<![CDATA[Abstract: This research aim to find out the effect of the learning models on achievement and mathematics communication ability viewed from cognitive style. The learning models compared were the cooperative learning of TPS type with AfL, cooperative learning of TPS type, and the direct learning mode. The research was quasi experimental. The population was all students of grade VII State Junior High School in Surakarta City. Sampling was done by stratified cluster random sampling technique. The hypothesis test used unbalanced two ways multivariat analysis of variance. The results of the research were as follows. (1) The cooperative learning model of TPS type with AfL gives better achievement and mathematics communication ability than the cooperative learning model of TPS type and the direct learning model, and the cooperative learning model of TPS type gives better achievement and mathematics communication ability than the direct learning model. (2) Students with the FI cognitive style had better achievement than students with the FD cognitive style, while students with the FI cognitive style had the same mathematics communication ability as students with the FD cognitive style. (3) On FD cognitive style and FI cognitive style, the cooperative learning model of TPS type with AfL gives a better achievement than the cooperative learning model of TPS type and the direct learning model, and the cooperative learning model of TPS type gives a better achievement than the direct learning model. On FD cognitive style, the cooperative learning model of TPS type with AfL, the cooperative learning model of TPS type, and the direct learning model gives the same mathematics communication ability. On FI cognitive style, the cooperative learning model of TPS type with AfL gives the same mathematics communication ability as the cooperative learning model of TPS type, and the cooperative learning model of TPS type with AfL and the cooperative learning model of TPS type gives a better mathematics communication ability than the direct learning model. (4) On the cooperative learning model of TPS type with AfL, the cooperative learning model of TPS type and the direct learning model, students with the FI cognitive style had better achievement than students with the FD cognitive style. On the cooperative learning model of TPS type with AfL, the cooperative learning model of TPS type and the direct learning model, students with the FI cognitive style and FD cognitive style had the same mathematics communication ability.Keywords: TPS, AfL, cognitive style, mathematics achievement, mathematics communication ability. ]]>
