The Research On The Development Characteristics Of Pupils’ Mathematical Visual Reasoning Ability

For a long time,Visual reasoning plays a far more important role in the work of mathematicians than is generally known.Until recent years,the role of visual reasoning in mathematics has been recognized and widely studied.This is because,on the one hand,recent cognitive science studies have recognized that vision itself has the nature of thinking.Even though many psychologists have pointed out that there are some limitations in the use of visual reasoning,they still affirm the great potential of visual reasoning in meaningful learning.On the other hand,computer and multimedia technology make mathematical visualization possible,which opens up a new possibility for visual reasoning to play a role in mathematical research and teaching.Therefore,it is reasonable to think that the status of visual reasoning in mathematics should be elevated from a useful learning aid to a fully recognized tool for mathematical reasoning and proof.The purpose of this study is to explore the development status of pupils’ visual reasoning ability in mathematics by using qualitative and quantitative methods.This study is mainly divided into the following parts.The first part includes introduction and literature review.The first is to clarify the background of the problem,the proposal of the research problem and the significance of the research.Then it combs the relevant literature,reviews the relevant research on mathematical reasoning,visualization and visual reasoning,and summarizes the relevant research on the meaning,process,type and function of visual reasoning in mathematics.The second part is the theoretical basis of this study.The first is to define the concept of mathematical visual reasoning,then divide visual reasoning into the five most common types,and then explore the educational meaning of visual reasoning in mathematics teaching in theory.Finally,according to Piaget’s cognitive development stage theory and solo classification,combined with the cognitive development level of primary school students,the mathematical visual reasoning ability is divided into three levels.The third stage is the investigation and analysis of pupils’ mathematical visual reasoning ability.By compiling the test volume of primary school students’ mathematical visual reasoning ability,and testing the students from grade 2 to grade 6,and then quantitatively analyzing the test results,the law,level and characteristics of the development of primary school students’ mathematical visual reasoning ability are finally summarized.The main conclusions are as follows: The mathematical visual reasoning ability of primary school students improves with the increase of grade,which can be divided into three sets: many of the students in grade two can reach the standard of Level ONE,most of the students in grade three and grade four can reach the standard of Level two,and many students in grade five and six can reach the standard of Level three.There are significant differences between the three sets.By analyzing the test results of the whole,different grades,different reasoning types and different levels,it is found that there is no gender difference in the mathematical visual reasoning ability of pupils.There is a significant positive correlation between visual reasoning ability and academic performance of primary school students,that is,the stronger the visual reasoning ability,the better the academic performance of mathematics.With the increase of grade,there are more types of mathematical visual reasoning ability and mathematical achievement has a significant correlation,and every increase in the score of mathematical visual reasoning test,students’ mathematical academic performance increases more and more.Based on the above research results,we give some suggestions on how to cultivate students’ visual reasoning ability.It includes: enhancing theoretical learning and improving teachers’ understanding of mathematical visual reasoning;Combined with students’ cognitive level,carefully select the teaching prototype;And reasonably arrange teaching links in combination with students’ life experienceFinally,based on the above research results,we give some suggestions on cultivating pupils’ mathematical visual reasoning ability from the aspects of curriculum,textbook and teaching.There are many deficiencies in this study,and we have made a lot of reflection and improvement.We believe that there are still many areas worthy of in-depth thinking and research on the problem of mathematical visual reasoning in primary school curriculum.We hope that this study can provide some direction and inspiration for future researchers.