Research On The Function Representation Of Senior One Students Under The New Curriculum Standard And New Textbooks

The function is one of the important contents throughout the high school ma thematics curriculum.The representation of function concept plays an important role in the solution of the function problem.The new curriculum standard and n ew teaching materials require students to master various representations of functi on to solve function problems.In recent years,the research on function represent ation mainly focuses on the conceptual representation of functions,but there is little research on the representation of function problems.Therefore,based on th e new curriculum standards,new textbooks,representational theories and related literature,this paper constructs the evaluation framework of function representat ion,and investigates the representation of function concepts and function proble ms.By referring to the evaluation framework of mathematical conceptual represe ntation of Dr.Li Shanlian,the evaluation framework of PISA core accomplishm ent and the evaluation framework of mathematical representation level of domest ic scholars in compulsory education stage,and combining with the characteristic s of function and the physical and mental development of senior high school st udents,the evaluation framework of functional conceptual representation ability and functional problem representation ability was constructed respectively.Based on the evaluation framework,questionnaire and interview,the following three q uestions are studied :(1)the status quo of function concept prototype,function c oncept representation richness and function problem representation level of senio r high school students?(2)is there any difference between the representational richness of function concept and the representational level of function problem?If so,what are the influencing factors?(3)when the function problem is repres ented,what are the characteristics of the transformation between representations?It is found that about 60% of the students' function concept representation p rototype are function images,among which the classroom teaching and the teac hing material content are important factors affecting the function concept prototy pe,and once the function concept prototype is formed,it is difficult to reach ahigher level with the deepening of knowledge.As for the richness of the repre sentation of function concept,more than 80% of the students can master three or more ways of representation,among which the specific function,image and analytic expression are the most mastered.As for the representation of function problem,70% of the students' representation ability of function problem is at th e level of 2-3,while most of the students are above the "connection level",but cannot reach the "reflection level".Moreover,the students' representation ability at the level of 2-3 is more inclined to the connection level,and their problem representation ability transitions from level 2 to level 3.Based on the investigation and interviews with students,this paper discusses the causes of the differences between students and teachers,and concludes that mathematics reading,existing knowledge and experience,emotion and motivatio n are important factors that hinder the representation of students' function proble ms.On the other hand,the explanation of function problems in classroom teach ing is also an important factor for the cultivation of students' transformation aw areness of representation It is suggested that teachers should enhance students' a wareness of representation transformation and students' deeper understanding of problems in their daily practice.As for the characteristics of inter-representational transformation,it is found that students have the ability of representational transformation regardless of the intra-system representation and inter-system representation,they have a good a wareness of inter-system representation transformation,and the inter-system repre sentation transformation is biased,and the intra-system representation transformat ion lacks awareness.Finally,according to the conclusion of the research,a variety of representati onal methods are selected for course teaching to increase the diversity of functi on concept prototypes:Pay more attention to students' math reading,existing kno wledge and experience,emotion and motivation;Suggestions for teachers to enh ance the consciousness of representational transformation in classroom teaching.