This study aims to describe the process of developing the device and producing a good quality guided inquiry model mathematics learning tool on linear program material for class XI SMA, and to describe the effectiveness of guided inquiry model mathematics learning which can train students' critical thinking skills on linear program material. This type of research is development research (RnD). The learning tools developed in this study are the Learning Implementation Plan (RPP), Students Worksheet (LKPD), and Critical Thinking Ability Test (TKBK) are developed using a 4-D development model which consists of four stages, namely the define stage, the design stage, the develop stage, and the disseminate stage. The research subjects for the trial class were 13 students of class XI MIPA 3 and the research subjects for the implementation class were 17 students of class XI MIPA 1. Based on the results of descriptive analysis, it was found that the learning tools developed were of good quality because they met valid, practical, and effective criteria. The learning device is said to be valid because all validators give a minimum score of 3 for each aspect of the assessment on a scale of 1-4 and the critical thinking ability test questions meet the valid, reliable, and sensitive criteria. The learning device is said to be practical because the teacher's activities in managing learning meet good criteria and the activities of students meet the active criteria. Learning devices are said to be effective because students 'responses to learning devices and learning activities meet the positive category, guided inquiry mathematics learning model to train students' critical thinking skills is achieved.

Understanding of mathematical concepts can be controlled well by the students if teachers can make students tend to be active pembelajaran.Untuk approach is needed to make students more active role in learning. One way that could condition the students play an active role in learning is the constructivism approach. This approach begins with giving problems to the students who ultimately students are expected to find their own way of solving the problem. In order for this study could be run better then the teacher should know the learning styles of each Shiva in order to adapt the way of good teaching. Observed learning styles are visual, auditory, and kinesthetic. The data source of this research in X Mipa 5 SMA Antartika Sidoarjo. Of the class was given a questionnaire about learning styles. Then the results of the questionnaire is reduced so that the two subjects are drawn from every learning style. Having drawn six subjects, administered tests problem solving with the criteria for having written a neat, use of symbols in the plant concept, task writing / composing, sensitivity to issues of artistic and understand about the form of the writing / reading From the results of these tests chrosscheked with interview , From the analysis of the test has been obtained, is obtained as follows. Profiles visual learning style has characteristics include in Lesson prefer casual, like raised his voice while reading, more like a lot of theory in practice, dislikes memorize and like math but weak in the count. Profile auditory learning style has characteristics include the time work on the problems less conscientious, like move their lips while reading, more like learning groups, dislike to memorize, like mathematics. Profile kinesthetic learning style has characteristics include the time learning like more prektek, sometimes like moving his lips while reading, more like learning groups, dislike to memorize, dislike math. Keywords: Learning Styles, Constructivist Approach.