Conference Information

The Fourth-Day Review of ICMT-4

LISTENING TO THE PLENARY 5

ICMT-4 invited Professor JeongSuk Pang to give a speech about "Looking back on mathematics textbook research in Korea: Challenges and future directions".

Professor Pang presented an analysis of 418 peer-reviewed papers published in the seven Korean professional journals in mathematics education. The categories of mathematics textbook research were divided into textbook analysis, textbook use, and textbook development. The intersections between the categories were specified to reveal what may have been hidden under the most prevalent textbook analysis research. Each category was subdivided into main topics and sub-topics. Furthermore, various cross-analyses were conducted among the topics, school levels, publication years, mathematics content strands, and research methods including research participants. In addition, research on foreign textbooks or comparative studies between different textbooks was further analysed.

The results show that: (1) There are 360 ​​researches on textbook analysis. The proportion distribution of different research topics is as follows: mathematical concepts (38.9%), the overall construction (18.9%), mathematical processes and competencies (15%), teaching and learning materials or activities (12.2%), mathematical terms or symbols (5.8%) and so on. Among them, the textbook research on elementary school students accounted for the most, as high as 57.5%, and among these studies, the research on mathematical concepts was the most. At the same time, 36.1% of the literature on the comparative study of textbooks is local comparative research, and 24.4% is international comparative research.

(2) There are 78 studies on textbook use. Among them, the review of appropriateness accounted for 41%, the recognition or use of textbook accounted for 33.3.%, and the research on the textbook understanding accounted for 25.6%. The proportion of studies focusing on elementary school is the highest (47.4%), and the proportion of articles using survey methods is the highest (51.3%).

(3) There are 25 research papers on textbook development. 76% of the research topics are related to the development direction and example, but the research on the development process and guide is very small.

On this basis, Professor Pang further introduced their research on the textbook development. The research question is "Do our curricular materials provide key activities for elementary school students to foster functional thinking?". Starting from the research questions, Professor Pang roughly described the general flow of elementary math textbook in Korea. In 2000, the Korean mathematics curriculum focused on knowledge and skills, and the enhancement of students' math thinking ability and the cultivation of problem-solving ability. In 2009, the Korean mathematics curriculum focused on the mathematical communication, and positive attitudes. In 2009, it focused on the cultivation of mathematical creativity. From 2015 to 2022, it focused on the cultivation of core literacy in math.

Then, professor Pang explained the development process of their textbooks. From the overall writing plan, the first draft, the second draft to the third draft, all have been reviewed by internal and external experts. During the revision process of the third draft, they conducted a field survey of students to collect students' responses in the classroom. By soliciting opinions from experts in and outside the field, as well as opinions from schools and relevant research groups, the revision was formed. Draft 4. Then, the final draft of the textbook was formed by collecting expert reviews. They constructed a framework of key instructional elements, including CONTEXT, TASK, FUNCTION RULE, VARIABLES. Among them, CONTEXT deal with the correspondence relationship with real-life contexts; TASK include various pattern task; FUNCTION RULE refer to the exploration of the relationship by focusing on the changes of two quantities. VARIABLE means that students can represent the correspondence relationship with symbols including variables.

Finally, building on the review on mathematics textbook research, Professor Pang analyzed what had been catalysts for the rapidly increasing textbook research and discussed the challenges and future directions of textbook research. These included methodological considerations, diversification of mathematics textbook research topics, international comparative studies on mathematics textbooks, alternative forms of textbooks, systematic process of textbook development, textbook selection and evaluation, and deviced to facilitate effective use of textbooks by teachers and students. In the discussion session, scholars discussed topics such as textbook selection, electronic textbooks, and technology use.

EXPLORING THE SYMPOSIUMS

Symposium 3

The theme of symposium 3 was "Uncovering some of the work involved in using digital resources: Looking across the borders of South Africa, China, and Sweden". Wang Chongyang from Beijing Normal University, firstly introduced the background of the symposium, emphasized the important role of digital resources in mathematics teaching and learning, and made a research report entitled " Mapping teachers resource systems in China :two case studies with pre-service and in-service teachers". The research takes the Documentary Approach to Didactics as the theoretical framework and mainly includes three different related studies. It discusses the use of digital resources by pre-service and in-service mathematics teachers from different perspectives, and concludes that the gap between freshmen and junior students in the use of resources is not obvious, but compared with in-service teachers, pre-service teachers have a more open attitude towards the resource system; Pre-service teachers' choice of research direction is more related to individuals and their tutors. The most difficult thing is not literature retrieval, but reading, summarizing and refining their own views on literature; In addition, excellent individuals do not mean that their cooperative team is excellent, but both pre-service and in-service teachers show interest and concern for the cooperative community.

Symposium 4

Symposium 4, with the theme of "Towards Innovative Practices in Mathematics Education: Teachers’ and Students’ Choice and Use of Digital Resources", consisted of six studies. Birgit Pepin (Eindhoven University of Technology), Sebastian Rezat (Paderborn University), Farzad Radmehr (Norwegian University of Science and Technology), Annalisa Cusi (Sapienza University of Rome) and others participated online. This symposium was chaired by Professor Fan Lianghuo. Among them, Farzad Radmehr made a report entitled "Problem-posing: An inclusive activity for improving teaching and learning of mathematics at university level". In this presentation, he discussed how Problem-posing (PP) activities could be used in the teaching and learning of mathematics at the university level. In particular, he discussed how to design inclusive PP activities for students with different prior knowledge and experience and also share how students perceived their engagement with this type of activity. Then, he also discussed how PP activities could be used to elicit students’ mathematical understanding and how students’ posed problems could be assessed. Finally, he hoped this presentation could encourage both tertiary mathematics educators and mathematics lecturers to use PP activities more often in research and practice alongside problem-solving activities. In the discussion session, the participants discussed topics such as the change of digital resources to the triangle relationship among students, teachers, and textbooks, and the initiative of students in using resources.

BROWSING PARALLEL SESSION

Parallel Session 9

Parallel Session 9 consisted of 8 studies from teams from Yamanashi University, Beijing Normal University, East China Normal University, People's Education Press and Gansu Provincial Institute of Education Science. They reported on topics such as textbook analysis, textbook comparison, textbook organization, and digital textbook development.

Hiroyuki Shimizu from the Yamanashi University, Japan, gave a presentation titled "Examining Curriculum Alignment in Mathematics in A Transition Period: An Analysis of The New Elementary School Mathematics Textbooks". The newly released national curriculum standards in Japan emphasize the shift from knowledge-oriented to competence-oriented, with special attention to the role of mathematical thinking and mathematical activities in mathematics learning. A theoretical framework of curriculum alignment in the earlier TIMSS curriculum analysis (Valverde, et al., 2002) was used to conceptualize the role of textbooks across three different aspects of curriculum as broadly defined: the intended, implemented, and attained curriculum. By considering textbook as potential implementation curriculum that lie between the intended and implemented curriculum, this study attempted to explore the extent to which the competency-oriented goals set forth in the latest national curriculum standards were reflected in the six mathematics textbooks available in Japan. To this end, the study used the textbook analysis method reported by Valverde et al. to develop a corresponding coding system from the disciplinary objectives of mathematical thinking and mathematical activities, and to code and analyze the proportional/inverse proportional units in elementary school mathematics textbooks. The results showed that the textbooks did not cover all types of mathematical activities emphasized in the national curriculum standards, and the types of problems included were somewhat limited. Therefore, teachers need to enrich and supplement the tasks and activities in the textbooks in order to achieve the new competency-oriented goals expected by the national curriculum standards.

Parallel Session 10

Parallel Session10 included eight studies, a number of scholars from West Michigan University in the United States, Sami University of Applied Sciences in Norway, East China normal University, Southwest University, South-Central University for nationalities, Northwest normal University, Zhejiang normal University and Zhangjiajie College of Jishou University reported on the comparative study of Chinese and foreign mathematics textbooks, the study of mathematics culture, also the research and use of electronic textbooks.

