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Item Open Access Improving the conceptual understanding of mathematics by solving real-life problems: a comparative analysis of methods and approaches(SDU University, 2025) Sagyndyk A.This study investigates how solving real-life mathematical problems can improve students’ conceptual understanding. A quasi-experimental design was implemented in two Grade 9 classrooms at a Kazakhstani secondary school. While both groups worked with the same real-life performance tasks, the experimental group (9A) engaged with them through rich tasks and the “5 Practices” model (Smith & Stein, 2018), fostering inquiry-based learning and mathematical discourse. The control group (9B) used traditional instruction methods. Quantitative and qualitative data were collected through pre-tests, posttests, performance tasks, observations, and reflection journals. Results showed significant improvement in both groups, but the experimental group demonstrated more consistent conceptual growth and deeper reasoning. The study concludes that combining real-life tasks with structured inquiry-based strategies enhances mathematical thinking, supports soft skill development, and contributes to more meaningful learning experiences.Item Open Access Improving Student Engagement and Academic Achievement Through Real-Life Applications of Proportion(SDU University, 2025) Alimzhanova Zh.This study investigates the impact of incorporating real-life tasks in the teaching of proportions on student engagement and academic performance. It is grounded in constructivist and situated learning theories and employs a quasiexperimental design. The intervention was carried out in a public school in Kazakhstan, involving 24 sixth-grade students in a single experimental group without a control group. The results demonstrated that real-life contextual problems enhance students’ motivation, functional mathematical literacy, and critical thinking skills. The research also includes a comparative analysis of Kazakhstani and Singaporean mathematics textbooks. Findings reveal that Kazakhstani materials emphasize formal procedures over real-world problem-solving, whereas Singaporean textbooks integrate contextual tasks more extensively. This highlights a need for curriculum modernization to better reflect practical applications and build essential competencies in mathematics education. The experimental phase involved a proportion unit designed around real-life scenarios such as calculating discounts, adjusting recipes, working with scale models, and budgeting. Students worked individually and collaboratively, completed pre- and post-lesson questionnaires, and took a summative assessment. The comparison of results before and after the intervention showed a clear improvement in both academic outcomes and student engagement.