Lianghuo Fan

• Doctor of Philosophy
• Distinguished Professor at East China Normal University; Emeritus Professor at University of Southampton，UK

We conducted a study on how Shanghai secondary mathematics teachers interact with textbooks. A conceptual framework was established for the study. Data were collected from 133 teachers in 13 randomly selected schools through a questionnaire survey and follow-up interviews with 24 of them. Results show that Shanghai mathematics teachers interacted w...

This paper presents a systematic survey of research on digital mathematics textbooks (DMTs), with a particular focus on the design and development of DMTs. A total of 65 studies on DMTs were identified and collected from different data sources including journal articles, dissertations and theses, conference proceedings and research reports over the...

Textbooks, as potentially implemented curricula, play an important role in supporting classroom teaching and learning. Mathematical connections, one of the essential and hot topics advocated in mathematics education, have been emphasized in national curriculum reforms in various countries. However, little is known about the connection networks repr...

Facilitators, i.e., individuals who lead professional development (PD) programs, play a crucial role in providing high-quality PD to teachers, which is particularly relevant in the context of teaching mathematics with technology given the ubiquitous calls to exploit the potential of digital mathematical tools (DMT). However, quantitative research i...

Professional development (PD) for mathematics teachers in China, especially in Shanghai, has received growing international attention. However, most of available research concerning Chinese PD has focused on successful practices, and far too little attention has been paid to less successfully organized PD practices, particularly for mathematics tea...

L.Fan@southampton.ac.uk Taking a broad perspective on algorithm in mathematics, the author presents a theoretical model about the learning and teaching of algorithm with focus on students' cognitive development. The model consists of three cognitive levels: 1. Knowledge and Skills, 2. Understanding and Comprehension, and 3. Evaluation and Construct...

Macao, a Special Administration Region of China (Macao SAR), is unique in that its mathematics education practice and research have integrated both the eastern and western traditions. Its participation in the Programme for International Student Assessment (PISA) since 2003 inspired the research culture in mathematics education in Macao from interna...

Textbooks, as potentially implemented curriculum, play an important role in school education. Earlier studies in mathematics education revealed that teaching using mathematics games had a positive effect on students’ learning. However, how mathematics games are presented in mathematics textbooks has rarely been systematically examined. In this stud...

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Due to rapid social and economic development in China over the last three decades, information and communication technologies (ICTs) have become increasingly available in Chinese classrooms and families. However, there is a lack of research regarding Chinese students' use of ICTs in mathematics learning. In this study, we examined how Chinese stude...

Studying the sources of teachers' knowledge and the importance of different sources is of great significance to promote the development of teachers' knowledge. This paper systematically analyzes 27 empirical studies on the sources of teachers’ knowledge in China and abroad in the past two decades or so in terms of methods and findings. The results...

In this survey paper we aim to provide an overview of research on mathematics textbooks and, more broadly, curriculum resources as instruments for change related to mathematical content, instructional goals and practices, and student learning of mathematics. In particular, we elaborate on the following themes: (1) The role of curriculum resources a...

In this paper we report on a survey study of teachers' perceptions of how mathematics textbooks, including broadly student books, teacher manuals, and exercise books, facilitate or hinder teachers' teaching in Shanghai educational settings. For the study we established a conceptual framework about teachers' teaching, partly drawing on Shulman's mod...

This article reports an empirical study aiming to investigate students’ use of mathematics textbooks in Shanghai and England, with a comparative perspective. The study used mixed methods to collect the data through student questionnaire, student focus group interview and classroom observation. 161 Shanghai seventh- and eighth-grade students and 206...

p>The Indonesian secondary school mathematics curriculum advocates the use of technology in teaching and learning of mathematics. The previous studies paid less attention to what type of digital tools that the teachers used and how they integrated them in the mathematics teaching. This study aimed at investigating Indonesian secondary school mathem...

