EFFECTIVE METHODOLOGIES FOR TEACHING TRIGONOMETRY IN ACADEMIC LYCEUMS TO DEVELOP STUDENTS’ MATHEMATICAL GIFTEDNESS AND RESEARCH COMPETENCE
Keywords:
Trigonometry teaching, academic lyceums, mathematical giftedness, research competence, problem-based learning, mathematical inquiry, differentiated instruction, mathematical modeling, digital technologies, creative problem-solving.Abstract
Teaching trigonometry in academic lyceums requires methodologies that develop conceptual understanding, advanced problem-solving ability, mathematical creativity, and research competence. This study examines the effectiveness of an integrated instructional model designed for mathematically gifted students in academic lyceums. The model combines problem-based learning, mathematical inquiry, visualization, differentiated instruction, digital technologies, collaborative investigation, and research-oriented assignments. A mixed-methods, quasi-experimental design is used to compare the learning outcomes of students taught through the integrated model with those receiving predominantly conventional instruction. Data are collected through diagnostic and achievement tests, mathematical creativity tasks, research project rubrics, classroom observations, student questionnaires, and interviews with mathematics teachers. The instructional activities require students to investigate trigonometric relationships, construct and interpret graphs, prove identities through different methods, model real-life situations, formulate hypotheses, and present evidence-based conclusions. The findings indicate that the integrated approach can improve conceptual understanding, procedural accuracy, flexible problem-solving, mathematical reasoning, and students’ ability to conduct elementary mathematical investigations. Gifted learners particularly benefit from open-ended problems, differentiated levels of complexity, independent exploration, and opportunities to compare alternative solutions. The results also show that teacher guidance, carefully sequenced tasks, access to dynamic mathematical software, and transparent assessment criteria are important conditions for successful implementation. The study is relevant to specialized mathematics education in Uzbekistan because academic lyceums need instructional practices that identify and support mathematical giftedness while preparing students for university study, academic competitions, and research-oriented activity.
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