This aim of this study is to describe the process of local conjecturing in generalizing patterns based on Action, Process, Object, Schema (APOS) theory. The subjects were 16 grade 8 students from a junior high school. Data collection used Pattern Generalization Problem (PGP) and interviews. In the first stage, students completed PGP; in the second stage, work-based interviews were conducted by the researchers to understand the process of conjecturing. These interviews were video tapped. The results show that the local conjecturing process can be grouped into two, namely local conjecturing based on proximity and local conjecturing by contrast. The local conjecturing process occurs at the stage of action in which subjects build a conjecture by observing and counting the number of squares separately. At the stage of process, the object and scheme were perfectly performed.