Decision making in the mathematical inquiry using technology and guide line for instructional design

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Using technology in mathematical investigation, we can observe more data, and we can use more strategies to solve the problems. We have many choices in mathematical investigation ; which data is important, which strategy is suitable, how should I interpret data and evaluate a solution, and which re-formulation of problem is suitable. To clarify them and to make guide line to make a instructional design of classroom activity about mathematical investigation using technology, we have done as follows ; (1) we made 20 case studies of mathematical investigations using technology (mainly, dynamic geometry software Geometric Constructor ), (2) we made two case studies of our lesson from viewpoint of teacher's decision making, (3) based on them, we made some guide-line for instructional design of mathematical lesson using technology, which was used in undergraduate and graduate program of mathematics education (4) and based on them, we have designed new mathematical investigations in our attached junior high school.