Research On The Cultivation Of Pupils' Mathematical Plausible Reasoning Ability ——Based On Whitehead's Understanding Theory

Reasonable reasoning is a way of thinking that infers some results through induction and analogy based on existing facts and experience and intuition.The Mathematics Curriculum Standard for Compulsory Education(2011 Edition)puts forward clearer requirements for reasonable reasoning.Reasonable reasoning and Deductive reasoning are both components of reasoning,which should run through the whole process of mathematics learning.We should cultivate pupils' ability of Reasonable reasoning in the process of mathematics learning.The word "emotion" in Reasonable reasoning requires us to pay attention not only to the Logical understanding in mathematics learning,but also to the Aesthetic understanding of students in mathematics learning.Whitehead is a famous British Mathematician and Philosopher,his ideas are deeply original and insightful.He presents a distinctive theory of understanding in his book "Modes of Thought".He believes that understanding includes at least two aspects: Logical understanding and Aesthetic understanding.Whitehead has to reconcile the understanding of logic and aesthetics,and finally makes an effort to obtain a coherent understanding.Aesthetic understanding promotes Logical understanding,and Logical understanding promotes Aesthetic understanding.Looking at the cultivation of pupils' mathematical plausible reasoning ability,it is found that there are the following problems in the current teaching: Teachers' understanding of plausible reasoning has deviation,improper application of aesthetic understanding factors in the teaching process,students' lack of awareness of the connection between Logical understanding and Aesthetic understanding,etc.This paper analyzes plausible reasoning in elementary school mathematics curriculum,hoping to bring enlightenment to the cultivation of elementary school students' mathematical plausible reasoning ability from the perspective of Whitehead's understanding theory.This article is divided into five parts:The first part is the introduction,which mainly expounds the reasons for choosing the topic,summarizes the literature research on the two topics of mathematical plausible reasoning and Whitehead's understanding theory,and defines the concepts of mathematical plausible reasoning and mathematical plausible reasoning ability,and expounds the research.purpose and significance,research methods and innovations.All these constitute the theoretical and practical basis of this subject,and are the logical starting point of this research.The second part mainly discusses and sorts out Whitehead's theory of understanding,which involves what is understanding,the way of advancing understanding,the incompatibility when it comes to concrete understanding,and the two aspects of understanding—logical understanding and aesthetic understanding.By discussing and sorting out,we can better grasp Whitehead's understanding theory.The third part is plausible reasoning in elementary school mathematics curriculum,understanding plausible reasoning in elementary school mathematics curriculum objectives and plausible reasoning in the four-part course content of "Numbers and Algebra,Graphics and Geometry,Statistics and Probability,Synthesis and Practice" specific applications.The fourth part is about the problems existing in the cultivation of elementary school students' mathematical plausible reasoning ability.Starting from Whitehead's understanding theory,combined with the literature,it analyzes the current situation of elementary school students' mathematical plausible reasoning ability.It is found that there are the following problems in the cultivation of elementary school students' mathematical plausible reasoning ability: First,teachers' understanding of plausible reasoning is biased.Second,the factors of aesthetic understanding are improperly used in the teaching process.Third,students lack the awareness of the connection between logical understanding and aesthetic understanding.The fifth part is the enlightenment of Whitehead's comprehension theory to the cultivation of elementary school students' mathematical plausible reasoning ability.Based on Whitehead's comprehension theory,it proposes strategies to solve the problems existing in the cultivation of elementary school students' mathematical plausible reasoning ability.Teachers should take adventures of ideas to Expand the understanding,rationally use the aesthetic understanding factors in the teaching process,and promote the combination of logical understanding and aesthetic understanding to improve the mathematical reasoning ability of primary school students.