This research is arranged to analyze: 1) the difficulties found by teachers in developing mathematics teaching models, 2) the effectiveness of verbal and non-verbal information construction strategy in teaching mathematics. The objectives of this research are then: to identify the effectiveness of verbal and non-verbal information construction strategy in teaching mathematics, and to find alternatives of developing the competency-based learning model. The research is carried out under descriptive qualitative method by class action research design. The subjects 'of the research are the students of SMA Negeri 1 Ponorogo.Generally in the cycle I the students show development in proposing creativity verbally and non-verbally when answering questions by making use of mathematical logic. But the researchers have not yet trust the result obtained in cycle Ias consistence, because there are still some students having sufficient scores within he framework of the 65 threshold level cognitively. The average score is 75.52, while there are some students show inactiveness in the learning process. The second cycle is then regarded important to carry out.The analysis taken up by observation upon students and teachers activities, tests, questionnaires and field notes shows the development in the second cycle for some aspects, like the average score and make-ups against threshold level. The average cognitive score is 85.33, against which the researchers decide not to continue to third cycle. The teachers' difficulties in developing the teaching models can be analytically solved by development in guiding students discussion technique, encourage students to ask questions or to pass down opinion, and relating the existing concepts and the new ones by making use of real appliance which are available around us. The students enthusiasm gives rise to the effectiveness of verbal and non-verbal information construction strategy in teaching mathematics.
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