| Mathematical key competencies are the important content of the new round of mathematics teaching reform in senior high school,which is not only closely related to the cultivation goal of individual development,but also the direction of mathematics curriculum development in senior high school.According to the idea of key competencies,the development of students is fundamental,which is important to cultivate students' scientific spirit,innovation consciousness,essential quality and key ability based on the curriculum content of high school mathematics.The complex numbers in senior high school are associated with many knowledge topics such as algebra,plane geometry,trigonometric functions,etc.,which showing a wide range of connections.Under the idea of key competencies,it is important for students to learn the knowledge of complex numbers in senior high school,because it is very helpful for students' knowledge understanding and individual development.The mathematics curriculum of senior high school has been revised for many times in recent decades,although the content of complex numbers has always been regarded as a basic part of mathematics in senior high school,the content of complex numbers has shown certain volatility since the founding of the People's Republic of China,which reflects people's value orientation about complex numbers and the thoughtful consideration about curriculum development.In recent years,some of the original contents of complex numbers in senior high school have been deleted,it makes complex numbers in high school become a lesson which is difficult but easy to teach,this means that it is easy to teach,but students have obvious problems in understanding basic concepts.The content is the basic element that constitutes the curriculum,The basic view of curriculum development theory holds that education is a process of changing people's behavior patterns,and the study about learners themselves is the basic source of educational goals.This paper focuses on the educational goal of promoting students' development.Based on the study of students' understanding level and behavior,this paper analyzes and discusses the curriculum content of complex numbers in senior high school,which is an in-depth development of the current research on complex numbers in senior high school.Therefore,this paper carries out research in the following four aspects.Firstly,this study establishes the basis for judging the educational value of complex numbers in senior high schools from three aspects: students' needs aboutindividual development,the educational function of mathematics and the basic requirements of senior high school mathematics curriculum,and the educational value of complex numbers in senior high school is discussed theoretically.The study of complex numbers in senior high school shows important value in six aspects: the development of students' knowledge structure,the change of mathematical concepts,the improvement of way of thinking,the development of key competencies,the infiltration of mathematics application consciousness and the improvement of personnel training mode.The theoretical analysis of the educational value about complex numbers lays a necessary theoretical foundation for the follow-up research.Secondly,in terms of the study of curriculum text,this study makes a longitudinal comparison from three aspects: the number of class hours,curriculum content and teaching objectives about the complex numbers in 11 versions of the senior high school mathematics syllabus or curriculum standards in China.Although there are some changes and fluctuations in three aspects,but these syllabuses or standards require learning about complex numbers as “a kind of number”,which showing the objective requirements of the extension of the numerical system,and putting forward relatively high teaching requirements for the representation and operation of complex numbers.This study also makes a horizontal comparison about the text of complex numbers in high school among China,the United States,Singapore,the United Kingdom and Australia,analyzes the curriculum objective of the complex numbers in different countries.It provides reference for the development of complex numbers curriculum in senior high school.Thirdly,as a further practical proof,this study analyzed and constructed the framework of students' understanding level about complex numbers in senior high school theoretically,and gave four levels of students' understanding about complex numbers in senior high school: conception,representation,connection,application.On this basis,under the guidance of experts and in combination with the current teaching practice,this paper designed a questionnaire for senior high school students' complex numbers understanding level,selected appropriate research samples and tested them,and analyzed the results.The test results show that most of the students have a better performance in the level of conception and representation levels of complex numbers comprehension in senior high school students,they can handle some conventional complex numbers problems easily,and have a better performance in the basic application of some knowledge memory and methods.But at the levels of connection and application of complex numbers,the performance of students isrelatively weak.Due to the influence of various factors,students in different types of schools also show certain differences.Students can memorize basic conclusions in complex numbers problem solving,but lack the necessary judgment in some more complicated problems,students' thinking is relatively common in solving complex numbers problems,they do not perform well on high-level problems.Although the geometry meaning of complex numbers is very important,students don't have a perfect understanding about that,they lack the necessary understanding about the basic concepts and operations of complex numbers such as imaginary units i,they also generally have difficulty to deal with complex numbers problems which relate to other knowledge topics.Finally,based on the results of theoretical analysis and practical research,this paper enumerates the basic content and constructs its framework of complex numbers in senior high school.Combined with the idea of the mathematical key competences in senior high school,this paper also gives some suggestions on the development of the curriculum and content of complex numbers.The basic status of the complex numbers curriculum should be firmly established in high school mathematics.In order to fully reflect the educational value of complex numbers in senior high schools,attention should be paid to the relative integrity of the knowledge system of complex numbers,to the key concepts of complex numbers,to enrich the geometric meaning of complex numbers,complex numbers and equations and other contents closely related to the development of complex numbers,as well as to the extensive relevance and historical and cultural value of complex numbers.The contents and results of this paper show the following three aspects of innovation: One of the innovations,there are not many researches on the complex numbers in senior high school,and almost all of them concentrated on the teaching design of complex numbers in senior high school.This paper conducted a more systematic research,including theoretical analysis,course text comparison,complex numbers learning evaluation,complex numbers content analysis,etc.,all of these work plays a necessary supplement role to relevant researches.Second,the fundamental purpose of education is to change students' behavior.Therefore,based on the needs of students' development,especially the needs of basic knowledge,this research tested students' understanding of complex numbers,analyzed students' typical performance,and discussed the knowledge factors that affect students' complex numbers understanding level in high school.In terms of research ideas,research methods and research results,this research shows good explorationsignificance.The third innovation,after a relatively systematic research,especially using specific methods to analyze the specific problems related to complex numbers in senior high schools,the relevant conclusions provide a more direct basis for the reform of complex numbers curriculum in senior high schools,rather than just relying on experience. |
PDF Full Text Request