Frederick K. S. Leung

Second international handbook of mathematics education

There is much debate within mathematics teacher education over ways in which professional and academic foci could be made to complement each other. On the one hand, teachers’ craft knowledge is emphasized, mainly as this relates to the particular and local level of teaching; on the other hand, the importance of academic subject knowledge cannot be denied. In this chapter the focus will be on how to blend and balance the two through activities in which teachers learn from other teachers, particularly the co-learning of teachers and teacher educators. It will discuss professional relationships, reflective practice, community building, and research in practice. Examples of research-based programs involving lesson study (LS) and the Learner’s Perspective Study (LPS) have moved the relevant research in this area to yet another level, in which theory and practice are combined. Projects such as these and others from diverse parts of the world will be presented and discussed.This chapter seeks to provide an integrating theoretical framework for understanding the somewhat disparate and disconnected literatures on “modelling” and “technology” in mathematics education research. From a cultural–historical activity theory, neo-Vygtoskian perspective, mathematical modelling must be seen as embedded within an indivisible, molar “whole” unit of “activity.” This notion situates “technology”—and mathematics, also—as an essential part or “moment” of the whole activity, alongside other mediational means; thus it can only be fully understood in relation to all the other moments. For instance, we need to understand mathematics and technology in relation to the developmental needs and hence the subjectivity and “personalities” of the learners. But, then, also seeing learning as joint teaching–learning activity implies the necessity of understanding the relation of these also to the teachers, and to the wider institutional and professional and political contexts, invoking curriculum and assessment, pedagogy and teacher development, and so on. Historically, activity has repeatedly fused mathematics and technology, whether in academe or in industry: this provides opportunities, but also problems for mathematics education. We illustrate this perspective through two case studies where the mathematical-technologies are salient (spreadsheets, the number line, and CAS), which implicate some of these wider factors, and which broaden the traditional view of technology in social context.

In Search of an East Asian Identity in Mathematics Education.

East Asian students have consistently outperformed their counterparts in Western countries in recent international studies of mathematics achievement. However, these countries do not seem to have an established theory of mathematics education, and their teaching has been criticized as traditional and old fashioned. In search of an East Asian identity in mathematics education, this paper discusses the features of the East Asian mathematics education and their underlying values in contrast to features and values in the West. These are presented in terms of six dichotomies,namely, product versus process; rote learning versus meaningful learning;studying hard versus pleasurable learning;extrinsic versus intrinsic motivations;whole class teaching versus individualized learning; and competence of teachers:subject matter versus pedagogy. It is argued that these features are based on deep-rooted cultural values and paradigms. A characterization of these features and an analysis of the underlying values are essential in this search for an East Asian identity in mathematics education.

The mathematics classroom in Beijing, Hong Kong and London

This paper reports a classroom observation study which intends to characterise the instructional practices in junior secondary mathematics classrooms in Beijing, Hong Kong and London, focusing on the different cultural beliefs pertaining to mathematics and mathematics teaching and learning between the Chinese and Western cultures. The results show that there are striking differences in classroom practices between the three places, and the differences seem to be related to the differences in attitudes towards mathematics and mathematics teaching and learning. The findings point to the potential of the cultural perspective in interpreting results of comparative curriculum studies.

Behind the High Achievement of East Asian Students

Hong Kong, Japan, Korea and Singapore are the only East Asian countries in the Third International Mathematics and Science Study (TIMSS), but students in these 4 countries outperformed their counterparts in the TIMSS mathematics test. An examination of the student background information showed that there was little commonality among the 4 countries which can be used to explain the superior achievement of their students. The only common background data for the 4 places were their high population density and large class size, which are, in general, not considered favorable factors for achievement. An investigation of the TIMSS attitude data also failed to locate common attitudes that were unique to the 4 countries and which can be used to explain the high achievement of their students. The questionnaire data however indicated that the superior results of the East Asian students might have been achieved at the expense of other aspects of the development of the students. The results also showed that students in the 4 countries displayed relatively negative attitudes towards mathematics, including the lack of confidence in doing mathematics. The predominant Confucian culture in the 4 countries will be discussed in an attempt to explain the negative attitudes of the East Asian students, but it is not clear how these cultural values can be used to explain their superior achievement.

Competent students, competent teachers?

