School Mathematics Textbooks in China

The following sections are included:

• Contents
• Preface

Curriculum content is an integral part of mathematics courses; it is the basic elaboration of the manifestation for humanities underpinned by mathematics. Therefore, curriculum content selection and organization are deemed as essential in the preparation of mathematics curriculum. The curriculum content of mathematics is based on its curriculum goals, the core part of which is selected from the basic mathematical system, organized and designed according to some logical order to form a knowledge and experience system. Therefore, the determination and organization of mathematical core content are given top priority in the preparation of mathematics curriculum. Currently, curriculum content has aroused widespread concern in international mathematics education and study. This chapter explores three basic questions with regard to the core mathematical content in high schools: (1) what is the benchmark for the selection of the core content, (2) what constitutes core content, and (3) how to organize core content.

This research made a detailed comparative study on the complex number contents in four series of textbooks from China (People’s Education Press, Shanghai Education Press), Japan and Singapore, focusing on the following questions:

Question 1: what are the similarities and differences of the four series of textbooks in content selection and arrangement for teaching complex numbers?

Question 2: what are the similarities and differences of the four series of textbooks in the presentation of the content?

Macroscopic and microscopic comparison models are established based on an overall comparison of textbooks from China and Germany. By using qualitative and quantitative methods, the geometry content in the Lambacher Schweizer mathematics textbooks from Germany (DE-LSM) and that in the textbook published by People’s Education Press, version A, from China (CN-PEP) are compared. Taking the subject of solid geometry as an example, we find that: DE-LSM covers a relatively narrower but more profound range of content and pays more attention to the cultivation of students’ comprehensive ability, while CN-PEP covers a wider range of content and focuses on the cultivation of spatial imagination. As for the writing style, DE-LSM is well organized and more targeted at the specific contents, while CN-PEP is more systematical and attaches more importance to the integrity of mathematical knowledge; a nd a s for the presentation of knowledge, DE-LSM emphasizes the application, while CN-PEP gives more attention to students’ intuitive perception.

This chapter focuses on the comparison of the contents of statistics and probability in six series of high school textbooks in China and other countries. By taking the content of binomial distribution as an example, the six series of textbooks published by People’s Education Press of China, Sukan Shuppan Publishing Company of Japan, Panpac Education of Singapore, Pearson Education of U.S., Wright Group of U.S. as well as the Cambridge University Press of UK are compared in three aspects, namely, selection of topics, design of learning tasks and presentation of content, sequentially relevant suggestions are made to the curriculum developers and textbook writers in China based on the similarities and differences. The study has found that the Chinese textbooks do not pay due attention to binomial distribution and the course needs to be deepened and extended. The Singapore’s textbooks and American Wright Group textbooks cover the most topics in the closest connection with other knowledge and both attach great importance to the teaching of binomial distribution. The Chinese textbooks have good command of the cognitive level of tasks though the number of tasks is too few and activity type is monotonous, while the two series of American textbooks use a variety of activity types and it is convenient for students to learn from multiple perspectives with a wide range of activities. In terms of presentation, the Chinese textbooks value the design of knowledge introduction, despite the lack of application materials; American Pearson Education stands out in the design of statistical activities especially in using simulations; while Singapore’s textbooks are unique in solving computation and internal mathematics problems with graphing calculator and give very detailed guidance for using the calculator. In general, the Chinese textbooks should be credited with its efforts in inspiring reflection and giving basic knowledge to students. It is suggested that we add a small number of topics at the time of revising the curriculum standard and textbooks, deepen the teaching and learning appropriately, use tables and graphs more often, introduce graphing calculator or software, and increase the amount of examples and exercises, in particular, those with applications to scientific context.

In order to steadily put forward the reform in the teaching of calculus in high schools and carefully construct high-school calculus course, we aim to obtain rich information and useful ideas by investigating high school calculus textbooks from other countries, which can form a basis for reviewing our calculus-teaching reform over the last decades. This is an efficient way for us to look back at the experiences and adjust strategies to construct a more appropriate calculus course for high schools in China.

