Abstract: The aims of this research were to determine: (1) which one providing the better mathematics learning achievement, the students using cooperative learning models of TAI type with RME, TGT with RME, or direct instruction model; (2) which one having the better mathematics learning achievement, the students with types of AQ either climbers, campers, or quitters; (3) at each learning models, which one having better learning achievement, the students with types of AQ either climbers, campers, or quitters; (4) at each studentsâ types of AQ, which one having better learning achievement, the students using cooperative learning model of TAI type with RME, TGT with RME, or direct instruction model. This research employed a quasy-experimental research method with 3x3 factorial design. The population of this research was all of the VIII grader of State Junior High School in Kulon Progo Regency. The sample was taken using stratified cluster random sampling, with 288 students as the sample consisting 95 students for first experiment class, 96 students for second experiment class, and 97 students for control class. The instruments that used to collect data were AQ questionnaire and test of mathematics achievement. The research hypothesis testing was done using a two-way variance analysis with unbalanced cells. The results of the research show that: (1) cooperative learning model of TAI type with RME gave better mathematics learning achievement than cooperative learning model of TGT type with RME and direct instruction model, and cooperative learning model of TGT type with RME gave better mathematics learning achievement than direct instruction model; (2) the students with AQ of climbers type have a better mathematics learning achievement than campers type and quitters type, and the students with AQ of campers type have a better mathematics learning achievement than quitters type; (3) at each types of the AQ, the students exposed to the cooperative learning model of TAI type with RME gave the better mathematics learning achievement than cooperative learning model of TGT type with RME and direct instruction model, and cooperative learning model of TGT type with RME gave better achievement than direct instruction model; (4) at each learning model, the students with AQ of climbers type have a better mathematics learning achievement than campers and quitters type, and the students with AQ of campers type have a better mathematics learning achievement than quitters type.Keywords: TAI with RME, TGT with RME, AQ, and mathematics learning achievement.