A Study On Integral Teaching Design Of Functional Concept Unit In Senior High School Mathematics

The National Mathematics Curriculum Standards for High School(2017)clearly puts forward six core competencies of mathematics,which means a focus of mathematics class has been shifted from simply leading students to memorize knowledge and train skills to developing students’ core competencies.How can teachers implement core competencies in classroom teaching? The Curriculum Standards advocate overall teaching.However,through literature review,it is found that most in-service teachers have not realized the practical significance of overall teaching and there is the lack of overall teaching design cases for reference.Therefore,the present study focuses on the overall teaching design of the unit of function concepts in high school mathematics.Firstly,based on literature review,this thesis summarizes and analyzes the status quo of the studies on the concepts and properties of function and the studies on unit teaching design,and defines the key concepts in the present study.By means of employing questionnaires,the thesis aims to investigate the understanding level of the Grade 1 students from senior high school on the content of the functional concept unit drawing on SOLO classification theory.The result exhibits that students are still at the stage of multi-point structure level,which manifests in the following aspects.Foremost,they do not comprehend the corresponding relationship and can not employ monotonicity,parity,and the combination of numbers and shapes to deal with inequalities as well as maxima and minima.What is more,they are not equipped with the capacity of studying comprehensively a new function from the definition domain,value domain(maxima and minima),monotonicity,parity,formula and image.With the in-depth exploration of students’ performance,the causes can be ascribed to the following points,involving low abstract capacity,weak awareness of the combination of number and shape,inferior network of function concept.Finally,based on the analysis of the questionnaire and according to the unit teaching design theory and the teaching content in the function concept unit,the present study suggests that the unit teaching design is conducive to promoting students’ mathematical competencies,developing students’ way of thinking to combine number and shape,and helping students establish a network of function concept.Subsequently,the thesis adopts the steps of mathematical unit teaching design proposed by Professor Lv Shihu,the unit teaching design on concept of function is devised obeying the rules embracing "content","analysis of the teaching elements","unit teaching goal set" and "design unit teaching plan".Several cases such as the start class,concept of function(first class),monotonicity of function(first class),are included in the teaching design.