Among them, Jon D. Davis and Nicholas E. witt from the University of Western Michigan in the United States carried out an investigation on the use of technology in electronic textbooks. The study examined a unit in the sixth grade Desmos (e-textbook) and Illustrative Mathematics (IM) e-textbook, which is a program that embodies MAT in an online form, covering how technical tasks are presented and how technology is used in the unit. This study is based on the framework used by Sherman and Cayton (2015) to study mathematical action technology (mathematical action technologies-MAT) as dynamic and static examples to solve students' mathematical problems. In order to understand the role of MAT in Desmos (calculator software) and Illustrative Mathematics (IM) electronic textbooks, the research first divided the contents of Desmos and IM, dividing IM electronic textbooks into 17 classes, and each Desmos course consists of 10-16 screens /slides. Each slide can collect students' data, and enable students to use various digital tools, such as graphic calculators, dynamic geometry, tables, etc.

FOCUSING ON THE CLOSING CEREMONY

Professor Liu Jian, Chair of the ICMT-4 Local Organizing Committee, made a summary of theconference. ICMT-4 was held in Asia and China for the first time. It was the first time to hybrid with online and offline, multi-venue real time communication across different time zones. It was also the first time to set the theme of "the relationship between curriculum reform and textbook development". More than 200 mathematics educators from nearly 20 countries participated in the ICMT-4. The conference received 113 submitted papers and nearly 400 officially registered representatives, and it generated extensive media attention. Then, professor Liu expressed his sincere thanks to the IPC, LPC, secretariat and core members, sub-forum moderators, volunteers, and breakout venue for their contributions to the ICMT-4. Then, taking a story of NCM textbooks as an example, he introduced the overall development of Chinese mathematics textbook research and practice. Finally, Professor Liu raised three questions: (1)How to balance the essence characteristics of mathematics and the cognitive trajectory of students? (2) How to enrich mathematics curriculum resources that are suitable for diverse learners through evidence-based and iteration? (3) How to maximize the role of mathematics textbooks in students’ growth and teachers’ professional development?

Professor Birgit Pepin, from Eindhoven University of Technology, as the IPC chairman of the ICMT-5, made a speech for the ICMT-5 to be held in Trondheim, Norway, from June 17 to 20, 2025. In the promotional video, Professor Iveta Kohanova from the Norwegian University of Science and Technology (NTNU), Chair of LOC of the Fifth Congress, introduced the famous scenic spots in Norway, and together with Professor Birgit Pepin, sent a sincere invitation to mathematics education researchers around the world.

Professor Fan Lianghuo, co-chair of the conference’s International Programme Committee, addressed the closing ceremony. He sincerely thanked every participant and organizer, especially the chairs of the ICMT-4 and the moderators of the parallel sessions, for their contributions to the conference. He also expressed regret that due to the COVID-19, the participants could not come to China to attend the conference. Then he expressed the vision that Chinese scholars would be able to attend the conference abroad after the COVID-19 is over. After that, he said that the papers of this conference will be published as soon as possible on the Asian Mathematics Education Center(AMEC) in the form of proceedings or in ZDM Mathematics Education and other journals as a special issue. Then he introduced that the ICMT-5 would be held in Trondheim, Norway. Finally, In memory of Professor Geoffrey Howson, honorary chair of the ICMT-1 International Program Committee and former Secretary-General of the International Committee on Mathematics Education, for his contribution to mathematics education, he declared the ICMT-4 over.

The Third-Day Review of ICMT-4

The third day of the conference was also filled with a variety of brilliant activities. Let's go to ICMT-4!

Listening To the Plenary 3

In the report of the third session of ICMT-4, Professor Gert Schubring, a professor from the Federal University of Rio de Janeiro, Brazil, and the chairman of the International Procedure Committee of the Second International Conference on Research and Development of Mathematical Textbooks (ICMT-2), was invited to make a speech. The theme of this report by Professor Schubring was "Thinking about the categories of mathematical textbook analysis from a historical perspective", which mainly guides the audience to think about the function and value of textbooks from the source in four aspects: how to analyze the context of textbooks, the important role of dictation, the development model of French textbooks, and the enlightenment of the development of Prussian textbooks.

In terms of the methodology of mathematics textbook research, Professor Schubring proposed that textbooks are not original, they are the product of textbook writers standing on the shoulders of predecessors, so text analysis needs to consider the background or situation. However, researchers have two common misunderstandings in understanding the background or situation: first, when studying the source of scientific knowledge, they often fail to take into account various "situations" of communication, especially the "teaching situations" in which such knowledge is elaborated, used and disseminated; second, other sources are roughly considered to be related to teaching activities, so they do not provide accurate source information, and they are used as "teaching situations". Therefore, when analyzing the text of textbooks, either the teaching situations that should be considered or the teaching situations that need to be studied in detail are ignored. In order to make text analysis more in-depth, people need to better understand the background or situation beyond the text. Bernard and Proust put forward the meaning of "contextualization" and determined its three dimensions: environment, situation and text system. The content of the textbook that needs to be analyzed in depth includes unit text and situation analysis, which requires hermeneutic analysis, that is, to understand and interpret the thoughts of others through symbols.

In terms of the important role played by dictation, Professor Schubring proposed that teaching materials should be transmitted orally in the form of teaching, in addition to printed text. Therefore, the analysis of teaching materials has three focuses: teaching materials, teachers and students. The interaction between them forms a triangular relationship in different forms.

In addition, Professor Schubring also proposed three models between teachers and textbooks. The first one is the reproduction mode: teachers and textbooks are at the same level, and teachers enrich textbooks with commentaries, or improve wrong or unclear propositions in textbooks. The second is the revision mode: teachers are the leaders of the teaching process and can freely use the textbooks. The third is the degenerate mode: textbooks are only selected by teachers for autonomous learning. No matter which model, the role of textbooks is quite important.

In terms of the developmental mode of teaching materials, Professor Schubring took French teaching materials as an example, and he analyzed three modes in the development and use of French teaching materials. The first mode starts from the original mode, which functioned as teaching materials but had no teaching characteristics, to the appearance of anti-Euclid geometry textbooks, and the publication of a series of textbooks including the application of arithmetic, algebra, geometry, calculus and physics. Finally, the public school system was established to make the textbooks return to preciseness. The second model is to set up a separate teacher's manual for teachers, including the principles of teaching methods, teaching objectives, and the interpretation and development of teaching. The third mode emerged in the post-revolutionary period, during which the first entrepreneur in the field of teaching materials appeared, which marked the great progress in the marketization of teaching materials. Its representative, Sylvestre Francois Lacroix, was determined to publish complete mathematical teaching materials.

In terms of the enlightenment of the development of teaching materials in Prussia, Professor Schubring believed that the case of Prussia reveals the productive role of teachers in reality. By analyzing the social and cultural background of Prussia in different periods, it is found that people are affected by different social and cultural backgrounds. The design of teaching materials will consider the contents of different social and cultural backgrounds, so the content of teaching materials is increasingly rich.

During the discussion, Professor Fan Lianghuo proposed that even in countries with centralized politics, the use of textbooks mostly adopts decentralized policies, so how to deal with the centralization and divergence in the use of textbooks. In addition, some scholars have proposed whether the emergence of digital textbooks will change the structure of existing paper textbooks, and how digital textbooks will affect the triangular relationship between teachers, students and textbooks. Professor Schubring explained these problems according to existing research. He believed that every teacher is a master of mathematics. From a higher perspective, teachers should be leaders. He/she should freely use textbooks, whether in a centralized school or a decentralized environment. In addition, Professor Schubring also pointed out that in order to make the content of digital textbooks or paper textbooks meaningful to students, teachers must coordinate and organize them. Therefore, textbooks in any form will not bring great changes to the triangular relationship between teachers, students and textbooks.

Listening To the Plenary 4

The fourth conference report topic was "Decoding the Implicit Information of Teaching Resources in Mathematics Teaching", brought by Professor Jane Remillard from the University of Pennsylvania in the United States. In the report, Professor Janine began by leading the audience to consider the question - "What do the mathematics curriculum materials and textbooks convey to teachers and students in addition to the content to be learned?" After briefly answering the two questions of "what should be communicated" and "how to communicate" from the perspectives of structure, self-perspective and traditional perspective, Professor Janine presented three studies completed by her research team in the past ten years. These studies used different research methods to answer the question of "what do curriculum resources communicate to teachers and students" from different perspectives.

