At present, there are some differences between the complex number teaching in senior high school and the requirements of "Ordinary High School Mathematics Curriculum Standards (2017 Edition, Revised in 2020)". Due to the influence of the college entrance examination on teachers, there are some prominent issues in teaching, such as compressing class hours, lacking holistic design, emphasizing on memorization and calculations, ignoring the understanding of the concept and the application of geometric meaning, making it difficult for students to understand the necessity of introducing complex number. Based on this situation, the study compares and analyzes the content of complex number in the six editions of high school mathematics textbooks: PEP A (published by People's Education Press, Edition A), PEP B (published by People's Education Press, Edition B), BNUP (published by Beijing Normal University Press), JPEP (published by Jiangsu Phoenix Education Press), HEP (published by Hunan Education Press) and SEP (published by Shanghai Education Press), in order to help teachers interpret the curriculum standards more accurately, and then better design the teaching content, and provide new ideas for the teaching of complex number.
This study primarily explores two questions: (1) What are the differences in the setting of complex number in the six versions of textbooks? (2) What is the guiding significance of comparing and analyzing the content of complex number in multi-version textbooks for teaching?
This study makes a multi-angle quantitative comparison and qualitative analysis of the complex number in the six editions of textbooks from four aspects: style structure, knowledge arrangement, example and exercise design, and mathematical culture, with the methods of literature research, comparative research, and content analysis, and using the research tools: concept map and the difficulty model of examples and exercises. The following conclusions can be drawn: (1) In terms of style structure, the six versions of textbooks have common characteristics: the column design structure is similar, the column form is rich and colorful, and the exercise design has a gradient; PEP A has the most abundant and the largest number of columns; PEP B and BNUP weaken the role of aside; SEP lacks the establishment of the overall knowledge structure system. (2) In terms of knowledge arrangement, SEP has the most unique chapter arrangement design; based on concept maps, PEP B has the highest comprehensive level of knowledge structure, with the advantages in knowledge content, breadth, and connectivity; PEP A has the highest level of knowledge depth and complexity of knowledge structure, but the requirement for the calculation of complex number is lower; HEP and BNUP focus on exploring the geometric meaning of multiplication of complex numbers. (3) In terms of example and exercise design, SEP has the largest number of examples, and JPEP has the largest number of exercises; PEP B, SEP, and HEP have diverse types of examples and exercises; PEP A and JPEP have the richest presentation of examples; the comprehensive difficulty level of the examples and exercises in the six editions of textbooks is relatively consistent, with PEP B slightly higher; PEP A ranks lowest in all four difficulty factors of mathematical cognition, operation, reasoning, and knowledge content. (4) In terms of mathematical culture, the column distribution of mathematical culture in PEP A and PEP B is the most balanced; the content of mathematics culture in SEP and HEP is the most substantial; the content distribution of mathematics culture in PEP B and BNUP is the most balanced and the most abundant; the application level of the history of mathematics in PEP B is the highest.
Based on the comparative conclusions of complex number content in the six editions of textbooks, the following teaching suggestions can be proposed: (1) Optimize and integrate the teaching content, advocate the large unit teaching of complex number: integrate complex number knowledge points with a comprehensive view, reconstruct the unit knowledge context, clarify the relationship between the teaching content and the core literacy, and build a "unit-hour" teaching framework. (2) Give full play to the column function, develop students' "four abilities" in a problem-oriented manner: learn from the presentation forms of columns in different textbooks, focus on the situational nature of problem creation, the guiding nature of problem presentation, the process nature of problem analysis, and the expansive nature of problem solving. (3) Configure diversified examples and exercises, cultivate mathematical thinking, and focus on the development of core literacy: refer to the rich examples and exercises resources of multi-version textbooks, and attach importance to the diversified teaching of examples and exercises and the innovative design of homework. (4) Pay attention to the infiltration of mathematical culture, help students establish a correct mathematical view and outlook on life: combine the development history and application value of complex number, integrate mathematical culture into the courses of complex number, and improve students' cultural literacy. (5) Advocate the integration of multi-version textbooks' teaching and optimize teaching design cases: integrate and reorganize the excellent materials from different versions of textbooks, present teaching design cases of integration of multi-version textbooks' teaching, and promote teachers' professional development.
谷歌
火狐
