therefore, possible further explorations involve the implementation of trainings, special courses, blocks of practical classes at advanced training courses for technological education teachers to develop their mathematical competence and analyze their effectiveness.