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The method used in this research is a mixed method with the research design that is explanatory sequential design. The result of this research are (1) Mathematical reasoning ability of grade VII students after being given learning by using PBL with mind mapping reached minimal completeness criteria; (2) the description of students' mathematical reasoning ability with independent field cognitive style were capable to present mathematical statements, propose conjecture, do mathematical manipulation, give reason to solution, and draw conclusion; and (3) the description of students' mathematical reasoning ability with field-dependent cognitive style were capable to present mathematical statements, yet incapable to propose conjecture, FDK students were less able to manipulate mathematics, while FDL students were incapable to perform mathematical manipulation, provide reason for solution, and draw conclusions.

The aims of this research were (1) to test the mathematical communication ability of Junior High School 3 Salatiga in learning SAVI model with flash media achieved learning completeness classically, (2) to test the average of students’ mathematical communication ability in learning SAVI model with flash media compared with the average of students’ mathematical communication ability in learning DL model, and (3)to analyze the influences of learning SAVI model with flash media to group of students with low, medium, and high mathematical communication ability. The method used in this research is mixed method. Data analysis used included proportion test, averages difference test, and gain test. The results were (1) the mathematical communication ability of Junior High School 3 Salatiga in learning SAVI model with flash media achieved learning completeness classically, (2) the average of students’ mathematical communication ability in learning SAVI model with flash media higher than the average of students’ mathematical communication ability in learning DL model, and (3) learning SAVI model with flash media influenced to group of students with low, medium, and high mathematical communication ability.

The purposes of this research were (1) the learning outcomes on the aspects of mathematical connection ability of students on learning REACT model reached learning criterion, (2) the learning outcomes on aspects of mathematical connection ability among students on learning REACT model better than the students on learning Expository model, (3) there were differences in learning outcomes in aspects of mathematical connection ability between students who have learning styles of VAK and (4) there was interaction between learning model and student learning style to learning outcomes on aspects of students. This research type was quantitative with population of student of class X and selected two classes as sample. Data collection techniques were observation, interview, tests, questionnaires, and documentation. The results were (1) the ability of students mathematical connections on learning REACT model can fulfill the learning mastery individually and classically; (2) the average of students on mathematical connection aspect in learning of REACT model was better than the average of students on mathematical connection aspect in learning of Expository model; (3) there was a differences in the students ability on the mathematical connection aspects based on the learning style of VAK; (4) there was an interaction between the REACT learning model and the learning style of the students on the mathematical aspects of connection.