The first research topic was "How authors of elementary mathematics curriculum materials communicate with teachers", and its research content focused on how primary school mathematics teaching resources provide support for teachers' teaching. The study selected five different versions of textbooks from grade three to grade five, with a total of 30 courses. Each guiding sentence in the textbook was coded by different levels, and the content of the textbook was divided into three parts: "Introductory", "Main Body of Lesson" and "Beyond the main body". The study found that the guiding sentences accounted for the largest proportion in the main body of the textbook, and there is a significant differences in the proportion of guiding sentences with different purposes in the textbook. Finally, Professor Janine also inspired the audience to think deeply about "what does the curriculum developer think primary school teachers need support with" and other issues.

The second research focused on the allocation of the relationship between teachers, students, resources and mathematics by curriculum guidance. Professor Janine first pointed out that the communication between curriculum materials and teachers is multi-modal, so the designers of curriculum materials will communicate their instructional intentions through visual and spatial modes of communication, as well as written language, and these designs also communicate tacit messages about social relations. Based on these views, with Flanders (Belgium), Sweden and Finland as the background, the research adopted the multimodal analysis framework of Bezemer and Kress (2008; 2015), under which, the analytical pathway was divided into three aspects, namely, Modes of communication and modal resources (including written text, image and layout), Structuring of interactions (including voice, locus of instruction and reading path) and Features of social relations (including distance and authority). The three aspects reflected the type of "communications" from "explict" to "tacit" ones. Finally, based on Engestrom's activity theory (1998), the study intuitively revealed the how kesson guides configurated social relations between teachers, students, artefacts and mathematics based on different cultural contexts.

The third study focuses on mathematics education in the digital age, and analyzes the use of online student-facing mathematics platforms (OSFP) for students in the United States. The research first investigated the use of teachers’ print and digital teaching resources in Flanders, Finland, Sweden and the United States. The survey results showed that the frequency of American students using online platforms was gradually increasing, while teachers in the other three countries/regions did not often use this resource. On the basis of this result, Professor Janine and his team focused on nine representative platforms in OSFP, and the research questions focused on "how do different OSFPs frame and structure teaching and learning interactions?" and "how are they shaping students’ learning experience". Based on the above research questions, Professor Janine and her team focused on students' learning experience through the "memorandum" function of the platform. Through developing a coding system, they summarized multiple platform features to see how they worked together. Finally, based on the three types of students learning experience identified, they provided suggestions for the design of OSFPs.

In the discussion session, Professor Zhang Jing from the State University of New York at Buffalo pointed out that the use of small sticks to assist in teaching multiplication table in mathematics textbooks of Beijing Normal University Press coincided with the findings of Professor Janine's research. In addition, the students from East China Normal University communicated with Professor Janine on how to conduct in-depth discussions on the content "outside the main body" in the textbook content, and how to study the feedback information from the textbook developers to teachers.

Exploring the Symposiums

Symposium 1

Symposium 1 consisted of 12 studies from Buffalo State/State University of New York, Beijing Normal University, Northeast Normal University, Minzu University of China, South China Normal University, Beijing Academy of Educational Sciences, Beijing Chaoyang Academy of Educational Sciences, and Shangcheng District Educational Evaluation & Monitoring Center. Liu Jian, Liu Qimeng, Zhang Dan, Dong Yaoyao, Zhou Da, Wang Tian, Xie Zhiyong, Dong Lianchun, Zhang Jing, Feng Pingting, Lin Danni, Wu Jiaqi discussed around the topic "The Key Features of NCM Textbook for Grade 1-6 and Its Relationship with National Curriculum Reform in China.". The symposium was divided into three parts, namely "Historical Review and Latest Progress of NCM1-6", "NCM and Students' Learning Opportunities", and "NCM and Teacher Professional Development". This symposium illustrated the development trends of NCM 1-6 in China.

At the beginning of symposium 1, Professor Jian Liu introduced the history of the NCM 1-6. Since the formation of the first edition of the NCM 1-6 Textbook in 1994,, as one of the most influential primary school mathematics textbooks in mainland China, its exploratory findings have become an important basis for the experimental draft of the national curriculum standards for compulsory education. It is also one of the most influential primary school mathematics textbooks in mainland China, and is one of the important driving forces of China’s Basic Education curriculum reform in the new century. In his report, Professor Liu Jian also mentioned that after nearly 30 years of development, this textbook, in its fifth edition, still maintained the spirit of exploration and reform, constantly searching for mathematical sources that are suitable for the growth and development of Chinese students. Professor Zhang Dan made a report titled " The connotation and iteration of "Context+Question strings"-- the Construction of NCM 5th Edition textbook, and systematically introduced the connotation and characteristics of " Context+Question strings" in NCM. The report pointed out that the process of unfolding " Context+Question string" forms the "five unification" , together with the process of occurring on mathematics knowledge, the process of students’ mathematics learning, the process of teachers’ guide to students and the process of achieving course objectives. Professor Zhang Dan also indicated that in the 5th edition of the NCM textbook, evidence-based research and iterative changes have been made to the "Context+Question string" to make it more consistent with students' authentic learning.

Symposium 2

The second symposium was hosted by Professor Liu Xiaomei from Capital Normal University. At the beginning of the seminar, Professor Liu Xiaomei pointed out that the seminar focused on the mathematics textbook published by Beijing Normal University, which mainly aimed at the "problem-based" textbook design concept and problem framework, the educational value of mathematics textbooks, the types and presentation of mathematical problems in the textbooks, and the in-depth understanding of textbooks, teaching design and practice based on problem theory. There are six reports in this topic, which were "Pursuing the educational standard of mathematics textbooks by building a problem-based system design — an overall introduction to the compilation concept of mathematics textbooks for grades 7-9 of Beijing Normal University Edition", "The task of raising questions in mathematics textbooks for Beijing Normal University Edition", "Recognizing the characteristics of geometric figures in thinking and answering reasoning questions", "From big ideas to big questions: practice and thinking of teaching units from the perspective of ability" "Research on the teaching scheme of problem solving for mathematics teachers in junior high school -- taking the discounted sales of the linear equation of one variable as an example", "The impact of teachers' teaching concepts and behaviors on students' problem posing: an exploratory study". The first three reports focused on thinking from the value orientation of education to the content of textbooks, and constructed the development prospect of textbooks in a macro way. The last three reports verified the role of textbooks in a microcosmic way through the specific practice of using textbooks. In the discussion session, Professor Qi Chunxia of Beijing Normal University had an in-depth exchange with the reporters on how to improve students' learning and development and how to reflect the significance of education orientation. Later, the host, Professor Liu Xiaomei, proposed the basis for task division and discussed with the reporters on different levels of mathematics textbooks published by Beijing Normal University.

Browsing Parallel Sessions

Parallel Session 7：

Parallel Session7 is composed of 6 studies by teams from Liaoning Normal University, Northwest Normal University, Beijing Normal University, Zhejiang Normal University, and Haiyan Education Research Center. They conducted research from the perspectives of learning progression, mathematical culture, textbook use, content analysis, and textbook development.

A research team led by Professor Zhang Chunli from Beijing Normal University gave a report titled “Research on The Consistency between Spiral Arrangement of Mathematics Textbooks and Learning Progression: Take The ‘View" Content of People's Education Press as An Example’”. This study examined the relationship between the spiral arrangement of mathematics textbooks and learning progression, using the "view" content in the people's education textbook as an example. The big idea in "view" knowledge is mainly "spatial capability". This study used spatial ability as the main variable for progression and classified it into three levels of intuitive imagination, analytical description, and reasoning abstraction. Knowledge and skills, and problem situation are two variables that influence spatial ability, the former being divided into identifying, drawing and reading pictures, and the latter into physical object, single geometry, simple combined geometry and complex combined geometry. Based on this, the study developed a coding sheet for analyzing the textbooks. The survey found that (1) the consistency between the topic design of textbooks and the learning progression of spatial ability reached an acceptable level; (2) the types of knowledge and skills presented by different grades were relatively single; and (3) with the increase of grade, the design of problem situation gradually transitioned from a physical object to geometry, from single geometry to composite geometry, and from simple composite geometry to complex composite geometry. The report stimulated a lot of discussions among the participants, and many meaningful questions were raised, such as —“What is the specific learning progression of "view"? “How is the learning progression constructed in the study?” and so on. The reporter answered these questions in detail and further explained the difference between "learning progression" and "learning trajectory".

