The study aims at examining the characteristics of open ended problem solving based on student cognitive styles, namely field independent and field dependent. The study was descriptive qualitative started by determining research subject using group embedded figure test (GEFT) to group students based on their cognitive and the result of GEFT, the reasearcher choose 6 subjects from 19 students of drade IX at SMPN 1 Ma�rang consisted of three subjects of field independent and three of field dependent. Afterwards, the researcher gave open ended problem solving test on algebra and geometry mate rials, and conducted interview. Data validity of the study employed triangulation technique. The results of the study reveal tha the steps and strategy of open ended problem solving of field independent subject and field dependent subject: (1) in the steps of open ended problem solving, field independent subjects overall were able to understand the problem, plan the solution, and conduct the plan up to recheck it. One of field independent subject even was able to draw conclusion form one of the problems given which was the algebra 2 problem. In contrast, the field dependent subjects overall had steps of open ended problem solving that only able to understand and recheck it, (2) in problem solving strategy, there was no difference between field independent subjects and field dependent subjects. The field independent subjects used open ended problem solving strategy by thinking backward, thinking inductively, and thinking forward. Similarly, the field dependent subjects also used open ended problem solving by thinking backward, thinking inductively, and thinking forward