This chapter proposes five elements for analysis of inquiry contents in high school mathematics textbooks, namely situation expression, problem statement, partnership, activity type, and context interaction; Their sub-indexes are described in detail to construct an analytical framework for the inquiry contents in high school mathematics textbooks. Based on the framework, the chapter presents an analysis of seven high school textbooks from China, Germany, Japan, UK, USA, France, and Singapore, and compares their characteristics of design in the mathematical inquiry. The result suggests that the German textbooks (DE-EDM) focus on the creation of abundant real situations and the design of the activities for peer cooperation; the textbooks published by the People’s Education Press of China (Version A, CN-PEP) emphasize the design of open-ended problems and usually express problems with interrogative sentences; the textbooks by Sukan Shuppan Publishing Company, Japan (JP-SKS) offer plenty of mathematical reading materials for students; the UK textbooks (UK-SMP) emphasize on the design of teamwork cooperation situations; the US textbooks (US-PHM) pay attention to the display of the role of the inquiry column in the textbooks as well as the application and development of knowledge in the inquiry; the French textbooks (FR-EDB) pay special attention to students’ inquiry into information technology and the application of information technology in mathematics; and Singapore’s textbooks (SG-PPE) attach importance to the cultivating of students’ capacity of speculation and explanation.

Examples in mathematics textbooks play a multi-functional role in mathematics teaching and learning, and the difficulty of examples reflects the difficulty of mathematics textbooks. With six series of high school mathematics textbooks from China, the United States, France, Russia, and Australia as samples, this chapter uses a composite difficulty model to analyze the difficulty levels of examples in the textbooks with respect to 5 factors — the problem context, the mathematical cognition, the computation complexity, the reasoning difficulty, and the topic coverage. The results compare difficulty characteristic of examples in the sample textbooks, which may provide references for the textbook compilation in China.

This chapter compares the designs of examples and exercises in senior high school mathematics textbooks from China, U.S. and Germany. By constructing basic designing principles of examples and exercises in mathematics textbooks, we established a comparison framework and relevant coding system for analysis. The study focuses on the content of “function”, and makes the comparison from both external and internal aspects. The external aspect mainly involves the quantity, types and materials of examples and exercises. The internal aspect concerning examples covers their exemplarity, typicality, fundamentality and treatment methods; the internal aspect concerning exercises involves hierarchy, variation and coverage. Comparison results show the commonalities and differences in the textbooks from the three countries. Based on comparative analysis, this chapter also offers suggestions to optimize senior high school mathematics textbooks’ examples and exercises design.

The application of information technology has become a major area of study for the international mathematical education field; however, as for the integration of information technology and mathematics curriculums, we should also consider how to make information technology an effective classroom teaching means. Our research idea is to compare both similarities and differences in information technology handling of China and other countries under a rational framework and then to explore how to adjust the information technology in the high school mathematics textbooks of China.

This chapter presents a comparative study on middle school mathematics textbooks selected from 10 countries including China, Australia, the United States, Britain, France, Germany, South Korea, Singapore, Japan and Russia. Using both quantitative and qualitative approaches, the comparison focuses, on the quantity, type, openness and difficulty level of all the exercise questions in the topics of “numbers and operations”, “equations”, “triangles”, “solid figures” and “statistics”. The results reveal that the exercise questions in these textbooks have their own distinctive features. For instance, the US and Australian textbooks offer simpler exercises, while the Russian textbooks contain the most difficult ones, and the exercises in the Chinese textbooks are above the average level in terms of difficulty. Further analysis shows the selected textbooks bear similarities as well, such as regional characteristics, prioritized exercise allocation, hierarchy of exercise design and the emphasis on the association of mathematics, real life and other disciplines. These findings shed some light on developing Chinese mathematics textbooks: increasing to some extent the amount of exercises, enhancing the openness of exercise conclusions and maintaining a reasonably difficulty level of exercises.

In the turn of the century China launched a school curriculum reform, and the new primary mathematics textbooks as per the National Mathematics Curriculum Standards for Compulsory Education (Experimental) (MOE of PRC, 2001) have been put into use in 2001, starting from certain experimental districts and then popularized to the whole country. In 2011, the Ministry of Education promulgated a revised version of the standards, the National Mathematics Curriculum Standards for Compulsory Education (2011 Edition) (MOE of PRC, 2012), and then the textbooks revised according to the 2011 standards have entered the school classrooms since 2013.

What happens to students since this round of curriculum reform? This question is concerned not only by the policy makers, reform designers, and school teachers, but also by the parents, and even by the whole society.

