The ability of representation is one of the important components to develop students thinking skills, because this capability is instrumental in helping students to transform abstract ideas into real idea and it can train students to improve problem solving skills with a variety of forms including pictures, diagrams, mathematical expressions, or words or written text. One model of learning that increases the ability of the mathematical representation is a learning model of problem-based learning. This research aims to: 1) determine a mathematical representation increased ability of students taught with problem based learning models 2) the interaction between the learning model of problem-based learning and grouping of students to increase the ability of the mathematical representation. This research is a quantitative research with an experimental method, that has pretest-posttest group design. The population was all students of class X SMA UnggulPidie Jaya by samples of two classes, namely class X3 as an experimental class and class X2 as the control class. The data collection was done by using test. Then analyzed by t -test and ANOVA at the 0.05 significance level after testing prerequisites are met. Based on the analysis we can conclude that: 1) to improve the mathematical representation of students who applied learning model of problem based learning is better than an increase in the ability of the mathematical representation of students who received conventional learning. 2) there is no interaction between the learning model and grouping of students to increase the ability of mathematical representation.
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