The research team led by Prof. Guo Yufeng from Beijing Normal University made three reports in Parallel Session7, taking "The Complexity of Mathematical Expressions in Mathematics Textbooks" as an example, which focused on the calculation of the complexity of mathematical expressions and selected the chapter of trigonometric functions in two editions of high school mathematics textbooks of different years, analyzed and compared the complexity of mathematical expressions in them, and came up with the difference in the complexity of mathematical expressions in the examples and knowledge sections of the two editions of the textbook. For the study, the participants raised questions about the differences in operators, operands, and rules of the combination in the mathematical formula expressions in the chapter of trigonometric functions in the two editions of the textbooks, and the implications of the findings for mathematics teaching, which brought important insights to the participants.

Parallel Session 8：

Parallel Session8 is composed of 7 studies conducted by teams from the University of Auckland, Universitas Islam Sultan Agung, Zhejiang Normal University, Inner Mongolia Normal University, Huaibei Normal University, Suzhou University of Science and Technology, Tianjin Normal University, and South-Central Minzu University. Reports were made on topics such as Indonesian textbook analysis, creative thinking, research progress in foreign textbooks, numbers and algebra, and mathematical concepts.

Piao Jiang and Weizhong Zhang from Zhejiang Normal University made a report entitled "Infiltration of creative thinking in junior middle school mathematics textbooks". Their research used the analytical framework of creative thinking in the middle school mathematics curriculum to conduct a quantitative analysis of creative thinking in junior middle school mathematics textbooks in China and Singapore. They found that Chinese mathematics textbooks should increase the amount of creative thinking, and pay more attention to the problem posing. At the same time, it is necessary to adjust the overall proportion of mathematical tasks related to creative thinking, and to focus more on mathematical communication and technology integration, and further infiltrate the cultivation of students' creative thinking in textbooks. In the subsequent discussion session, the participants had an in-depth discussion on the proportion of creative thinking tasks and students' learning opportunities in the textbooks.

Financial Supports Exhibition

The sponsors of the conference, Beijing Normal University Publishing Group (www.bnupg.com.cn), East China Normal University Press (www.ecnupress.com.cn), Shanghai Science and Technology Publishers (www.sstp.com.cn), Qingdao Publishing House (www.qdpub. com) and Beijing Dayan Education Group (www.dayanmath. com) also set up exhibition posters in the venue.

On the last day of ICMT-4, the conference will bring participants one conference report, two special seminars, 16 oral reports and the closing ceremony of the conference. Welcome to continue to pay attention! For more information, please consult the official website of the conference: https://icmt4.org.cn/ Or contact the Secretariat of the General Assembly, whose email address is: icmt4@bnu.edu.cn

The Second-Day Review of ICMT-4

The second day of ICMT-4 continues! For four consecutive days, please follow our lens to "walk" into ICMT-4 and experience the wonderful moments of ICMT-4.

Listen To The Plenary

In the report of the second conference of ICMT-4, Professor Sebastian Rezat, a full-time professor of mathematics education at the University of Paderborn in Germany and the chairman of The 3rd International Conference on Mathematical Textbooks (ICMT-3), was invited to serve as the speaker of the report. The topic of Professor Rezat's report was "Students learn mathematics from textbooks and other resources". Professor Rezat mainly reflected on the future development of textbooks from three perspectives: student resource system, text reading ability and data collection method.

In the research perspective of the student resource system, Professor Rezat proposed that students are the first users of textbooks, and researchers should re-examine the role of textbooks from the perspective of students, especially the perspective of the student resource system. With the increasing diversification of teaching resources and the continuous development of information networks, the learning resources that students can access are also increasingly diversified. The research shows that mathematics textbooks are in a rather disadvantageous position among students' numerous learning resources at this stage. Even compared with some informal publications, textbooks do not have advantages in students' choices. For example, students prefer to use handouts or notes collated by themselves rather than textbooks. The reason is that both of the first two can provide students with all kinds of help needed for mathematics learning from the perspective of meeting students' personalized needs. On the other hand, the help provided by the compilation of textbooks is relatively weak. Professor Rezat's research also reveals that even when faced with the same set of textbooks, there are huge differences between different students' modes of using textbooks and their favorite modules. Therefore, as a resource that every student can own, the question of how to make textbooks play a more important role in the resource system of various students has become an important topic in the field of textbook research.

From the perspective of text-reading ability, another core point of view put forward by Professor Rezat was to fully realize the important role of students' text-reading ability in the use of mathematics textbooks. Researchers need to pay attention to the possible preferences and difficulties faced by students in close reading mathematics textbooks, as well as how to provide support for them. Studies have shown that students from different countries often have common problems when reading their own mathematics textbooks, that is, it is difficult to understand formal mathematical languages and symbols. In the use of most mathematics textbooks, students need the help of teachers to understand the meaning of a lesson, which greatly suppresses the individual's ability to acquire knowledge through reading.

In terms of the research perspective of data collection methods, Professor Rezat mainly presented a number of existing studies, and said that the current mathematics textbook research has not entered the scene of students' actual use of textbooks, so they can not understand the way students use textbooks and the difficulties they face. This is because, in the data collection part of the existing academic research, researchers are more likely to use interviews and surveys, rather than recording their use behavior in the process of students' actual use of textbooks. In order to solve this problem, some researchers have begun to use digital collaboration tools to analyze students' tagging methods and styles in the process of using textbooks. Some researchers also explore the use mode of students' textbooks by analyzing the log files used in students' textbooks, and paying attention to the learning contents that students think are important or difficult in the process of analysis, to further improve the effect of the use of students' textbooks and provide a data basis for the compilation and revision of textbooks. He later pointed out that the development of electronic textbooks is not only to move paper textbooks to the network, but also to consider how to make full use of a series of advantages brought about by the digitization and digitization of textbooks. The advantage of process data analysis is one of the most prominent. In the discussion session, scholars also raised their own questions about students' reading ability, the negative impact of digital materials and whether online videos related to mathematics are part of curriculum resources. Professor Rezat provided his own opinions on the questions based on existing research. To solve a problem, he believed that reading does not necessarily mean reading aloud but trying to understand the text given. In response to the second question, he pointed out that at the present stage, students can consult a lot of relevant knowledge about mathematics on the Internet, and the convenience of the Internet has both advantages and disadvantages, and the advantage being that it can enrich the content of teaching materials, and the disadvantage is that students are less motivated to consult textbooks, or are even unwilling to read them. Finally, Professor Rezat suggested that it would be a very interesting project for the future to reveal the relationship between students’ learning of mathematics at school and their preferences for textbooks.

Listen To The Voices Of Young Scholars

The Youth Academic Forum was not only a favorable carrier to promote the development and innovation of excellent Chinese traditional culture, but also a good platform for young scholars to show their academic charm. With ICMT-4 as the background, the forum aimed to gather outstanding scholars and front-line educators at home and abroad to discuss mathematics teaching materials, so as to contribute to young people to enrich the connotation of teaching materials. The forum was divided into four sections: background introduction of the conference, self-introduction of young scholars, ice-breaking games and brainstorming, hosted by Liu Qimeng, an assistant researcher at the China Institute of Educational Innovation at Beijing Normal University. First of all, by introducing the origin and development of the conference, Mr. Liu Qimeng enabled young scholars a deeper understanding of the International Conference on the Research and Development of Mathematics textbooks (ICMT). He pointed out that the significance of this youth academic forum was not only to explore the problems and exchange views in the development of mathematics textbooks at the present stage, but also to provide an opportunity for all young scholars to interact with each other cooperate in future research, contributing to the construction of mathematics textbooks for the younger generation. Secondly, many outstanding young scholars, such as Dong Lianchun, lecturer of the School of Science of the Minzu University of China, teacher Xie Zhiyong from South China Normal University, Dr. Yan Jiajie from Beijing Normal University, Dr. Li Kunli from East China Normal University, and so on, introduced themselves and gave a brief overview of their research interest on teaching materials. In order to break the tense atmosphere of the meeting, the forum opened an ice-breaking game with "mathematics textbook puzzles". Firstly, teacher Liu Qimeng put forward some nouns in mathematics textbooks, such as “equivalent variants”, “false scores”, and so on. Then, two different young scholars were asked to describe puzzles. Such an "ice-breaking" approach will not only help highlight the purpose of this session, but also narrow the gap between young scholars. In such a relaxed and interesting atmosphere, the forum ushered in the fourth session-brainstorming, which consisted of seven topics.

