| The Mathematics Curriculum Standards for Senior Secondary Schools(2017 Edition)suggests that senior secondary mathematics is oriented towards the development of students’ mathematical literacy and requires teachers to create appropriate contexts,inspire and guide students to grasp the essence of mathematical content,and advocate students to adopt independent thinking,independent learning and cooperative communication in learning.The trigonometric function is a key component of senior secondary mathematics,and is also a hot topic in the Advanced Level Examination.In The Mathematics Curriculum Standards for Senior Secondary Schools(2017 Edition)suggests that senior secondary mathematics is oriented towards the development of students’ mathematical literacy and requires teachers to create appropriate contexts,inspire and guide students to grasp the essence of mathematical content,and advocate students to adopt independent thinking,independent learning and cooperative communication in learning.The trigonometric function is a key component of senior secondary mathematics,and is also a hot topic in the Advanced Level Examination.In th s paper,we have analysed the past three years’ exam questions and found that the average score of trigonometric functions is around 17 marks each year,which shows that trigonometric functions have a very important position in the HKALE.However,in the actual teaching of trigonometric functions,teachers usually emphasise the combing of problems,the application of methods and the standardisation of formats,often neglecting the more essential aspects of teaching trigonometric functions-the generation of concepts,the identification of definitions and the derivation of formulas.Based on the pressure of the current situation of the college entrance examination and the teaching intensity,the time for students’ investigation in the classroom is still suppressed,resulting in classroom teaching still being dominated by teachers’ teaching and students’ practice,which does not meet the requirements of the curriculum.This study will therefore explore the use of problem-driven classroom teaching to solve these problems and improve the current situation.As the great mathematician Halmos once said,"Problems are the heart of mathematics",and problem-driven teaching is a method of teaching that is based on "problems".The problemdriven approach is a teaching method based on "problems" in which students can investigate solutions and construct knowledge based on the problems proposed by the teacher.In view of this,the author explores the problem-driven and trigonometry theory,the analysis of curriculum standards and teaching materials,the investigation of the current situation,the case study and the teaching design,with the guidance of the problem-driven teaching theory and the goal of opening up the knowledge chain of trigonometry in high school,hoping that the problem-driven teaching method can facilitate teachers to effectively complete the teaching tasks and cultivate students’ core literacy.This paper is based on Ossubert’s theory of meaningful learning,Vygotsky’s theory of "nearest development area" and constructivist theory.The purpose is to grasp the essence of the teaching content of trigonometric functions and to define the concepts of trigonometric functions,teaching design,problems,mathematical problems and mathematical teaching problems;secondly,we analyse the curriculum standards and teaching content of trigonometric functions and use questionnaires and teacher interviews to understand the teaching of trigonometric functions.Based on the research of literature and the author’s own understanding,the evaluation elements of teaching cases are proposed,the existing teachers’ trigonometry teaching cases are evaluated,and the problems in trigonometry teaching are summarised;then the basic principles of problem design and how to create a reasonable and effective problem situation are summarised,and the trigonometry teaching strategies and Finally,the conclusions,innovations,shortcomings and prospects of this paper are given.Based on the study of the current teaching situation,the problems in the teaching of trigonometric functions are pointed out from both students and teachers,and the basic principles of problem design are summarised: the principles of inspiration,appropriateness,cascading,and wholeness.The teaching strategies for trigonometric functions in high school are: firstly,to trace the origin and extract the essence of the content;secondly,to create situations to stimulate students’ interest;thirdly,to go deeper and deeper to grasp the connection between problems;fourthly,to inspire and guide to expand students’ thinking;fifthly,to solidify the application and strengthen the understanding of knowledge;and sixthly,to summarise and reflect to improve the evaluation methods.The basic steps of trigonometric function teaching design are given based on the construction of teaching strategies,and the teaching design is carried out for the radian system in trigonometry,the concept of arbitrary angle trigonometric function and the induction formula. |
