International Portal of Teacher Education

Source: Journal of Mathematics Teacher Education, Volume 13, No. 3, p. 265-287. (June 2010).
(Reviewed by the Portal Team)

This study aims to develop a better understanding of Chinese and U.S. teachers’ beliefs concerning effective teaching within a cultural context.
The study addresses to the following research question: What is effective mathematics teaching for teachers in Eastern and Western cultures?

Participants
Nine Chinese teachers and 11 U.S. teachers were selected for the study.
All the selected teachers are “distinguished” mathematics teachers according to local criteria in their respective regions. Both Chinese sample and the U.S. sample of teachers are specialists—just teaching mathematics.

Data collection and analysis
Each of the selected teachers was interviewed using semi-structured questions. The questions were constructed according to Ernest’s (1989) model of three aspects of mathematics teachers’ belief. These three aspects include teachers’ views about mathematics, teaching mathematics, and learning mathematics.

The findings from this study reveal that although sharing some common beliefs, the two groups of teachers think differently about both mathematics understanding and the features of effective teaching.

The sample of U.S. teachers put more emphasis on student understanding with concrete examples, and the sample of Chinese teachers put more emphasis on abstract reasoning after using concrete examples.
The U.S. teachers highlight a teacher’s abilities to facilitate student participation, manage the classroom and have a sense of humor, while the Chinese teachers emphasize a teacher’s solid mathematics knowledge and careful study of textbooks.
Both groups of teachers agree that memorization and understanding cannot be separated. However, for the U.S. teachers, memorization comes after understanding, but for Chinese teachers, memorization can come before understanding.

Finally, the findings of this study have a number of implications for future studies that examine cross-cultural beliefs of effective teaching from teachers’ perspectives. 

One of the unique contributions of this study is to situate the discussion of effective teaching in a cultural context.

The findings from this current study and other studies (Cai 2005; Cai and Wang 2006) also showed an inconsistency between the teachers’ beliefs and their practices.
This phenomenon is especially conspicuous in this cross-cultural study because the inconsistency for the Chinese sample of teachers is much more obvious than that for U.S. teachers.

Ernest (1989) created a model to explain the inconsistency between what the teachers believe about effective teaching and what they practiced in classroom. According to Ernest, the teacher’s espoused beliefs of teaching and learning mathematics are subject to the constraints and contingencies of the educational context, and then transformed into classroom practices. With a full consideration of the powerful influence of the social and cultural context that the teachers are exposed to, as well as two groups of teachers’ teaching that were documented and analyzed (Cai 2005; Cai and Wang 2006), the Ernest model is appropriate to explain the finding about the inconsistency between the teachers’ beliefs and their practices.

References
Cai, J. (2005). U.S. and Chinese teachers’ knowing, evaluating, and constructing representations in mathematics instruction. Mathematical Thinking and Learning: An International Journal, 7, 135–169.

Cai, J., & Wang, T. (2006). U.S. and Chinese teachers’ conceptions and constructions of representations: A case of teaching ratio concept. International Journal of Mathematics and Science Education, 4, 145–186.

Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics teaching: The state of the art (pp. 249–254). New York: The Flamer Press.