Curricula in different places of the world are consistently undergoing changes and reforms to meet the capacity needed for citizenship of the 21st Century. Applying the idea of HFE to Curriculum Ergonomics, design of interventions in curriculum should with best efforts aim to fit the users (teachers and students) for creating an optimal enhanced le...

The paper departs from research published in an earlier thematic issue published by ZDM Mathematics Education in 2013 on mathematics textbook research and development by presenting a review of the literature in other languages and including books. Overall, the paper provides a brief overview of the more recent development of research in this area s...

Focusing on issues about the development of mathematics textbooks from a cultural perspective, this study examined a widely-used curriculum resource series, One Lesson One Exercise, published in China, and its adapted English series, published in the UK, to explore how cultural influence is manifested in the two series of resource books. For the st...

This chapter presents a comparative study aiming to examine how geometric proof is treated in secondary school mathematics textbooks in China, Indonesia, and Saudi Arabia, and explore the similarities and differences revealed in these three countries’ textbooks. The results show that, although all the selected textbooks from these countries introdu...

This chapter summarizes and discusses the state of the art of research on mathematics textbooks and other resources and their use as depicted in this volume. The discussion focuses on three questions: First, what are the theoretical and methodological tools used in order to conceptualize and investigate textbook and resource use? Second, what can w...

In this commentary we provide an analytical look at the four studies reported within this theme of the volume and we discuss related issues and insights that we obtained from these studies. We offer a focused view of each study in the same order as presented in the four preceding chapters, and we conclude that these studies not only provide new ins...

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We conducted an intervention-based study in secondary classrooms to explore whether the use of geometric transformations can help improve students’ ability in constructing auxiliary lines to solve geometric proof problems, especially high-level cognitive problems. A pre- and post-test quasi-experimental design was employed. The participants were 13...

The development of technology in the field of mathematics education has been rapid and fast over the last few decades. There are significant changes with respect to the tools of demonstration, devices and display, tools for calculation, drawing and graphing, computer-assisted learning platforms and internet. Technology is obviously having an impact...

The article described a new cognitive development model for the teaching of algorithm based on the author's own work on establishing a new algorithm for polynomial division. The model put forward a theoretical framework consisting of three levels of cognitive development in relation to the learning of algorithm.

In international mathematics education research, mathematics textbook research has developed very rapidly in the last few years and it currently appears to be in the most active period. Accordingly, it is necessary to carefully examine and clarify some fundamental issues in mathematics textbook research as a field of scholarship in order to better...

The chapter “Cognition, Metacognition, and Mathematics Literacy” introduces the concept of mathematics literacy based on PISA and Chinese approaches. The chapter addresses the issue of how students’ math literacy can be promoted in the classroom, reviews cognitive-metacognitive pedagogies that have the potential for achieving it, offers examples of...

The comparison of whole numbers is a fundamental concept as well as a skill that should be introduced to young learners in mathematics. However, studies on how this important topic is presented in mathematics textbooks is rarely reported and discussed in research literature. This study is intended to examine how equality and inequality of whole num...

This chapter aims to provide readers with a comprehensive review of related literature on how Chinese mathematics teachers pursue pre-service training and in-service professional development, and how they teach in classrooms. The results suggest that China (Mainland) has established a highly unique and unified pre-service mathematics teacher educat...

Indonesia has the fourth largest education system in the world in terms of student population; yet due to a variety of reasons, internationally there is little literature available about Indonesian education, particularly in its historical change and development. This paper focuses on Indonesian national school mathematics curriculum, and provides...

Starting from the context of mathematics learning in the East and West, this paper discusses the position and role of algorithms within school mathematics and argues that learning of algorithms has suffered from an alleged dichotomy between procedures and understanding, in that algorithms have been associated with low-level cognition. The paper fir...

The model method has been widely recognised as a signature pedagogy of Singapore primary mathematics, and because of Singapore’s outstanding performance in mathematics in both TIMSS and PISA, there has been an increasing interest in this method in mathematics education worldwide. Focusing on the design and development of the model method, in this p...

