Introduction:

In contemporary education, considerable emphasis is placed on the implementation of pedagogical techniques that promote effective teaching through active engagement of students with educational content. Among these approaches, problem-based learning (PBL) stands out as a method that fosters the development of creative thinking, autonomy, and problem-solving abilities among students, while also facilitating the application of acquired knowledge in practical contexts. This study aims to investigate the influence of employing problem-based learning methods in preparing 10th grade students for an external summative assessment in the domain of mathematics.

Theoretical Basis of the Study

Summative assessment serves as a means of evaluating the educational accomplishments of students upon completion of specific sections or cross-cutting topics within the curriculum. It also encompasses the assessment conducted over a designated educational period, such as a quarter, as well as external assessments. These assessments entail the allocation of points and grades, while providing valuable insights on student progress to teachers, parents, and students themselves.

External summative assessments are carried out upon the culmination of particular levels of education, encompassing primary, basic, and secondary education. The benchmarks utilized in these exams adhere to international standards, such as the Cambridge Primary (grade 5), IGCSE (grade 10), AS-level, and A-level (grades 11-12). External summative assessment exams feature multiple components, including closed and open-ended questions that require both concise and detailed responses.

Upon the completion of external summative assessments, students in 12th grade receive an NIS Grade 12 Certificate. This certificate holds recognition by esteemed universities in Kazakhstan, as well as by leading international organizations. [1]

The issue we encountered revolved around our school's performance in mathematics during external summative assessments, as we ranked last within the Nazarbayev Intellectual School network. Notably, there existed a disparity between internal assessments and external assessments. The aim of this action research was to enhance the quality of mathematics outcome measures among 10th grade students. The study pursued the following research question: How does the integration of problem-based learning impact students' effective preparation for external summative assessments in mathematics?

Problem-Based Learning (PBL) technology has been utilized in higher education since the mid-20th century, serving as an interactive learning method. Initially employed by universities in the United States and Canada during the 1950s, PBL later proliferated across European universities during the 1960s. The introduction of this technique initially occurred in the Faculty of Medicine at Case Western Reserve University. Recognizing the contemporary context characterized by an information and technological "explosion," which entails rapidly evolving requirements for future professionals, PBL emerged as the training model best aligned with this situation. [2]

The traditional approach to higher education emphasizes the passive transfer and rote memorization of existing knowledge. Students grapple with the monotonous task of memorizing vast amounts of information that, in their estimation, may not always directly pertain to their forthcoming professional endeavors. Consequently, apathy, detachment, and occasionally disillusionment arise. Frequently, students tend to forget a substantial portion of the material they have learned once an assessment has been completed. Moreover, the retained information often proves challenging to apply when attempting to solve problems across related subject areas, especially within the realm of real-world professional application. [3]

The foundation of PBL rests upon a constructivist approach, which has garnered opposition from critics of this teaching method. In line with the constructivist trend, which emphasizes student participation in the construction of new knowledge through the reevaluation of experiences, PBL brings about significant changes in the learning process itself. It assumes an active and socially-oriented character, thereby embracing a more interactive format.[4]

The study involved the participation of all 10th grade students at NIS in Aktau during the academic year 2022-2023. A purposive sampling technique was used to recruit 129 participants for the research sample. To establish a control group, 88 participants were selected from the 10th grade students at NIS Aktau during the academic year 2021-2022. The experimental class consisted of 10th grade students at NIS Aktau in 2022-2023, while the control class consisted of 10th grade students at NIS Aktau in 2021-2022. The experimental class received training using drill methods with PBL, whereas the control class received training using drill methods without PBL. Data collection methods included tests to measure problem-solving skills and questionnaires to gather student responses during PBL training. Within the framework of problem-based learning (PBL), practice-oriented case assignments served as the primary teaching tool, which students studied in practical classes. The Vocational Education and Training (VET) was implemented through the following main stages: 1. Teachers provided students with descriptions of exam problems that required solving and evaluating their work against a mark scheme. 2. Students familiarized themselves with the case, analyzed it, and identified key problems requiring solutions. 3. Students worked independently or in groups to solve the problems. They conducted research, gathered information, performed analyses, and developed solutions [5]. 4. In subsequent practical classes, students presented their work results, engaged in discussions, and collectively arrived at the most optimal solution. 5. Additional mathematics lessons were organized outside of regular school hours. The questionnaire comprised 6 questions aimed at identifying factors including: - Motivation to learn - Perception of teaching methods - Level of satisfaction with training The data collection methods also included midterm mock exams to measure problem-solving skills. A quantitative approach was employed to compare students' final scores and identify patterns and regularities. 1. Systematization and analysis of the obtained data: • The collected data on students' regular exam preparation activities were processed and analyzed, taking into account their academic performance. • Data on the use of various pedagogical methods and technologies were summarized and analyzed to identify their impact on students' success. 2. Cross-analysis of the data: • Furthermore, the obtained results of data analysis for each factor (regular activities, method and technology usage, individualized approach, parental involvement) were cross-compared and analyzed together to identify common patterns and interrelationships between these factors.

Research findings The examination of the questionnaires revealed that students in the experimental group exhibited a higher level of motivation towards their learning compared to students in the control group. Additionally, they demonstrated a greater acceptance of Problem-Based Learning (PBL) teaching methods and expressed higher satisfaction with their training. In relation to the study on the preparation for external summative assessment, several factors influencing student achievement were identified: 1. Regular exam preparation sessions were found to positively impact student performance. 2. The utilization of diverse pedagogical methods and technologies proved to be effective in preparing students for exams. 3. Adopting an individualized approach that considers students' unique characteristics and needs also contributed to successful outcomes in external assessments. 4. Involving parents in the exam preparation process also yielded positive outcomes in terms of academic performance. Based on the collected data, it can be concluded that the effective organization of student preparation for external summative assessment is a crucial component of academic success. It is recommended to further investigate and implement contemporary methods and technologies to enhance student performance in future endeavors. The research results demonstrated that the experimental group, which received training using PBL methods, achieved higher outcomes compared to the control group that underwent drill-based instruction without the integration of PBL. The average score for the experimental group was 52.2%, while the control group achieved an average of 41.97%. This difference was found to be statistically significant. Consequently, our school's ranking within the NIS network improved from 15th place to 10th place. Furthermore, the results of the experimental group surpassed those of previous years. For instance, in 2019, the average was 49%, in 2021 it was 39.65%, and in 2022 it was 41.97%. These findings indicate that the implementation of PBL can enhance students' problem-solving skills.

References 1.Educational program AEO “Nazarbayev Intellectual Schools” – NIS-Programme URL: https://www.nis.edu.kz/storage/app/media/NIS-Programme/NIS-Programme_RU.pdf 2. The Aalborg PBL-model – Progress, Diversity and Challenges. Aalborg : Aalborg Univer- sity Press, 2006. 13 p. 3. Newman M.J. Problem Based Learning: an Introduction and Overview of the Key Features of the Approach // Journal of Veterinary Medical Education. 2005. No 32 (1). Р. 12–20. 4. Dolmans D., Schmidt H. What directs self-directed learning in a problem based curriculum// Problem Based Learning: a Research Perspective on Learning Interactions.Mahwah, NJ : Lawrence Erlbaum, 2000. Р. 251–262. 5. Barrows H. Generic Problem-Based Learning Essentials. 2004. URL: http://www.pbli.org/pbl/generic_pbl.htm. 6. Savin-Baden M. Facilitating Problem Based Learning: Illuminating Perspectives.Buckingham : Society for Research in Higher Education / Open University Press, 2003.