This study aims to determine: (1) Which has the mathematics learning achievement better, a model of cooperative Thinking Aloud Pairs Problem Solving (Tapps), cooperative Two Stay Two Stray (TSTS) or direct instruction, (2) Which has the achievement better mathematics learning, students who have the cognitive style field independent (FI) or students who have the cognitive style field dependent (FD), (3) in each cognitive style, which one has the mathematics learning achievement better, a model of cooperative Thinking Aloud Pairs Problem Solving (Tapps), cooperative Two Stay Two Stray (TSTS) or direct learning, (4) on each of the learning model, which one has the achievement of better mathematics learning, students who have the cognitive style field independent (FI) or students who have the cognitive style of field dependent (FD. This study is a quasi-experimental research. The populations in this study were all students of class VII SMP N 5 Metro 2015/2016 school year. The sampling technique was conducted by stratified cluster random sampling. The balance test performed using one way analysis of variance with different cells before carrying out a study of three groups of population. The data analysis technique used to test the hypothesis is two-way ANOVA with different cell with a 3x2 factorial design. Lilliefors prerequisite test method to test for normality and Bartlett methods for homogeneity. From the analysis concluded: (1) cooperative learning model Thinking Aloud Pairs Problem Solving (Tapps) generates mathematics learning achievement better than cooperative learning model Two Stay Two Stray (TSTS), cooperative learning model Thinking Aloud Pairs Problem Solving (Tapps ) generates mathematics learning achievement better than learning direct, cooperative learning model Two Stay Two Stray (TSTS) generates mathematics learning achievement better than learning Direct, (2) students with cognitive style Field Independent (FI) had mathematics learning achievement better than students with cognitive style Field Dependent (FD), (3) the individual cognitive style, cooperative learning model Thinking Aloud Pairs Problem Solving (Tapps) generates mathematics learning achievement better than cooperative learning model Two Stay Two Stray (TSTS ), cooperative learning model Thinking Aloud Pairs Problem Solving (Tapps) generates mathematics learning achievement better than learning direct, cooperative learning model Two Stay Two Stray (TSTS) generates mathematics learning achievement better than learning Direct (4) on each model of learning, mathematics achievement of students with cognitive style Field Independent (FI) have better mathematics learning achievement than students with cognitive style Field Dependent (FD).