Horizontal and vertical mathematization processes of 10th grade students: The case of Law of Sines

Realistic Mathematics Education (RME) has gained significant attention in Vietnam over the past decade due to its potential for enhancing mathematics instruction. This study investigates the process of mathematicization undertaken by students as they transition from solving a real-world contextual problem to discovering and applying the Law of Sines. The primary problem involves determining the angle formed by the crossbar and the hanging rope of a disco ball. Guided by the principles of RME, the mathematicization process encourages students to model this scenario as a triangle with two given side lengths and a specified angle between one side and the base. With teacher facilitation, students construct a general mathematical model and subsequently reinvent the Law of Sines. They apply this law to solve the initial problem and further extend their understanding by tackling a similar contextual scenario. The study involved 40 students, who engaged with worksheets designed to present relevant problems. Their problem-solving processes were documented and analyzed using qualitative methods. The findings contribute to the development of a teaching approach for introducing the Law of Sines within the framework of RME, specifically tailored to the Vietnamese educational context. This approach underscores the progression of students' understanding through the integration of contextual problem-solving and theoretical reinvention.