Abstract: This research was aimed at searching and finding: 1) the most effective mathematics learning model among three models, including problem posing model with learning cell technique, problem posing model without learning cell technique, and direct learning model, 2) more effective student’s cognitive style of field independent and field dependent, 3) more effective student’s cognitive style of field independent and field dependent on each model, and 4) the most effective mathematical learning model among three models, including problem posing model with learning cell technique, problem posing model without learning cell technique, and direct learning model on each student’s cognitive style. This type of the research was a quasy-experimental research. The population was all students of grade VIII of state junior high school in Sukoharjo regency in 2013/2014. The size of the samples was 302 students consisted of 102 students in the first experimental group, 101 students in the second experimental group, and 99 students in control group. The data instruments used were documents of student’s early achievement, cognitive style questionnaire, and mathematics achievement test. The data was analyzed using analysis of variance. The conclusions of the research were as follows. (1) Problem posing mathematics learning model with learning cell technique is more effective than problem posing model without learning cell technique; problem posing mathematics learning model with learning cell technique is more effective than direct learning model; and problem posing learning model without learning cell technique is more effective than direct learning model, (2) Students having field independent cognitive style have greater achievement than those having field dependent cognitive style, (3) Dealing with problem posing model with learning cell technique, students having field independent cognitive style and field dependent cognitive style have the same achievement; dealing with problem posing learning model without learning cell technique, students having field independent cognitive style have greater achievement than those having field dependent cognitive style; and dealing with direct learning model, students having field independent cognitive style have greater achievement than those having field dependent cognitive style, and (4) To students having field independent cognitive style, problem posing model with learning cell technique, problem posing model without learning cell technique, and direct learning model give the same student’s achievement; to students having field dependent cognitive style, problem posing model with learning cell technique gives higher student’s achievement than problem posing model without learning cell technique and direct learning model, and problem posing  model without learning cell technique gives higher student’s achievement than direct learning model.Key Words: problem posing, learning cell, cognitive style, achievement

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