A Study On The Correlation Between Geometric Reasoning And Algebraic Reasoning

The meaning of mathematical reasoning education is to cultivate a good thinking strategies and enhance a person’s ability to respond to. So cultivate students’geometric reasoning and algebraic reasoning to learn math well is particularly important. Students’ geometrical reasoning and algebraic reasoning ability’s cultivate is receiving increasing attention from mathematics education at home and abroad, The purpose of this study is to discuss the performance of our country each stage of geometrical reasoning and algebraic reasoning study ability level. On the basis of the cognitive sequence of students’ development of geometric reasoning and algebraic reasoning,and the differences in students of different grades. The elementary school stage is preliminary cognition of the reasoning, The junior middle school stage geometrical reasoning hold a dominant position. Senior high school stage the geometrical reasoning and algebraic reasoning ability has been becoming mature, this stage is focused on training the geometrical reasoning and algebraic reasoning of flexible use, among them,the number form combining is the dominant idea of connecting the two kinds of reasoning.This paper on the basis of the teaching material content requirements, Different forms of periodic analysis of reasoning, Combining with the results of mathematicians to distinguish the difference and contact between the geometric reasoning and algebraic reasomng.In the first place, after have a preliminary situation of reasoning, analyze the status of reasoning ability. By identifying the difference between reasoning and proof to make students understand the relationship between them. Through the analysis of teaching material contents and the teaching goal, from a macro to understand geometrical reasoning and algebraic reasoning in the development of mathematics application order, analysis the geometrical reasoning and algebraic reasoning’s introduction of the order among the primary school stage, junior middle school stage, senior high school stage.In the second place, due to a poor research on this part, there is no well-defined notion both in geometrical reasoning and algebraic reasoning. The author summarized a general basic concepts and characteristics on geometrical reasoning and algebraic reasoning through consulting literature materials and so on, understanding to the development of the geometrical reasoning and algebraic reasoning and the link between the reasoning and teaching. Analysis of what the topic is suitable for using geometric reasoning, and what kinds of them must to be use the algebraic reasoning, what the topic is suitable for combination with them to solve.Once again, pointed out that as long as there is mathematics exist, there will be a geometry and algebra. Geometrical reasoning and algebraic reasoning is good for develop mathematical thinking, is also the propellant in the development of mathematics. Deal with the relationship between the two,can help students learning mathematics well.In this study, obtaining main conclusions are:(1) Promote the connection between the geometry and algebra, lead students transform reasoning ability smoothly; (2) Pay attention to the development of students’ reasoning ability, follow the differences between reasoning according to students’ aptitude. In order to better to improve the reasoning ability of teaching and training, to find out more contact between them in time is necessary; (3) First have to promote the teacher’s own mathematical reasoning literacy, and deep understanding of the essence of geometry and algebra and infiltration in teaching according to their aptitude; (4) Promote the communication of mathematics knowledge in a timely manner both at home and abroad, especially the communication between teachers will help more between the development of teachers and students.