Mathematical communication skills are important for students in understanding and conveying mathematical ideas, while the AQ determines how well students overcome difficulties in learning mathematics. The purposes of this study are to determine the learning quality Discovery Learning model with realistic approach, to know the effect of AQ on mathematical communication skills, and to determine patterns of mathematical communication skills in terms of students’ AQ categories. This research applied mixed methods with concurrent embedded design. The results showed: the learning quality of the Discovery Learning model with realistic approach at the planning and implementation stages was good, while the evaluation stage did not meet the criteria; AQ has a positive influence on students' mathematical communication skills; The climbers students showed good achievement on the indicators 1-3, while the indicator 4 showed quite good achievement, the campers students showed fairly good achievement on all indicators, the quitters students showed poor achievement on all indicators.