Analysis of Learning Obstacles in Mathematical Connection Ability on Circle and Arc Material

Abstract

Mathematical connection skills are essential in mathematics. Ideally, students connect concepts, relate mathematics to other fields, and apply them in daily life. However, these skills remain low, especially in circle material, such as the relationship between central and inscribed angles. This study describes learning obstacles related to mathematical connection skills in circles and arcs. The approach is descriptive qualitative. The research subjects consisted of 17 grade XI students and one mathematics teacher. Data collection instruments included a written test of 4 essay question with item validity coefficients ranging from 0.515to 0.796, where all items exceeded the  threshold of 0.482, a learning experience questionnaire, and semi-structured interviews with teachers. The research findings identified three types of obstacles. Epistemological obstacles are evident in students' errors in understanding the relationship between central angles and inscribed angles (reversed), and erroneous arguments regarding the distance of a point to the center. Didactic obstacles stem from procedural and mechanistic learning, a lack of real-world application examples, and limited interactive learning resources. Ontogenic obstacles are reflected in difficulties visualizing word problems and errors in basic algebraic procedures. These three barriers collectively weaken mathematical connection skills, particularly in indicators of connections between mathematical concepts and the connection of mathematics to everyday life. This research contributes to mapping learning barriers, which can serve as an empirical basis for teachers and researchers in developing anticipatory didactic designs and interactive learning media to enhance students' mathematical connection skills in a more meaningful and sustainable manner.