Analysis of the meaning of continuity and differentiation: A study on graph problems

Continuity and differentiability are concepts that students must master to effectively learn and solve problems in a variety of contexts. Thus, this study sought to elicit students' interpretations of the relationship between continuity and differentiability, particularly in graphic problems. Through a qualitative approach, this study involved 195 third-year undergraduate students from various Indonesian universities. Ten of them agreed to an in-depth interview for exploration and clarification. Thematic analysis was conducted to deduce patterns from the responses of participants based on the findings. This study discovered three types of meanings that students construct when they solve problems: 1) physical meaning; 2) analytical meaning, and 3) covariational meaning. The three findings could serve as a conceptual framework for future learning processes that emphasize continuity and differentiability. Additionally, our research revealed that Indonesian undergraduate students are unfamiliar with the graphical problems associated with the two concepts. Thus, future research will focus on developing learning strategies that incorporate a variety of representations to improve students' conceptual understanding of calculus concepts.