Abstract This study aimed at investigating the effectiveness of SWOM strategy on developing branching thinking skills and solving numerical physics problems for language secondary stage students with different field dependent (FD) and field independent (FI) cognitive style in the first semester of academic year 2022/2023. This study depended on a quasi-experimental design. Data were collected through a hidden figure test, a branching thinking skills test, and a solving physics problems skills test. The study sample consisted of (60) participants from first grade Secondary Stage, which was distributed into two groups: experimental group (n=30) and control group (n=30). The results revealed the following: there is a significant effect of SWOM strategy on enhancing students' branching thinking and solving numerical physics problems skills. There are significant differences in solving numerical physics problems between students with field different field dependent (FD) and field independent (FI) cognitive style. The researcher recommends that physics teacher should pay attention to students' differences in cognitive styles, especially in the FD/FI cognitive style. Keywords: SWOM Strategy, Branching Thinking, Physics Problems, Cognitive        Style, Field Dependent, Field Independent.