Study On Transformation Between Number And Graph From The Perspective Of Teaching

Mathematical idea is our understanding of the nature of the specific mathematicscontent and methods on the level of awareness and the concept, and it is the essence andsoul of mathematics. The idea of transformation between number and graph is one ofhigher level mathematical idea and it reflects the basic spirit of the equivalenttransformation. The curriculum standard of elementary mathematics has a clearrequirement on the transformation between number and graph which is one of theimportant part of elementary mathematics examination. In addition, the transformationbetween number and graph is also a transformation between two important mathematicalrepresentations—analytical representation and graph representation, so it is one ofimportant way of transformation between mathematical representations. Transformationbetween number and graph include two forms—transformation from graph to number andfrom number to graph. Transformation from graph to number is the basis of analyticgeometry, while transformation from number to graph do not have fixed mode, whichis the focus of this study. Therefore, in terms of the cognition on transformation betweennumber and graph and its education significance, research on the transformation betweennumber and graph is valuable.In this paper, we mainly take the method of theoretical studies and first study thetheoretical structure of the transformation between number and graph. Secondly, wemainly discussed the mathematical cognition on transformation between number andgraph and its education significance based on two types of the most typical problemsabout transformation between number and graph—absolute value and the PythagoreanTheorem. And finally, we put forward some suggestions and thinking on the issue ofblend the transformation between number and graph in the teaching. This thesis focus on the discussion of cognition on transformation between number and graph and itseducation significance with the help of analyzing some related examples, rather thansimply showing the beauty of transformation between number and graph by examples.