Lianghuo Fan

Cognition, metacognition and mathematics literacy

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 relevant tasks, and describes a quantitative study that compares math literacy of students who were exposed to a meta-cognitive pedagogy to a control group who studied ‘traditionally’, with no explicit metacognitive scaffolding. The theoretical and practical implications are described.

How Chinese Teachers Teach Mathematics And Pursue Professional Development: Perspectives From Contemporary International Research

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 education system; pre-service teachers learned more advanced mathematics courses and showed better motivation toward their training as compared with other countries such as the UK and US. China has also established its unique and well-institutionalized teacher professional development system for in-service teachers, with Teaching Research Groups (TRG) at the school level and Teaching Research Office at different government levels playing a crucial role. About teaching, it was found that Chinese mathematics teachers planned their lessons carefully; they adopted more whole-class teaching strategies, emphasized two basics (basic knowledge and basic skills), teacher-student interaction and students’ engagement academically and the method of teaching with variation, and assigned homework daily for reinforcement as well as assessment of students’ learning. Some issues and suggestions on future research in these areas are raised at the end of the chapter

A new algorithm for division of polynomials

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 this paper, I present a new general theorem about division of polynomials, which provides a new and explicit algorithm for division of any two polynomials. A method of expressing a polynomial in polynomials of lower degrees is also obtained, as a corollary of the algorithm

School mathematics textbooks in China?comparative study and beyond

This book contains 13 chapters based on a major national research project in China with focus on comparison of mathematics textbooks from more than 10 different countries.

A Comparative Study on the Presentation of Geometric Proof in Secondary Mathematics Textbooks in China, Indonesia, and Saudi Arabia

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 introduced mathematics topics related to geometric proof, they differed considerably in three aspects: the number of examples, the distribution of contents and, to a lesser degree, the types of proof. The textbooks in China contain the highest percentage of geometric contents and pay the most attention to the topic of geometric proof itself. The national mathematics curricula are clearly a main factor for the differences revealed.

About the teaching and learning of proof and proving: cognitive issues, curricular issues and beyond

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 insights into various cognitive and curricular issues in the teaching and learning of proof and proving , but also raise additional issues in relation to curriculum , textbooks and teacher education and professional development. Based on our analysis, we contend that mathematics education research in the area of proof and proving is still at an early stage, given that most studies are relatively small-scale and exploratory in nature. Further theoretical and methodological work, and more in-depth studies, especially larger-scale confirmatory and experimental studies, are needed to move research in this area forward.