Listen To The Voices Of Young Scholars

The Youth Academic Forum was not only a favorable carrier to promote the development and innovation of excellent Chinese traditional culture, but also a good platform for young scholars to show their academic charm. With ICMT-4 as the background, the forum aimed to gather outstanding scholars and front-line educators at home and abroad to discuss mathematics teaching materials, so as to contribute to young people to enrich the connotation of teaching materials. The forum was divided into four sections: background introduction of the conference, self-introduction of young scholars, ice-breaking games and brainstorming, hosted by Liu Qimeng, an assistant researcher at the China Institute of Educational Innovation at Beijing Normal University. First of all, by introducing the origin and development of the conference, Mr. Liu Qimeng enabled young scholars a deeper understanding of the International Conference on the Research and Development of Mathematics textbooks (ICMT). He pointed out that the significance of this youth academic forum was not only to explore the problems and exchange views in the development of mathematics textbooks at the present stage, but also to provide an opportunity for all young scholars to interact with each other cooperate in future research, contributing to the construction of mathematics textbooks for the younger generation. Secondly, many outstanding young scholars, such as Dong Lianchun, lecturer of the School of Science of the Minzu University of China, teacher Xie Zhiyong from South China Normal University, Dr. Yan Jiajie from Beijing Normal University, Dr. Li Kunli from East China Normal University, and so on, introduced themselves and gave a brief overview of their research interest on teaching materials. In order to break the tense atmosphere of the meeting, the forum opened an ice-breaking game with "mathematics textbook puzzles". Firstly, teacher Liu Qimeng put forward some nouns in mathematics textbooks, such as “equivalent variants”, “false scores”, and so on. Then, two different young scholars were asked to describe puzzles. Such an "ice-breaking" approach will not only help highlight the purpose of this session, but also narrow the gap between young scholars. In such a relaxed and interesting atmosphere, the forum ushered in the fourth session-brainstorming, which consisted of seven topics.

Teacher Zhang Bin, a mathematics teacher and researcher from Gansu Educational Science Research Institute, first made a speech. She put forward her own ideas on how the next generation of mathematics textbooks reflect "core literacy". She stated that, although that the curriculum standards of compulsory education have advocated the use of project-based learning in synthesis and practice, most junior middle school mathematics teachers are still very confused about how to carry out project-based learning. Therefore, the compilation of teaching materials should also reflect the instructions on how to carry out project-based learning in junior middle school. Then Dong Lianchun also shared his view on the current situation of junior high school teachers' understanding of project-based learning. He pointed out that many teachers still consider that project-based learning can be completed in one class. As teachers tend to structure their classes according to the content of teaching materials, the compilation of teaching materials should take on the role of changing teachers' stereotypes of project-based learning. Teacher Liu Qimeng commented on this topic by saying that mathematics textbook is a kind of teaching material for students and that it is an important part of the mathematics teaching resource system. In the case of academic work, for example, the thoroughness of the literature review determines the height of our research to a large extent. Extending to the process of learning mathematics, the degree of students' mastery of materials is also an important factor in their success in learning. This may be an important reason why the paper version of mathematics textbooks are more popular than the electronic ones, and exploring the role of teaching materials for students needs to be discussed in its essence. Du Jiannan, a doctoral student at Beijing Normal University, also pointed out that the relationship between the next generation of mathematics textbooks and curriculum reform should be oriented towards "educating people" and "mathematical culture" as the starting point, so that teaching materials can give full play to the function of spreading culture, and truly implementing "establishing morality and cultivating people." Scholars then had an in-depth discussion on the topics such as the presentation of the next generation of mathematics textbooks and how to reflect the "integration of learning, teaching and evaluation".

Browse Parallel Session

Parallel Session 5：

Parallel Session 5 was composed of five studies from Hangzhou Normal University, Wenzhou University, Fujian Normal University, Northeast Normal University, Northwest Normal University, Guancheng Wulin Middle School. They made reports on topics such as international comparison of textbooks, sense of measurement, statistical models, probability exercises, and so on.

Sun Xinghua's team from Northeast Normal University made a report entitled "A Comparative Analysis of the Time Content in Textbooks from Eight Countries". Their research conducted a cross-country comparative analysis of primary school mathematics textbooks from eight countries including China, Japan, South Korea, Singapore, France, Germany, Russia and the United States based on the content of "time". The research used the content analysis method to focus on three aspects: the cognitive development of children's time concept, the content of time concept, and the core content in national curriculum standards and textbooks. They found that these textbooks, in terms of their structure and grade distribution, had both similarities and differences. In the follow-up discussion session, Chinese and foreign participants discussed topics such as the textbook revision related to the "sense of measurement".

The title of the report by Xie Qinnan from Wenzhou University and Zhang Qinqiong from Fujian Normal University was "An Empirical Study on Fifth Grade Students Using Statistical Model to Solve Practical Problems". This study was based on New Century Mathematics (NCM), one of the mainstream textbooks in China. Taking the unit "Fallen Leaves on Campus" in the field of synthesis and practical teaching in Grade 5 as an example, by means of the method of personal interview, it was found that students would utilize descriptive models and inferential models when solving the tasks of "calculating the area of a fallen leaf" and "counting the number of leaves of a tree". And it was also found that students have a shortage in awareness of selecting representative data and difficulties in solving the problem. Finally, they put forward two suggestions for the compilation of mathematics textbooks: to increase the activities and opportunities for students to choose appropriate data; and to consider whether students could complete the tasks in the textbook. During the discussion session, the participants discussed topics such as the level division of students' statistical thinking and the differences across student backgrounds.

Parallel Session6：

Parallel Session6 consisted of 6 studies by teams from Coastal Carolina University, Achva Academic College, Beijing Normal University, Capital Normal University and Liaoning Normal University. They presented topics such as content analysis of mathematics textbooks, international comparison of mathematics textbooks, research on teaching resources, and construction of teaching models.

Deepak Basyal from Coastal Carolina University, USA, gave a presentation on “Investigating The Features of Nepali 8th Grade Mathematics Textbook”. In developing countries like Nepal, many teachers use mathematics textbooks as the primary (and in most cases the only) curriculum resource. Therefore, it is important to have rich mathematical tasks in textbooks to improve teaching and learning. This study attempted to investigate the types of tasks found in grade 8 mathematics textbooks in Nepal. Based on existing literature and theory, the study constructed an analytical framework with four dimensions: representational style (symbolic, visual, verbal, and combined), cognitive level (memorization, procedures without connections, procedures with connections, doing mathematics), context (context-embedded, non-contextual), and problem type (open-ended, closed-ended). The results showed that most of the tasks were of low cognitive level and there were no high level "doing mathematics" tasks; most of the tasks were given in a symbolic form and there were few pictorial representations; 87% of the tasks were not related to real life; and only 8 of the 1359 tasks were open-ended. This also showed that there is an imbalance in the different features represented in the rich mathematical tasks in the Grade 8 mathematics textbooks in Nepal. In the discussion that followed, participants had an in-depth exchange on the coding of textbooks, textbook editions, structure, and the characteristics of tasks in different content areas of textbooks.

