ABSTRACT:. This research aimed to know: (1) which one gives better mathematics learning achievement, Indonesian Realistic Mathematics Education (IRME) learning approaches, constructivism learning approach using hypnosis in teaching technique or conventional learning approaches, (2) which one gives better mathematics learning achievement, students who have visual, auditory or kinesthetic learning styles, (3) in each of the learning approach, which one gives better mathematics learning achievement, students with visual learning styles, auditory or kinesthetic; (4) in each of the studentâs learning styles, which one gives better mathematics learning achievement, IRME learning approaches, constructivism learning approach using hypnosis in teaching technique or conventional learning approaches. This research used the quasi experimental research method with a 3x3 factorial design. Its population was the students in VII Grade of MTs in Ponorogo. The data samples of the research were taken by using the stratified cluster random sampling technique. The data collection tehnique used documentation, questionnaire, and test method. The documentation was used to know the scores of mathematics in Elementary School National Examination, and was used for balance test among the classes IRME learning approach, constructivism learning approach using hypnosis in teaching technique, and conventional learning approaches. The questionnaire method was used to determine the students learning style, while the test method was used to determine studentâs achievement in mathematics subject rectangle. The data of the research were analyzed by using the unbalanced two-way analysis of variance at the level of significance is 5%. The results of study showed that: (1) use of IRME learning approaches on learning the material rectangle gives mathematics achievement better than the constructivism learning approach using hypnosis in teaching technique and conventional learning approaches, while the constructivism learning approach using hypnosis in teaching technique gives mathematics achievement better than the conventional learning approach; (2) the three types of learning styles, visual, auditory, and kinesthetic provide the same effect on mathematics achievement; (3) in each of the learning approach, the three types of learning styles, visual , auditory, and kinesthetic provide the same effect on mathematics achievement; (4) on the various types of studentâs learning styles, the use of IRME learning approaches in the learning of material rectangle gives mathematics achievement better than the constructivism learning approach using hypnosis in teaching technique and conventional learning approaches, while the constructivism learning approach using hypnosis in teaching technique gives mathematics achievement better than conventional learning approaches.Keywords: learning approach, IRME, constructivist, hypnosis in teaching, conventional, learning styles