Assessment is an essential process for gathering information about students’ learning and achievement. This process should be integrated with learning and teaching to establish ways for teachers to understand their students’ learning and make informed decision about their instruction. In this paper, our focus is on a new approach to mathematics ass...

This chapter presents a study investigating the reasons behind the success of mathematics master teachers in their acclaimed teaching career in the Chinese mainland. Data were collected from 31 mathematics master teachers in four provinces and three municipalities through questionnaires and interviews. The results revealed that the master teachers...

This book responds to the growing interest in the scholarship of mathematics teaching; over the last 20 years the importance of teachers? knowledge for effective teaching has been internationally recognised. For many mathematics teachers, the critical link between practice and knowledge is implied rather than explicitly understood or expressed. Thi...

The book is the 2nd edition based on the author's PhD thesis completed at the University of Chicago in 1998, with some new work and contents added, compared to its 1st edition. Since the publication of the 1st edition, the book has been a most widely read and cited book in the field of teacher education and professional development in China, listed...

This paper presents a survey study aiming to systematically examine, analyse and review relevant research focusing on mathematics textbooks and hence identify future directions in this field of research. The literature surveyed is selected from different data sources, including mainly journal articles, research theses and conference proceedings. Th...

School textbooks have received increasing attention in the international research community of mathematics education over the last decades. Nevertheless, mathematics textbook research as a field of research is still at an early stage of development, and its philosophical foundations, theoretical frameworks and research methods for disciplined inqui...

The First Sourcebook on Asian Research in Mathematics Education: China, Korea, Singapore, Japan, Malaysia and India provides the first synthesized treatment of mathematics education that has both developed and is now prominently emerging in the Asian and South Asian world. The book is organized in sections coordinated by leaders in mathematics educ...

Over the last 15 or so years, the Singapore mathematics curriculum and textbooks have attracted a considerable amount of attention internationally,particularly from educational researchers, reformers and policy makers. This phenomenon is closely related to people’s interest in searching for the reasons for Singapore students’ outstanding performanc...

Taking a broad perspective on algorithm in mathematics, the author presents a theoretical model about the learning and teaching of algorithm with focus on students’ cognitive development. The model consists of three cognitive levels: 1. Knowledge and Skills, 2. Understanding and Comprehension, and 3. Evaluation and Construction. The model suggests...

The last two decades or so have witnessed the increasing impact of technology on mathematics teaching, learning and assessment. The rapid increase of impact is particularly evident in the development of mathematics curriculum. In this article, the author will draw on his recent experience as chief editor of two latest series of secondary mathematic...

The Singapore Mathematics Assessment and Pedagogy Project (SMAPP) is a major research project undertaken by a group of mathematicians and mathematics educators to develop and investigate an innovative and systematic approach to assessment suited to the needs of mathematics teaching and learning in Singapore schools. A key research effort of the pro...

Mainly drawing on the author’s experience in textbook development for Singapore schools and research in this area, this paper presents six principles and discusses relevant processes for developing mathematics textbooks. These principles include curriculum principle, discipline principle, pedagogy principle, technology principle, context principle,...

The concept and method of mathematics assessment in Singapore schools have undergone some important developments, and in a sense, a paradigm shift, over the last decades. This chapter traces the events and efforts that led to a broadening of the role of student assessment in mainstream Singapore schools and that gave rise to the use of assessment m...

This article reports an exploratory study on using performance assessment in mathematics instruction in a high-performing secondary school in Singapore. An intact mathematics class participated in the study, and received chapter-based performance tasks as intervention during regular mathematics lessons for about one and a half school years. The per...

Educational researchers and practitioners have in recent years paid mounting attention to the importance of new assessment (or the so-called alternative assessment) strategies in Mathematics instruction to better reflect the new desired educational goals and shifted values in education. However, research is wanting in this area, particularly in Sin...