This chapter reports an investigation we carried out in 2011 on pupils’ academic ability in mathematics in the certain experimental districts. Compared with the West, Japan shares more similarities with China in mathematics education, such as the school system, curriculum contents, etc. Therefore, we selected the mathematical test papers for grade 6 of the “2010 National Survey of Academic Level in Japan”, in which the examined contents and questions are more in line with the learning process and cognitive development levels of Chinese pupils. It is hoped that the assessment of the pupils’ mathematics learning quality could reflect the effectiveness of the new textbooks used in the experimental districts.

Textbooks are the materialized carriers of curriculum. As an important media for teaching and learning, they play an irreplaceable role in classroom instruction. They do not only provide an authoritative version of didactics in a particular knowledge domain, but also present each generation of students an official approved authoritative version of human knowledge and culture (Monica, 2006). The writing quality of the textbooks, to a large extent, determines the quality of teaching. In recent years, textbook studies, particularly those on textbook writing, have received more and more attentions in mathematics education research. The first large-scale study focusing on textbooks is known as the TIMSS study, which involved thousands of textbooks from approximate 50 countries (Schmidt et al., 1997). During the 10th International Congress on Mathematical Education (ICME-10) held in Denmark in 2014, textbook was proposed as the theme of one discussion group for the first time in the history of ICME. In addition, there have been many overseas scholars probing into the representation and task design of primary school mathematics contents (e.g., fraction) in their mathematics textbook studies. The domestic studies on primary school mathematics textbooks mainly focused on the contents, structure, representation, usage, mathematical culture, history, comparison as well as writing features, etc. Nevertheless, the existing studies, both domestic and overseas, on the writing features of primary school textbooks remain far from adequate, hardly able to satisfy the needs of the development of primary school mathematics textbooks. Therefore, this paper intends to make a relevant investigation in order to provide appropriate references to the development and characteristic improvement of primary school mathematics textbooks in China.

In this chapter, the representations of basic mathematical thoughts in mathematics textbooks are chosen as the object of study; using the methods of content analysis and speculation with typical topics in school mathematics textbooks as examples, we analyze the likelihood and forms to represent the basic mathematical thoughts in mathematics textbooks. Research shows that as one of the important components in mathematics curriculum, basic thoughts should be regarded as an important element in mathematics textbooks and must be well represented in textbooks; meanwhile, the representations should be subject to the criteria whether they could facilitate students to understand such thoughts so as to gain further development in mathematics. There are mainly three basic channels to represent the basic mathematical thoughts in textbooks: first, specific chapters could be set to explicitly and systematically elaborate the thoughts; second, they could be represented by integrating with the specific content of mathematical concepts, formulas and algorithms, by which the knowledge, skills and thoughts could be represented clearly; third, a narrative interposed or sparse infiltration could also be adopted in the explicit representation of knowledge and skills. Whether the basic mathematical thoughts could be consciously represented in textbooks depends basically on the value orientation of editors over curriculum content, or simply put, whether the textbook writers take a knowledge-based orientation or thoughts-and-methods-based orientation, or lays emphasis on both. Currently, an all-purpose textbook representation mode for all basic mathematical thoughts has not yet been discovered.

This paper investigated the usage of history of mathematics (HM) in 27 mathematical textbooks published between the late 19th century and the 1920s in the United States. The result shows that there are considerable HM materials in these textbooks, and their presentation forms can be divided into two categories: explicit and implicit. The explicit presentation includes famous quotations, mathematical characters, notes on specific topics, historical sketches of mathematical disciplines, as well as mathematical terminology, literature, problems, thoughts and methods in proving theorems; while the implicit presentation are involved in compiling mathematical exercises and introducing basic mathematical concepts. Among them, mathematical problems and historical notes on specific topics are most-used presentation forms. Then, five methods of approaching the HM materials in the textbooks were classified as: ornamentation, supplementation, duplication, accommodation, and reconstruction. The characteristics of the usage were also analyzed, and it is found that: the HM usage in a mathematical textbook is closely related to the HM knowledge at the time when the textbook published, the HM literacy of the editor of the textbook, as well as the value of HM and the scientific humanism ideological trend at that time. Compared with the textbooks one century ago, today’s Prentice Hall edition textbooks have made little significant progress in the HM usage.

Competition mathematics was introduced to China in 1956, and was developed as a complement and enhancement for in-class instruction. This chapter first provides an introduction to the organization, the training system and learning materials, and then discusses the influence of competition mathematics on students’ mathematical ability as well as the existing problems of competition-oriented education in China.