A Research of development of the structural thinking and understanding in mathematics learning

Abstract

This paper has made it clear numerically how much the structural thinking and understanding of students is in the learning content of mathematics and how much the difference of their structural thinking between the grade and the upper grade is in the very same learning content. I performed the experiment by using the method of the tree concept mapping. Many students of a junior high school, two senior high schools and a college took part in the experiment. The tree concept maps drawn by the students were analyzed by five teachers with a transfer coefficient. As the result, the following facts proved to be obvious. (1) In the new learning content, the values of three average of the transfer coefficients for the maps drawn by the students of the junior high school, the senior high schools and the college are almost equal. (2) In the very same learning materials of the junior high school and the senior high school, the value of the average of the transfer coefficients of the maps drawn by the students of the college is about 0.09 larger than that of the students of the junior high school, and is about 0.06 larger than that of the students of the senior high school. (3) The value of the average of the transfer coefficients of the students who understand the learning content structurally is about 0.43 larger than that of the students who don't understand it structurally.