Conference Agenda

Formation of a model of an inquisitive, intelligent, thoughtful, sociable, consistent, fair, caring, risky, harmonious, reflective student through the organization of research work in mathematics lessons. To show students the importance of organizing research work in mathematics lessons in educating a person with comprehensively developed high moral values, who is ready to apply the acquired knowledge in the process of continuing education in unfamiliar situations.
The article discusses how students can develop their research skills through small research activities. The work of various scientists is analyzed, the results of jointly planned classes on the development of students ' motivation for learning and research skills are analyzed. In the course of organizing research work in action, effective points of joint planning of teachers were identified and outlined. As a result of the study, it was found that the compilation of problems related to real life in a practical direction develops the ability of thinking to synthesize, analyze.

Conducting meaningful research work in mathematics lessons is the basis for developing students ' deeper understanding of the subject and the ability to apply it in real life. The fact that students learn, Act and reflect in a repeated cycle can lead them from academic knowledge to practical insight and the development of its positive attitude to learning, as well as personal and social responsibility.

The purpose of the study: to study the logical abilities of students through a problematic learning approach

to increase interest in their work, to teach students to work consciously on themselves, as well as to achieve solid knowledge, high learning outcomes through this method of teaching.
Research objectives:
Definition of the theoretical, basis of problem-based learning in the scientific and methodological literature;
- Consider ways to solve problems in the development of students ' thinking;
- Pedagogical and psychological description of the level of development of students;
Scientific forecast of the study: if the organized work is organized systematically, purposefully, it will be possible to develop students ' thinking through problem-based learning approaches.

A mathematical study is a long-term, open-ended study consisting of a set of questions, the answers of which are interconnected and mutually contribute to obtaining a solution. The problems are open-ended, unfinished, because students always come up with new questions based on their observations. Additional characteristics of student research include the following:
Students use the same methods used in mathematical research. They work through data acquisition, visualization, abstractions, and proof cycles.
Students communicate with each other through mathematical language: they describe their thoughts, write their judgments and predictions, use symbols, prove their conclusions, and study mathematics.
If the study consists of class or group work, then students become a community of mathematicians, exchanging experience and complementing each other with questions, assumptions, theorems.

Influence of mathematical research work on the subject
The student has a high memory and ability to concentrate, develops the ability to quickly complete a task in unfamiliar situations, and develops the skills of logical thinking, effective use of information.
It is clearly seen that the student is more motivated in the learning process, the ability to identify and find an effective solution to the problem is improved, and he gets pleasure in solving it.
The student has a high ability to think creatively, is able to identify complex patterns using mathematical approaches, such as mathematical language, developed creative thinking, and the ability to visualize tasks in space.
Every research work shows that students can think critically, analyze and present something new, new ideas with energy, whether on their own or in a group. When we find mathematical patterns, we feel that real pleasure is experienced through emotion.

The gendered choice and role of mathematics in pre-tertiary education is maybe one of the most pertinent research topics in education literature (e.g., Ellison & Swanson, 2023; Else-Quest et al., 2010; Uerz et al, 2004; Van der Werfhorst et al., 2003). While Finnish girls outperform boys in mathematics in the comprehensive school, it seems that once they have a possibility to make educational choices after the comprehensive school, the interplay of the internal versus external frame of reference for academic self-concept (Marsh & Shavelson, 1985) sets in motion and leads girls away from math (see also Marsh, 1990; Marsh et al., 2015). In Finland, this has been reported in students’ choice both between the two tracks of the Finnish dual model of upper secondary education (academic vs. vocational), among the different vocational programs, and within the relatively open syllabus of academic upper secondary education (Kupiainen & Hotulainen, 2019). In the current presentation, we set to explore the interplay of students’ gender and math choice in the academic upper secondary education, and its relation to students’ later educational choices.

In the dual model of Finnish upper secondary education (academic and vocational tracks, 56 % vs. 44 % of the age cohort, respectively), ninth grade students have a right to choose among all programs across the country but entrance to academic track schools is based on students’ ninth grade GPA (grade point average). Reflecting girls’ better achievement, they form a majority among academic track students (56 %). Yet, reflecting a longstanding gender-imbalance in students’ attitude toward mathematics and despite Finnish girls outperforming boys in the OECD PISA study (e.g., Hiltunen et al., 2023) and their better grades in math in the comprehensive school (Kupiainen & Hotulainen, 2022, p. 140), there is a clear gender difference in students’ choice between the Basic and Advanced syllabi in mathematics at the upper secondary level after the comprehensive school where all students follow the same syllabus for all subjects (Kupiainen et al., 2018).

The context of the presentation is a recent study of the impact of the Finnish higher education student selection reform of 2018 on academic upper secondary students’ study choices and wellbeing. Despite the long tradition of the Finnish matriculation examination with separate exams for each subject, Finnish tertiary education student admission has traditionally relied on a combination of field-specific entrance examinations and matriculation examination results. In 2018, a reform decreed that half of students in all fields of study shall be accepted based solely on their matriculation examination results and the other half solely on an entrance examination. The main goal of the reform was to speed Finnish students’ slow transit from secondary to tertiary education as due to a backlog of older matriculates vying for a place, two thirds of new matriculates have been yearly left without a place in higher education. The reform was backed by research on the drawbacks of the earlier entrance examination-based student selection (Pekkarinen & Sarvimäki, 2016) and tied the credit awarded for each subject-specific exam to the number of courses covered by the exam. The reform raised vocal criticism, mainly for Advanced Mathematics bringing most credit with its biggest course-load even in fields where it might appear of less value. Yet, the only earlier study on students’ relative success in the matriculation examination showed that on average, students of Advanced Mathematics fared in all exams they included in their examination (average 5,6 exams) better than students sitting for the exam in Basic Mathematics or with no mathematics exam, also allowed in the Finnish system (Kupiainen et al. 2018).