Elena Naftalie from Achva Academic College, Israel, presented on "Experimental Mathematics and Interactive Resources at Schools: Leading Teachers Towards A Change". The study focused on how mathematics teachers transform from learners to reflective teachers in a technological environment. In particular, the design and use of interactive resources were discussed, and the case types, presentation modes and organization of interactive resources were carefully delineated. The presentation was followed by a variety of questions from scholars from all over the world. For example, considering that teachers prefer to use the blackboard for teaching, how to make teachers be better receptive to technological tools in their research? In response to that question, Elena Naftalie described how teachers can be guided step by step through training activities to understand and use technology. Another question was how should teachers achieve a shift in roles from teacher to learner in response to the motivation of the online teaching environment in the last two years? Elena Naftalie noted that technology is challenging new knowledge for teachers, and their research team tried to help teachers achieve a shift in roles through multiple cycles of coaching.

Watch The Poster Exhibition

In addition to exchanges and reports, the conference also exhibited seven groups of posters from different universities and publishers, including mathematics education researchers from China, South Korea, Norway and other countries. The themes of the posters were "discussing the present situation and improvement of Information Technology Integration in Junior Middle School Mathematics textbooks from the Perspective of Deep Learning", "exploring the present situation and improvement of the Integration of Information Technology into Junior Middle School Mathematics textbooks from the Perspective of Deep Learning", "Mathematics Reading and Writing Teaching suggestions in Senior High School Mathematics textbooks", "structural Analysis of Mathematics textbooks in Junior Middle Schools in China", "Research on the characteristics of compiling Mathematics textbooks in Primary Schools in Germany", "Measurement tasks in (Norway) Local Children's textbooks", "Comparative Analysis of addition and subtraction in Mathematics textbooks in Korea and Singapore" and "trend changes in Analytical methods in Mathematics textbooks".

On the 3rd day of ICMT-4, the conference will bring participants 2 plenaries, 2 special seminars and 12 oral reports, etc. We will continue to record the exciting moments of the day, and welcome your attention. For the conference program, please check the conference website: https://icmt4.org.cn/ or contact the conference secretariat at icmt4@bnu.edu.cn

The First Day Review of ICMT-4

The 4th International Conference on Mathematical Textbooks Research and Development, representing the highest level, the most influential and the most widely participated in the field of international mathematical textbook research, opened on November 14, 2022, in Beijing Normal University. The conference was held online and offline at the same time, linking the main venue with six sub-venues.。

The conference will last for four days. Starting from today, please follow our lens to "walk" into ICMT-4 and feel the wonderful moments of ICMT-4.

Focus On The Opening Of ICMT-4

At the opening ceremony starting at 1:30pm, Frederick Leung, President of the International Commission of Mathematical Instruction, Gu Mingyuan, Honorary President of the Chinese Society of Education, Tian Gang, President of the Chinese Mathematical Society, Shen Jiliang, First level Inspector of the Textbook Bureau of the Ministry of Education, China, Zhou Zuoyu, Vice President of Beijing Normal University, and Zhu Xudong, Dean of Faculty of Education of Beijing Normal University addressed the opening ceremony respectively. The Conference was chaired by Professor Qi Chunxia, Chair of the conference’s International Programme Committee. According to statistics, there were more than 4,000 online participants.。

Frederick Leung pointed out that mathematics textbooks have been playing a key role in mathematics learning, and the reform of textbooks needs to be paid more attention. Gu Mingyuan believes that Mathematics is closely related to people's daily life and is not as difficult as people imagine, where the key is textbook compiling for primary and secondary schools. Tian Gang highlighted that mathematics is the basis of science and technology. Mathematics education is one of the core aspects of basic education, in which textbooks could to a degree decide the methods that teachers design curriculum and organize class, and guide students' understanding, thinking and feeling. Shen Jiliang said that Chinese textbooks construction should adhere to the guidance of core quality, encourage the diversification, promote the specialization of the development team, and explore the digitalization of teaching resources more in-depth in the future. Zhou Zuoyu said in his speech that under the global circumstances, mathematicians and mathematics educators from different countries and regions should keep close contact, think globally and act locally, work hard to strengthen international cooperation and promote the construction of high-quality teaching materials system. Zhu Xudong called for building a localized knowledge system, academic system and discourse system of mathematics education, which could constantly promote the international development of mathematics education.

Listen To The Plenary

The conference invited Professor Shi Ningzhong, a famous Chinese statistician and mathematics educator. The title of this conference presentation by Professor Shi is “A review and the development of Chinese elementary school mathematics textbooks”.

1. Through the review of the 100-year history of Chinese mathematics curriculum and teaching materials, it can be seen that Chinese mathematics education began in 1867 (the sixth year of Tongzhi's reign) with the establishment of the School of Arithmetic in the Tongwen Hall in Beijing; from the promulgation of “The Constitution of the Elementary School” in 1904 to the “Compulsory Education Mathematics Curriculum Standards (2011 Edition)”, a total of 20 curriculum standards were issued (including charters and syllabus); formal elementary school mathematics textbooks, which began with The Mathematics of Penmanship, edited by Dickowen and Zou Liwen and published by the American and Chinese Printing House in 1875, have been published in more than 200 sets since then.

2. Since the new century, the Chinese mathematics curriculum has undergone a process from the Double Basics (basic knowledge and skills) to the Four Basics (basic knowledge, skills, ideas, and activities experiences) and from the Four Basics to Core Literacy, and it emphasizes on that students should not only acquire knowledge and skills, but also increase their ability to observe the real world with mathematical insight, think about the real world with mathematical thinking, and express the real world with mathematical language.

3. Traditional mathematics teaching materials guide students to know integers, fractions, and decimals with the help of the authentic background, and guide students to master the calculation methods of integers, fractions, and decimals through practical meaning. This kind of mathematics teaching material is not conducive to students’ understanding of the essence of mathematics and the formation and development of their mathematical literacy. Therefore, the concept of “counting units” is introduced as an instrumentality to effectively solve the above problems in the “Compulsory Education Mathematics Curriculum Standards (2022 Edition)”, hoping that teaching materials will achieve the consistency of the cognition and operations of numbers in the future, that is a process of mathematization.

Finally, the moderator, Professor Liu Jian, suggested that top-down curriculum design based on the nature of mathematics is very important and can give important insights to mathematics teachers; at the same time, the majority of mathematics educators are called upon to carry out bottom-up empirical research based on classroom and child observation, especially at the primary level.

Exploration Workshop

The workshop focused on the quality monitoring and evaluation of mathematics textbooks in basic education, composed of six scholars from Central South University for Nationalities and Hubei Ethnic Education Research Center, including four reports, which are respectively named as "Research on the Quality Monitoring and Evaluation Index of Mathematics Textbooks in Basic Education", "A Comparative Study of the U.S. Evaluation Criteria for Quality Instructional Materials Tool-- Grades 1-5 as an Example", "Evolution and Prospect of the Textbook Policy for Elementary Education of China in the Past Seven Decades” and "A Comparative U.S.-China study of Quality Criteria for Junior High School Mathematics Instructional Materials”. These four reports discussed respectively about the characteristics of the evaluation standards for teaching materials in major countries in the world, the generation, framework, content and process of the evaluation standards for teaching materials in the United States, the similarities and differences between the evaluation standards for teaching materials in China and the United States in terms of evaluation basis, content and procedure, and studied the evolution of 81 textbooks policy texts in China from 1949 to 2021 from the perspectives of authority, integrity and pertinence. The host, Mr. Zhou Da, had an in-depth exchange with the reporters on the course and future development direction of mathematics textbook reform, and the importance of comparison between Chinese and American textbooks.

Browse Parallel Session

Parallel Session1：

Parallel Session2 includes 6 studies. Several researchers from Ateneo de Manila University, Wayne State University, Capital Normal University, Northeast Normal University and Tianjin Normal University were made on topics such as mathematical textbook content and language, mathematical textbook policy, mathematical textbook use, Comparison of mathematics textbook.

