Research On The Evaluation Of The Understanding Of The Periodic Concept Of Function

Mathematical concepts are the logical basis for deriving mathematical theorems and formulas,Concept teaching is an important part of mathematics teaching,Promoting conceptual understanding is the main purpose of mathematics teaching,Therefore,understanding and evaluation of mathematical concepts have become a hot topic in mathematical education research.Function periodicity,as a basic property of functions,occupies an important position in the main line of functions.This research is based on the mathematical concept understanding model of Lesh&Landau,and establishes a two-dimensional model to evaluate the students'understanding of the periodic concept of function.In this study,143 high school students from an ordinary high school in Y City were used as research objects.Through paper-and-pen tests,questionnaires,and interviews,the 143 students'perceptions,representations,connections,and applications of periodic concepts of functions were analyzed.Obstacles and errors in understanding the periodic concept of the function,the factors affecting the concept understanding,the degree of correlation between the concept understanding level and the test results:The students' understanding of the periodic concept of the function is general,there is no significant difference in the degree of understanding of the concept of gender,the degree of understanding of the excellent class is higher than that of the ordinary class;the concept of the perception of the concept is the worst,and the representation of the concept is relatively best.First,the perception of concepts:students can identify and explain some of the more basic concepts;give examples of periodic functions and write the minimum positive period;state the concepts according to their own understanding.However,students have problems understanding many keywords in the concept of periodicity of functions.Second,conceptual representation:image representation is better than symbolic representation.Without grasping the essential characteristics of the image,the understanding of symbols is more one-sided.Third,the application of concepts:the ability to periodically use functions to solve general mathematical problems and problems in real life,but not flexible enough.Fourth,the connection of concepts:Most students are able to establish connections between concepts,but they have less connection with periodic concepts of functions and other concepts,and have not formed a knowledge network.Fifth,obstacles to understanding:(1)Difficulty in understanding keywords such as"arbitrary" and "existence"(2)Difficulty in understanding image features(3)Difficulty applying formula.Sixth,misunderstanding:(1)the periodic function domain can be a bounded set(2)a function with periodicity must have an image(3)a function with periodicity must have a minimum positive period(4)The letter T in the formula is the period(5)The image of the periodic function is infinitely extended,repeated,symmetrical,and regularSeventh,the degree of understanding of concepts has a certain degree of relationship with students' learning methods,learning attitudes,and teaching methods.The final exam results are significantly positively related to the understanding of concepts.