Applying Hamilton’s vector formula in mathematics education: enhancing student mathematical skills through innovative teaching methods

The relevance of this discussion is driven by the need to improve mathematics teaching methods to enhance students’ mathematical competencies, particularly critical thinking and problem-solving skills. With its broad didactic potential, Hamilton’s vector formula becomes an essential tool in the educational process. The study aims to examine the impact of integrating Hamilton’s vector formula on the development of students’ mathematical competencies. The research methodology includes a literature review, expert evaluations, a pedagogical experiment with control and experimental groups, testing, and student surveys. The study results showed that using Hamilton’s vector formula promotes the development of students’ critical and analytical thinking, increases their confidence in solving complex problems, and improves overall mathematical competencies. The experimental group demonstrated higher test scores and practical task performance than the control group. Students noted that working with Hamilton’s vector formula helped them better understand geometric concepts and see the practical application of theoretical knowledge. The survey showed a positive perception of the new methodology, although some initial difficulties were noted. The practical significance of the results lies in developing recommendations for the effective use of Hamilton’s vector formula in the educational process, which can significantly improve the quality of students’ mathematical training and contribute to their successful learning process in the future.