One team of researchers from Wayne State University conducted a study on the effects of curriculum pacing polices on teachers' decision-making in instruction. This study investigates the effects of a curriculum pacing regime on teachers’ decision-making in elementary mathematics classrooms. The school district had adopted new textbooks in mathematics for all grades three years prior to the conduct of this study, including pacing directives. Teachers in a large urban school district in the United States were interviewed to understand how they make decisions about what is taught each day, and how teachers perceive pacing guides and other directives related to curriculum use. The study includes document analysis of district pacing guidelines and directives; signs, symbols, and communiques used to convey and enforce pacing guidelines; language of school district leaders about the function of curriculum pacing; and the written messages in professional development materials offered by textbook publishers related to pacing. Preliminary analysis indicates that teachers consider multiple factors in deciding what to teach when, even when the school district policy directs teachers to base such decisions on the pacing guide alone.

Parallel Session2：

Parallel Session2 includes 6 studies. Six researchers from Western Michigan University, Northwest Normal University, Northeast Normal University, East China Normal University, Beijing Normal University and Jianan Primary School were made on topics such as Japanese textbook comparison, mathematics culture, higher-order thinking skills, and difficulty comparison of textbook exercises.

The Jane-Jane Lo team from Western Michigan University in the United States made a report entitled "Using a Narrative Framework to Analyze Textbooks the Affordances and Challenges". They used the narrative framework developed by Dietiker to analyze and compare Chinese and American mathematics textbooks from four mathematical story elements: characters, actions, settings, and plots. They found that this story framework makes the image of elephant more complete, and can be strengthened by giving the mathematical conceptions underlying the central ideas of the mathematical story a more prominent role. Also, this framework can be used for cross-culture textbook analyses of other important mathematical ideas. In the follow-up discussion session, Jane-Jane Lo explained to the participants' questions that they tried to give an elephant map for the textbook, and used such an innovative framework to do original analysis. Guihua Huang 's team from Beijing Normal University in China made a report entitled " Analysis of Higher-Order Thinking Skills (HOTS) content in Chinese high school mathematics textbook". In response, Huang 's team emphasized that the key to teachers' cultivation of students' HOTS lies in understanding the textbook and HOTS. After that, Professor Chunxia Qi said that the above issues are of great value, but they are relatively open and macroscopic and need to be further explored continuously.

Parallel Session3：

Parallel Session3 is composed of 4 studies from teams from The Education University of Hong Kong, Northwest Normal University, and East China Normal University. The topics such as the comparison of statistics and probability between China and the UK were shared.

Among them, Xiaoyu Xu from the Education University of Hong Kong shared on "A Comparative Analysis of the Linear Equation Unit in Secondary Mathematics Textbooks in Chinese-English Bilingual School ". This study presents a comparative study aiming to examine how linear equation unit is arranged in secondary school mathematics textbooks (i.e., IB, IGCSE, and Chinese textbooks) in Chinese-English bilingual schools. Four aspects of linear equations in different textbooks are compared: the number of examples, the distribution of contents, the learning activities, chapter review exercises. Her research found that The textbooks in China contain the highest percentage of linear equation contents and pay the most attention to explaining and analyzing how to set the unknown variable and using the concept of the linear equation to solve real-life problems. In the follow-up discussion session, Xiaoyu Xu responded to the participants’ questions about the differences between Chinese and American mathematics textbooks, emphasizing that China and the United States have different cultural and educational backgrounds, different textbooks, and different understandings of logical thinking. American mathematics textbooks may be relatively simpler，and children prefer to discuss in mathematics classes.

Lianghuo Fan's team from East China Normal University reported on "Investigating Teachers Interactions with Textbooks: Findings from Secondary Mathematics Teachers in Shanghai, China". Their study focused on the degree and difference of interaction between mathematics teachers and textbooks. Participants discussed questions such as “Do different ages of teachers interact with textbooks differently? ” and “How teachers use textbooks to make adaptations for formative assessment ?”.

Parallel Session4：

Parallel Session4 includes six studies, six scholars from University of New Hampshire, Cornell University, Syracuse University, Hangzhou normal University and Freudenthal Institute reported on the topics such as the comparison of the content of teaching materials, the arrangement of teaching materials and the learning path of teaching materials.

Mary Ann Huntley from Cornell University analyzed algebra in six American high school mathematics textbooks to explore students' opportunities to learn algebra. The study points out that there are great differences in algebra learning opportunities in different versions of textbooks, which largely depends on the textbook writers' views on algebra. This study uses the curriculum survey (SEC) K-12 mathematical classification to encode the algebra content in six mathematics textbooks, and encodes students' cognitive behavior based on three types of cognitive processes (knowledge, application and reasoning). It is concluded that although the textbook provides specific teaching cases through teachers and students using relevant tools to solve practical problems, the textbook also provides learning opportunities for students, and this study enriches the value of the textbook. In the later discussion session, Professor Fan Lianghuo raised the question of the selection criteria for the research object, that is, the scope of use of textbooks in the United States, which is also the first issue to be clarified when carrying out textbook research. As the education policies of different countries are different, it is necessary to consider the differences of different regions when selecting teaching materials. Finally, the host Cao Chen said that the current research on teaching materials also began to pay attention to students in learning specific mathematical content, teaching materials how to better develop students' ability in different mathematical content, which is worthy of further research.

On the 2nd day of ICMT-4, the conference will bring participants 1 plenary, 12 oral reports, and the Young Scholars Forum, etc. We will continue to record the exciting moments of the day, welcome your attention. For the conference program, please check the conference website: https://icmt4.org.cn/ or contact the conference secretariat at icmt4@bnu.edu.cn

The 4th International Conference on Mathematics Textbook Research and Development Opens in Beijing

The strength of mathematics determines the development level of modern science and technology as well as the future of the society． Since mathematics education has been an important part of modern school education， and mathematics textbooks have almost become the most important learning materials for everyone＇s mathematical literacy and the main vehicle for mastering mathematics， the quality of mathematics textbooks is recognized to be of great significance for the change and development of mathematics education． In recent years， the research on mathematics textbooks has received increasing attention in the international mathematics education community． Understanding textbooks and their development， and understanding how textbooks are used to facilitate teachers＇ professional work， to support students＇ learning， and to promote and influence curriculum reform have become important fields of mathematics textbook research internationally． The 4th International Conference on Mathematical Textbooks Research and Development， representing the highest level， the most influential and the most widely participated in the field of international mathematical textbook research， opened on November 14， 2022， in Beijing Normal University．

Guests gather to send a common message on the high－quality development of mathematics textbooks

At the opening ceremony starting at 1：30pm， Frederick Leung， President of the International Commission of Mathematical Instruction， Gu Mingyuan， Honorary President of the Chinese Society of Education， Tian Gang， President of the Chinese Mathematical Society， Shen Jiliang， First level Inspector of the Textbook Bureau of the Ministry of Education， China， Zhou Zuoyu， Vice President of Beijing Normal University， and Zhu Xudong， Dean of Faculty of Education of Beijing Normal University addressed the opening ceremony respectively． The Conference was chaired by Professor Qi Chunxia， Chair of the conference’s International Programme Committee， and the opening ceremony was held in a combination of online and offline， with more than 4，000 participants online．

Frederick Leung pointed out that mathematics textbooks have been playing a key role in mathematics learning， and the reform of textbooks needs to be paid more attention． In addition to providing opportunities for mathematical researchers to participate in exchanges， the conference also provided a platform for extensive discussion of mathematics textbooks． Gu Mingyuan believes that excellent textbooks do not teach students rote knowledge， but teach students the basic concepts and logical thinking of mathematics． Mathematics is closely related to people＇s daily life and is not as difficult as people imagine， where the key is textbook compiling for primary and secondary schools． Tian Gang highlighted that mathematics is the basis of science and technology． In mathematics education， textbooks could to a degree decide the methods that teachers design curriculum and organize class， and guide students＇ understanding， thinking and feeling． That’s why the importance of textbooks in mathematics education has been widely recognized internationally． Shen Jiliang said that China＇s mathematics education has its own advantages． Through the efforts of more than 20 years since the 21st century， Chinese mathematics textbooks has formed a featured system that can reflect Chinese characteristics and the structure of ＂one standard with multiple copies＂． In the future， Chinese textbooks construction should adhere to the guidance of core quality， encourage the diversification， promote the specialization of the development team， and explore the digitalization of teaching resources more in－depth． Zhou Zuoyu said in his speech that Beijing Normal University has made important contributions to the reform and development of mathematics curriculum and textbooks in China． Under the global circumstances， mathematicians and mathematics educators from different countries and regions should keep close contact， think globally and act locally， work hard to strengthen international cooperation and promote the construction of high－quality teaching materials system． Zhu Xudong called for building a localized knowledge system， academic system and discourse system of mathematics education， which could constantly promote the international development of mathematics education， as well as high－level research products of mathematical education．