Following the movement of problem solving in the US and other parts of the world in the 1980s, problem solving became the central focus of Singapore’s national school mathematics curriculum in 1990 and thereafter the key theme in research and practice. Different from some other countries, this situation has largely not changed in Singapore mathemat...

This study examined how selected school mathematics textbooks in China, Singapore, and USA at the lower secondary grade level represent problem-solving procedures. The analysis of problem-solving procedures was carried out in two layers – general strategies, which adopted Pólya’s four-stage problem-solving model, and specific strategies, which cons...

Traditionally, assessment in our local schools is l argely confined to written tests or examinations where students are mainly assessed on their mathematical knowledge defined in the syllabus and textbooks, and the mastery of proc edural skills in solving routine problems. As assessment is one of the key motivators of stude nt and teacher behaviour...

This study compared how selected mathematics textbooks from Mainland China and the United States at the lower secondary grade level represent various types of problems for classroom teaching and learning. The examination of problems was carried out based on the classifications of problem types established in the study, including routine problems ve...

This paper is published in Chinese.

This paper is in published in Cinese.

This study was mainly intended to investigate how maths teachers in secondary schools develop their pedagogical knowledge. The study looked into the lives of participating teachers, including their school experiences, pre-service training and in-service experiences, to investigate the sources of their pedagogical knowledge. Data was collected from...

This chapter summarizes some research-based evidence that characterizes how Chinese learn mathematics, and then points out needed directions to understand Chinese learners and their learning of mathematics. The discussion is situated in a comparative context by focusing on the following four important issues: (1) Are Chinese learners really higher...

This chapter primarily aims to provide readers with an overview and synthesis of the performance of Chinese students, mainly from Mainland China, Hong Kong, and Taiwan, as revealed in large-scale international comparative studies in mathematics education conducted over the past few decades. Overall, the results from those international comparisons...

This chapter presents a study which investigated how teachers and students used textbooks within and beyond Chinese mathematics classrooms. Data were collected from 36 mathematics teachers and 272 students in 12 secondary schools in Fuzhou and Kunming, two major cities in Mainland China, through questionnaires, classroom observations, and interview...

Among a large variety of programs offered at the Ninth International Congress on Mathematical Education (ICME 9) held in Tokyo/Makuhari, Japan from Judy 31 to August 6, 2000, was the Forum of All Chinese Math Educators. The Forum, subtitled “Festive and Academic Gathering of Chinese Descendants and Other Interested Parties”, was the first of its ki...

1 ) ( a x a x a x a x f n n n n + + + + = − − L by a binomial of c x x g − = ) ( , without mentioning if this classical method can be applied when the divisor is a polynomial of degree being higher than 1, and some further explicitly stated that it is not applicable to such a divisor. For example, Larson, Hostetler, and Edwards claimed, "synthetic...

The book is based on the author's PhD dissertation completed at the University of Chicago in 1998, with some new work and contents added. It has been a most widely read and cited book in the field of teacher professional development in China, and listed as a main reference text in a number of universities in China. The English version is available...

A most important theorem in polynomial algebra is the so-called "Division ) ( b x b x b x b x g m m m m + + + + = − − L , where 0 , 0 ≠ ≠ m n b a , there exist unique polynomials q(x) and r(x) so that ) ( ) ( ) ( ) ( x r x g x q x f + = and deg r(x) < deg ) (x g When m > n, clearly q(x) = 0, () rx = ) (x f . When n m ≤ , to obtain q(x) and r(x), a...

This paper reports an action research in a mix-ability P5 EM2 class in a Singaporean primary school. The general purpose of the action research is to explore how to implement journal writing effectively in primary mathematics classrooms in the context of Singaporean educational system. The paper offers a relatively comprehensive description of the...

Division of polynomials has fundamental importance in algorithmic algebra, and is commonly encountered in many areas of mathematics as well as in scientific and engineering applications. The existing classical algorithm for polynomial division fails to provide an explicit way of determining the coefficients of the quotient and the remainder. In thi...