Mathematical Inquiry about the Sequence of Rational Numbers Coming Nearer Infinite to √2 and the Natural Number and Its Limit Value

Abstract

　　 The purpose of this paper is to investigate senior high school student’s mathematical inquiry about the sequence of rational numbers coming nearer infinite √2 and the natural number and its limit value, which focus on discovering mathematical character thinked by the example of the sequence of rational numbers, such as thinked about the example, thinked through the example, thinked beyond the example. We investigated student’s mathematical inquiry by teaching units about the sequence of rational numbers by qualitative methods.

　　 As a result of our discussion, we obtained several insights:

　(1) By thinking back own problem solving process and various interpretations about the sequence of rational numbers coming nearer infinite √2 and the natural number and its limit value, a student’s mathematical inquiry is encouraged to consider several methods of discovering the mathematical character.

　(2) Substantial questions that students want to think deeply and prove are generated about convergence of the sequence of rational numbers and its limit value through comparing several sequences coming nearer to the same mumber and these recurrence formulas. Student’s questions accelarate to consider and discuss about the sequence of rational numbers and its fundamental truth.