Information Disclosure on the Preparations and Main Agenda of the International Conference

The conference’s International Programme Committee consists of 20 experts from more than a dozen of countries， including current and past president of the International Commission of Mathematical Instruction， Freudenthal Prize awardees and other world renowned scholars in mathematics education． Professor Qi Chunxia， Deputy Director of the Institute of Curriculum and Teaching of Beijing Normal University， served as Chair of the International Procedures Committee， and Professor Fan Lianghuo， Director of Asian Center for Mathematics Education of East China Normal University， served as Co－chair of the IPC．

The Local Organization Committee of the conference was composed of 22 experts and scholars from 17 Chinese universities and scientific research institutions， including a few from Hong Kong， Macao and Taiwan， who are important representatives in the field of mathematics teaching materials research in China． Professor Liu Jian， Director of the China Institute of Education Innovation， Beijing Normal University， served as Chair of the Local Organization Committee， and Professor Zhang Chunli and Cao Yiming served as cochairmen．

Because of the covid－19 pandemic， the conference was held online and offline at the same time， linking the main venue with six sub－venues． In addition to the main venue at Beijing Normal University， Asian Centre for Mathematics Education of East China Normal University， Northeast Normal University， Southwest University， Central China Normal University， Tianjin Normal University， Zhejiang Normal University and Zhuhai Campus of Beijing Normal University have set up sub－venues respectively．

The conference was held in Asia for the first time since its launch． Nearly 200 mathematics educators from more than 20 countries， including China， the United States， the United Kingdom， Japan， South Korea， Germany， Brazil， Israel， the Netherlands， Norway， New Zealand， Indonesia， and the Philippines etc．， submitted 113 papers， with nearly 400 officially registered representatives． The opening and closing ceremonies are broadcast worldwide， and the plenaries would be watched in the main venue and the six sub－venues at the same time． The joint efforts of scholars from all over the world would certainly exchange and share of the theoretical achievements and practical wisdom of international mathematics textbook research at the conference．

The conference lasts for 4 days， during which there are 5 plenaries， 4 symposiums， 1 workshop， 68 oral reports and 7 Poster ＆ Sponsor Exhibition． Professor Shi Ningzhong of Northeast Normal University in China， Professor Jane Remillard of the University of Pennsylvania in the United States， Professor Sebastian Rezat of Paderborn University in Germany， Professor Gert Schubring of the Federal University of Rio de Janeiro in Brazil and Professor JeongSuk Pang of the Korean University of Education were invited to make reports on the conference． On the basis of setting up oral report topics such as mathematical textbook development， mathematical textbook content and language， mathematical textbook use and student achievement， historical research on mathematical textbooks， comparative research on mathematical textbooks， mathematical textbook policy， other disciplines and mathematical textbooks， the Congress would pay more attention to the relationship between curriculum reform and textbook development， and the meta－research of mathematical textbooks for the first time． At the same time， the challenges faced by mathematics textbooks in the context of the epidemic situation would also be discussed．

Exploring the Origin of the International Conference on Mathematics Textbook Research and Development

In 2014， a team led by Professor Fan Lianghuo， Chair in Education and Director of the Research Center for Mathematics and Science Education at the University of Southampton， and Professor Geoffrey Howson， former Secretary General of the International Commission on Mathematical Instruction and former Chair in Mathematics Curriculum Studies at the University of Southampton， jointly planned and organized the first International Conference on Mathematics Textbook Research and Development （ICMT）， which is then held every two or three years in different regions of the world． After eight years of development， the conference has become the most important and comprehensive academic conference in the field of international mathematics textbook research， focusing on many important research fields of mathematics textbook research， and it also had had a positive impact on the research and development of textbooks in other disciplines． Following the success of the ICMT－1 in Southampton， UK， ICMT－2 was held in Rio de Janeiro， Brazil in 2017， and ICMT－3 in Paderborn， Germany in 2019， and this conference， ICMT－4， now， in Beijing， China． The conference will also provide a stage for Chinese mathematics educators to show the development of Chinese mathematics textbooks and the latest academic research achievements of mathematics textbooks to the world．

It is understood that the 5th International Conference on Mathematics Textbook Research and Development， ICMT－5， will be held in Norway． At the closing ceremony of this conference， Professor Birgit Pepin， Chair of the International Program Committee of ICMT－5， who is Director of the Engineering Education Research Center of Eindhoven University of Technology， Netherlands， will introduce the next conference to the participants．

For more information about the conference， one may visit the conference website： https://icmt4.org.cn/ or contact the conference secretariat at icmt4＠bnu.edu.cn．

edu.china.com.cn report

The 4th International Conference on Mathematics Textbook Research and Development to Open November 14

Textbooks are an important educational resource for students， teachers and schools， playing an important role in the development of mathematics curriculum and in improving the quality of mathematics teaching and learning． In recent years， there has been an increased international interest in textbook research and development． Understanding how textbooks and their development are integrated into the professional work of teachers， how they promote and influence curriculum reform and how they support student learning， have become important directions in the field of textbook research．

The inaugural International Conference on Mathematics Textbook Research and Development， now called ICMT－1， was initiated and held at the University of Southampton， UK， by a team lead by Professor Fan Lianghuo， Chair in Education and Director of the Centre for Research in Mathematics and Science Education and Professor Geoffrey Howson， former Secretary General of the International Commission on Mathematical Education and Chair in Mathematics Curriculum Studies at the University of Southampton． Since then， the ICMT conference has been widely regarded as the most important and comprehensive international conference in the field of mathematics textbook research， with focus on many important areas in mathematics textbook research， and the conference series has had a positive impact on the research and development of textbooks in other subject areas as well． Following the success of ICMT－1 in the UK， ICMT－2 was held in Brazil， and ICMT－4 in Germany． Now the Fourth International Conference on Mathematics Textbook Research and Development， or ICMT－4， hosted by Beijing Normal University， will be held on November 14， 2022．

In addition to the main conference venue at Beijing Normal University， the Asian Center for Mathematics Education of East China Normal University， Northeast Normal University， School of Mathematics and Statistics of Central China Normal University， Department of Education of Tianjin Normal University， Southwest University， and School of Teacher Education of Zhejiang Normal University will set up online venues， and a number of heavyweight guests will deliver speeches at the opening ceremony．

ICMT－4 is the first time that the International Conference on Mathematics Textbook Research and Development is held in Asia since its inception． Nearly 400 mathematics educators and teachers from Asia， Europe， South America， North America， and Oceania would gather to share their academic achievements and practical experiences in textbook research．

It is understood that the conference program will include five plenary speeches to be delivered by Professor JeongSuk Pang （Korea National University of Education， Korea）， Professor Janine Remillard （University of Pennsylvania， USA）， Professor Sebastian Rezat （Paderborn University， Germany）， Professor Gert Schubring （Federal University of Rio de Janeiro， Brazil）， and Professor Shi Ningzhong （Northeast Normal University， China）． In addition to the themes of mathematics textbook development， mathematics textbook content and language， mathematics textbook use and student achievement， historical studies of mathematics textbooks， comparative studies of mathematics textbooks， mathematics textbook policy， and other disciplines and mathematics textbooks， the conference will， for the first time， cover the issues about the relationship between curriculum reform and textbook development， meta－studies of mathematics textbook research， and the challenges that mathematics textbooks face and their roles in the context of the current covid－19 epidemic．

The 4th International Conference on Mathematics Textbook Research and Development will also provide an international platform for Chinese mathematics educators to present the evolution of the development of Chinese mathematics textbooks and the latest academic research results of mathematics textbooks to the world． For more information about the conference， one may visit the conference website： https://icmt4.org.cn/ or contact the conference secretariat at icmt4＠bnu.edu.cn．

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Announcement on Postponement of ICMT-4

the first announcement for ICMT4