Abstract : We will talk about issues arising from the development of a mathematics enrichment programme for high school talents in Hong Kong. The process of identifying mathematics talented students, the design of the curriculum and the organization of learning activities for such students towards the development of their talents and interests will be discussed.

Abstract : This talk reports on the investigation of how the pre-service teachers learn the students' incomplete understanding of the concepts of limits through the mathematical discourse during which they have attempted to share, to elaborate and to justify their own ideas while discussing the underlying concepts behind the solution procedures of a limit problem. Three students (one sixth Former and two fifth Formers) and two pre-service teachers participated in the study. The episodes of their dialogues were videotaped. Excerpts of the videotape data show a plausible fusion of horizons between the thinking of the students and that of the pre-service teachers while tackling a limit problem.

Abstract : Mathematics is apparently a performers' subject. Have we emphasized too much its competitive spirit? While we hear much publicity about attracting and admitting the best students into universities, we also hear ready laments over the less able students. How are we to start from where our students are?

Abstract : Many researches have found that age, ethnicity, gender, major, learning style and math self-efficacy are some of the major factors in learning mathematics. Different major and age groups of students have different level of understanding of mathematics. Their future career was decided by those variables.

It is very important for math educators to know how different learning style, cultural background, ethnicity, and math self-efficacy influence students' interests and their future careers. Many researches have shown that personal self-efficacy, past experiences, gender and ethnicity differences of expectations particularly for non-traditional careers can be used to predict individual's future behavior (Hackett, Betz, Casas, and Rocha-Singh, 1992).

This paper reports the results of a study of 198 students in Taiwan. The study investigates whether academic variables (GPA, math classes taken) are related to math self-efficacy, affinity to study of mathematics and learning style. We did find significant relationships among these variables. This can be put into the context of the reputation of Asian students as doing well in comparison with students from other part of the world in grade level achievements and in math and science competitions. This is documented in research papers and the public press. However, we find a lack of research papers about the learning of these students. In particular, to contribute to the research, we report variation among students in all variables. The Taiwanese students, despite coming from a relatively small population have variety worth acknowledgement by math educators.

Abstract : The outcomes of mathematics learning, students' conceptions of mathematics in particularly, are inevitably influenced by the lived space of mathematics the students situate. Previous research reveals that the lived space of mathematics learning in Hong Kong is relatively restricted, arriving at a narrow conception of mathematics among the students. A RGC (Research Grant Council of Hong Kong) competitive earmarked research was conducted among 400 Secondary One students from ten schools, aiming at broadening students' conceptions of mathematics by the systematic introduction of variations. The schools were provided with non-routine problems in their normal mathematics class for one academic year. Their attitudes toward mathematics, their conception of mathematics, and their problem-solving performance were measured both in the beginning and at the end of the year. Hierarchical regression analyses revealed that their problem-solving performance was generally enhanced and their conceptions of mathematics changed. The effect depended on the level of use of the non-routine problems and the academic standards of the students.

Abstract : Mathematics is an important discipline. Mathematics education draws attention of educators from all over the world. The findings of the differences of mathematics achievements between American students and students of other countries were reported. The results showed that Asian students always outperformed their American counterparts (Stevenson, Lee, Stigler,1986; Chen, Uttal, 1988; Cai & Silver, 1993). Cross-national studies of mathematics education in China and the U.S were under conduct since 1980 ( Cai, 1997; Cai & Silver, 1993; Stevenson, Chen, & Lee, 1993; Stevenson & Lee, 1990; Stevenson & Stigler, 1992; Stigler, Lee, Lucker, & Stevenson, 1982; Stigler, Lee, & Stevenson, 1987, 1991; Stigler, & Perry, 1988; Uttal, Lummis, & Stevenson, 1988). These studies investigated a variety of factors related to student's achievements in mathematics, including effects of society, culture, student, and school characteristics. As to the factor of school characteristics, the similarities and differences of teachers and teaching between two countries were discussed, which meant researchers have already realized the role of teacher characteristics in mathematics education. Meanwhile, teachers' professionalism has been a focus in the field of teacher education since 1980's. Previous studies (Berliner, 1986; Bereiter & Scadalia, 1993; Arlin, 1993; Sternberg, 1995. ) showed that professional teachers' typical character is pedagogical expertise.

Teachers' professional knowledge of mathematics is a critical topic among mathematics education studies. And apparently, cross-national study is now an effective way to study issues of mathematics education. The purpose of this study is to compare the professional knowledge of mathematics teachers in elementary school in China and the United States. The focus of this study was four-fold:

1. To find out the similarities and differences of professional knowledge of mathematics teachers between two nations.

2. To explore the factors that lead to the similarities and differences.

3. To explore the relationship between the teachers' professional knowledge and their teaching activities.

4. To explore the effects of teaching style on the students' mathematics achievement by comparing teachers' classroom activities between two countries.