This research aims to test: (1) the effectiveness between problem posing learning model with Indonesian realistic mathematical education approach and problem posing learning model on written mathematical communication skills; (2) the effectiveness between field-independent and field-dependent cognitive styles on written mathematical communication skills; (3) the effectiveness between problem posing learning model with Indonesian realistic mathematical education approach and problem posing learning model on the written mathematical communication skills from each cognitive style; and (4) the effectiveness between field-independent and field-dependent cognitive styles on written mathematical communication skills from each learning model. This quantitative research employed a quasi-experimental method. The research sample consisted of 240 fifth-grade elementary school students in Jebres District, Surakarta, Indonesia. Data collection techniques included tests of written mathematical communication skills and cognitive styles. The data were analyzed using prerequisite (normality, homogeneity, and balance), hypothesis, and multiple-comparison tests. The findings prove that: (1) PP model with Indonesian realistic mathematical education approach is more effective than the PP and direct instruction models; (2) field-independent cognitive style is better than field dependent; (3) PP with Indonesian realistic mathematical education is as effective as the PP model, but more effective than the direct instruction model, and the PP model is more effective than the direct instruction model in each cognitive style; and (4) in the PP learning model with Indonesian realistic mathematical education approach, field-independent cognitive style is same skill as with field-dependent, but field-independent is better than field-dependent cognitive style in the PP and direct instruction learning models.