It is required to think how to foster people living in a new age where science and technology such as information technology and globalization are progressing. NCTM ,111d the Ministry of Education of Japan have set forth the policy corresponding to it. Also 'computer related equipment is gradually supplied. Teachers must be oriented to the appropriate use of information technology in the classroom. Furthermore, NCTM and the Ministry of Education of Japan suggest the possibility that a mathematics lesson will change by computerization and promote it vigorously so that it may become powerful for students' future lives. Students were taught by teachers in mathematics lessons in Japan so far. Now, it becomes possible to make a .mathematics class where students are in the : center. Research about it is increasing. Students can discover the problem, reason about it,and draw a conclusion by themselves. In this paper, I focused on the introduction of drawing tools, and emphasized that the drawing tool could make the route for students to think, set the problem, reason , generalize, discover a new problem, and solve it. Students can discover mathematical relationships by doing mathematical investigations and by using inductive reasoning. However, if a teacher does not change the present lesson structure, the introduction of drawing tools does not have much epoch-making chance. The reformation of teachers' consciousness to place students at the center of a lesson is important. In this paper, I regard the route to problem solving by students as mathematical investigation, and define the step where mathematical investigation is performed. Also, I reflect upon the lesson plans necessary for mathematical investigation
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