Learning obstacle instrument analysis of proportion concept with praxiology framework

This study explores the development and application of a praxiology-based instrument designed to identify and address learning obstacles in the teaching of the concept of proportion in early algebra. Proportion plays a crucial role in connecting concrete numerical concepts with abstract algebraic thinking; however, many students face significant challenges when transitioning from numerical to algebraic representations. The study utilizes a praxiology framework, which emphasizes the relationship between the type of mathematical task, the techniques employed by students, and the underlying theoretical principles that shape students' understanding. This framework provides a deeper understanding of how task design can influence students' mathematical practices, making it particularly effective for diagnosing learning obstacles in proportion-related tasks. The instrument, which was applied to seventh-grade students in Bandung, Indonesia, consists of five types of tasks aimed at developing students’ skills in arithmetic-algebraic representations and solving linear equations in both abstract and contextual forms. By predicting students' potential solutions and analyzing their problem-solving strategies, the study highlights how the praxiological approach facilitates the identification of key difficulties in students' understanding of proportion. The findings demonstrate that this approach not only helps to diagnose learning obstacles more effectively but also supports the creation of targeted instructional strategies that improve students’ grasp of proportional reasoning. This research contributes valuable insights into the use of praxiology in mathematics education, offering a robust framework for analyzing and overcoming learning obstacles in early algebra instruction.