Abstract In an attempt to investigate East Asian teachers’ competence in mathematics, a small-scale exploratory study conducted in Hong Kong and Korea replicating Mas study (Knowing and Teaching Elementary Mathematics, Lawrence Earlbaum Associates, Mahwah, NJ, 1999) is reported in this chapter. It was found that although Hong Kong and Korean teachers possessed conceptual as well as procedural understanding of mathematics, the majority of their reported teaching strategies were procedurally rather than conceptually directed. Compared with their Shanghai counterparts in Mas study, they lacked a profound understanding of mathematics, they had not organized their mathematics understanding into an explicit knowledge package which they could talk about readily, and they were weak in strategies for exploring mathematics.

From the Few to the Many: Historical Perspectives on Who Should Learn Mathematics

Today we take for granted that everybody should be offered the opportunity to learn mathematics. However, it was not until well into the 20th century that “mathematics for all” became an achievable goal. Before then, the geographical location of schools in relation to children’s homes, the availability (or non-availability) of teachers capable of teaching mathematics, parental attitudes to schooling, economic circumstances of families, and social and psychological presuppositions and prejudices about mathematical ability or giftedness, all influenced greatly whether a child might have the opportunity to learn mathematics. Moreover, in many cultures the perceived difference between two social functions of mathematics—its utilitarian function and its capability to sharpen the mind and induce logical thinking—generated mathematics curricula and forms of teaching in local schools which did not meet the needs of some learners. This chapter identifies a historical progression towards the achievement of mathematics for all: from schooling for all, to arithmetic for all, to basic mathematics for all; to secondary mathematics for all; to mathematical modelling for all; and to quantitative literacy for all.

Mathematics Education in East Asia

Students in East Asia have been performing extremely well in international studies of mathematics achievements such as TIMSS and PISA. On the other hand, education practices in East Asian countries look different from Western practices, and some practices look very backward and contradictory to what are considered as good practices. Given these intriguing phenomena, this plenary panel aims to discuss different aspects of mathematics education in these East Asian countries, and illustrate its salient features with examples. These aspects include classroom teaching in regular schools and tutorial schools, and pre-service and in-service teacher education and development. The reasons behind the distinctive features of mathematics education in East Asia are then explored, and it is argued that the common Confucian Heritage Culture (CHC) that these countries share best explain these features. This panel presentation is not meant to promote the superior student achievement or good educational practices in East Asia. Rather, it highlights the cultural differences between CHC and Western cultures, rather than the superiority of one over the other. A cultural explanation also means that simple transplant of educational policies and practices from one culture to another will not work. The panel points to the important role culture plays in accounting for educational practices and student achievement.

Comparing Educational Achievements

When George Bereday, the famous comparative educator from Columbia University in New York (see e.g. Bereday 1964), first heard of the work of the International Association for the Evaluation of Educational Achievement (IEA) in the early 1960s, he said that the IEA researchers were comparing the incomparable. Perhaps he meant that it was impossible to compare pupils and schools from different cultures. Perhaps he meant that there were so many differences between systems of education that it was impossible to compare them. After all, the pupils begin school at different ages, the curricula are different, the ways in which teachers are trained are different, and, and, and, …!

The Secondary School Mathematics Curriculum in China.

This article attempts to give an up-to-date account of the secondary school mathematics curriculum in China. The teaching objectives and curriculum contents are discussed, and the public examination papers and classroom teaching methods are briefly described.

Differentiation in key learning areas for gifted students in regular classes: A project for primary school teachers in Hong Kong

Gifted students usually require much less time spent in practising and revising basic skills; instead, they benefit greatly from opportunities to work through the curriculum at a faster pace (acceleration). Teachers currently working with mixed-ability classes do not always find it easy to differentiate their teaching approach in this way, so there is a need to facilitate in-service professional development to provide teachers with practical strategies for implementing effective differentiation for gifted learners. In response, a project for primary school teachers was organized by a university in Hong Kong. The purposes of the project were (a) to enhance the confidence of teachers in planning and delivering differentiated lessons in specific key learning areas (KLAs) with particular reference to gifted students; (b) to empower teachers with knowledge and strategies necessary for designing and implementing a differentiated curriculum in KLA domains and (c) to establish a professional development practice that connects local academics with schools and teachers. The project was implemented by inviting curriculum leaders, panel chairpersons and subject teachers from primary schools to attend a 3-hour lecture and a 6-hour workshop in which differentiation practices were explored. The project was later evaluated based on feedback from participants and university consultants. Overall, the feedback was positive, but suggestions are provided here for enhancing future projects of a similar nature.