This research aims to see how the mathematical thinking abilities of students who have a field independent cognitive style are based on Shafer and Foster's theory. This research uses a descriptive approach. The sample for this research is 3 class VII students of SMP Negeri 6 Purworejo. The technique for selecting subjects in this research was purposive sampling technique. The data collection techniques used were mathematical thinking test methods, interview methods and documentation. The data analysis technique used is reduction, presentation and drawing conclusions. The results of research regarding the level of mathematical thinking ability based on Shafer and Foster's theory in solving algebra material problems showed that students at SMP Negeri 6 Purworejo who had a field independent cognitive style in solving the reproduction level were able to know basic facts, namely knowing and writing down any information that could be known in questions and determine the problem correctly, at the completion of the connection level students are able to integrate information, namely explaining the steps to solve the problem correctly and applying the right algorithm to solve the problem, at the completion of the analysis level students are able to mathematize situations, namely being able to change real problems into mathematical form by make equations and make generalizations, namely being able to find the correct answer.
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