Teaching Research On Problem-solving Of College Entrance Examination Based On Mathematics Culture

Since American mathematician Wilder proposed the view that mathematics is a cultural system in the 1980s,international mathematics education has a trend of development-Mathematical and Cultural Education.And in 2017 mathematics college entrance examination outline clearly clarified the test point of mathematical culture.The next year it promulgated the "General High School Mathematics Curriculum Standards(edition of 2017)".The concept of the New Curriculum Standard proposes contents that optimizing curriculum structure,highlighting main lines,selecting contents,penetrating mathematics culture,which leads students to perceive the scientific value,application value,cultural value and aesthetic value lying in mathematics.At present,domestic research in this area focuses on studying mathematical and cultural college entrance examination questions,while lacking capability analysis and countermeasure research.This paper will present a multilevel and multi-angle approach to the problem-solving teaching of the college entrance examination questions that penetrate mathematical culture by combining the teaching experience of first-line teachers,so as to cultivate students' excellent mathematical literacy.First of all,this article is based on the reading of a large number of college and first-line teachers' articles,then analyzes and studies the country's 72 mathematical and cultural college entrance examination questions selected during the decade of 2008-2017.The research in the third chapter summarizes the examination of the penetration of mathematical culture across the country in the past decade and divides it into four areas:mathematics and mathematical history,mathematics and life,mathematics and technology,mathematics and humanities.The presentation of the examination is divided into two forms:explicit and implicit,and the analysis shows that there are more implicit presentation methods than explicit ones and we need to draw more attention.If teachers do not introduce mathematical culture in class,students will not appreciate the pleasure and significance brought by mathematical culture,what's more this teaching method does not meet the development of students' core qualities.On the other hand,based on the study of propositional features of the college entrance examination questions that penetrate mathematical culture,This paper analyzes the characteristics of the questions of mathematical and cultural college entrance examination questions from three aspects:rationality,inheritance and application of mathematical knowledge.Secondly,it focuses on analyzing the four levels of students' ability to face the mathematical and cultural college entrance exam questions:knowledge level,thinking level,experience activity level,and will quality level.And the abilities required at each level have been carefully analyzed.The knowledge level mainly starts from construction of knowledge network system and the mastery of mathematical thinking methods;The level of thinking mainly focuses on the characteristics of mathematical and cultural college entrance examination questions,and it is studied from four aspects;reading comprehension ability,logical thinking ability,intuitive imaginative ability,and computational ability;At the level of experience activities,it mainly researches practice and exploration ability and inductive integration ability;the will quality aspect is to inspire students from the spiritual level to overcome all difficulties actively and proactively.In the end,this article puts forward teaching suggestions of cultivating students'mathematical culture.The teaching suggestions are based on the analysis of students'abilities.The purpose is to improve the students' mathematical ability and mathematical literacy.The specific teaching strategies are further divided into new courses and senior three review courses based on the ability of four levels.New courses focuses on the introduction of situations,active thinking,attaching attention to practice and exploration ability;Improving the knowledge system,deepening the thinking,and cultivating the ability of induction and integration during the review courses.In addition,teachers should also constantly improve themselves,do their best to enrich themselves,master the essence of mathematical culture,and be an excellent inheritor of mathematical culture.In the process of learning,students need to learn to self-regulate or turn to help when facing much pressure.Meanwhile they should learn to develop the strong will of historical celebrities,promote their mathematical learning.and be a successor of mathematical culture.