Introduction. This article examines the demonstration exam as a new form of midterm assessment for assessing the results of on-the-job teaching practice in the training of future mathematics teachers. It discusses its content and ways of incorporating it into the mathematics teacher training process in the context of educational and professional standards, taking into account the principle of continuity.

Materials and Methods. The primary research methods include analysis of scientific and methodological literature on the preparation, organization, and conduct of demonstration exams at universities, as well as diagnostic techniques including observation, description, interview, and questionnaires.

Results. This article describes the structure and content of a demonstration exam as a form of midterm assessment of students' on-the-job training in the pedagogical education program (major: Mathematics and Computer Science). The main types of exam questions are presented: developing a lesson plan, conducting a lesson fragment, and self-analysis. The advantages of using a demonstration exam to summarize pedagogical training compared to traditional reporting methods are explored. The specifics of organizing and conducting a demonstration exam, as well as the assessment criteria, are highlighted. The results of a pilot study of this certification format at a pedagogical university are analyzed, and the difficulties students encounter when preparing for and passing the demo exam are identified.

Discussion. The article proposes assignments to address the deficits in methodological knowledge and skills identified during the testing process. Assignments are highlighted for selecting techniques to motivate the study of mathematical material; for drawing on knowledge from various subject areas to reveal the content of mathematical material; and for developing the ability to analyze one's own and students' activities in the classroom.

Conclusion. The study demonstrates that a demonstration exam can serve as one of the stages of competency assessment following on-the-job teaching practice. This form of assessment allows students to practice the key stages of the demonstration exam algorithm, allowing future mathematics teachers to develop a professional growth strategy. To mitigate methodological difficulties in preparing for the demonstration exam, it is recommended to use a system of special propaedeutic assignments in mathematics teaching methods classes.

The content of a demonstration exam for assessing general and professional competencies based on the results of the industrial (pedagogical) internship of future mathematics teachers was determined;

A deficit in the methodological knowledge and skills necessary for successful completion of the exam was identified;

A series of methodological assignments was proposed aimed at drawing on knowledge from various subject areas, introducing various methods for motivating students' cognitive activity, and creating conditions for participants to transfer acquired knowledge and skills to new work environments.

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