Development of teaching materials for Cayley Hamilton matrix theorem on fixed pulley problem

Abstract

The National Education System encourages the provision of teaching materials that support independent learning according to the Merdeka Curriculum. However, physics learning is still dominated by general textbooks that lack contextualization. Learning modules are an alternative, but most of them have not integrated advanced mathematical approaches systematically, especially in solving physics problems involving systems of linear equations. The Cayley-Hamilton theorem on matrices of order 2 and 3 is a relevant approach for fixed pulley dynamics material that is often considered difficult by students. The commonly used substitution-elimination method is considered less efficient, while the matrix approach offers a more systematic solution. Based on this, this study aims to develop teaching materials based on the Cayley-Hamilton theorem on matrices of order 2 and 3 in solving fixed pulley problems. The research method used is R&D. This study consisted of three stages, namely define, design, and develop through literature study and feasibility validation by expert assessors, user assessors, and students using a Likert scale. The validation results showed that the teaching materials obtained an average score of 4.50 with a percentage of 90.1% from expert assessors and 4.76 with a percentage of 95.16% from user assessors, resulting in an overall average of 92.63%, which is classified as highly feasible. In addition, the practicality test results showed an average score of 4.78 with a percentage of 95.60%, indicating that the developed learning module has a very high level of practicality. Thus, this teaching material is declared feasible and effective for use as teaching material in physics learning activities and has the potential to be tested as supporting material in preparing for the Olympics.