A new article about teachers’ conception of effective mathematics teaching. The article investigates the perspectives of teachers from China and the U.S., and I find it particularly interesting because it focus on the issue of cultural beliefs. I think this is an interesting concept, and I’ve used it before in one of my own articles. The idea of cultural beliefs comes from results of cross-national studies where researchers have identified clear differences in the teaching practices of teachers from East-Asian and Western countries.

In the study referred to in the article below, 9 Chinese teachers and 11 U.S. teachers were interviewed. The semi-structured interviews that were used in the study were constructed according to Ernest’s traditional framework of three aspects of mathematics teachers’ beliefs. The study showed that the teachers from these two countries held quite different beliefs about good mathematics teaching. These views were also closely connected with their views on the nature of mathematics.

Conceptions of effective mathematics teaching within a cultural context: perspectives of teachers from China and the United States

Journal    Journal of Mathematics Teacher Education
Publisher    Springer Netherlands
ISSN    1386-4416 (Print) 1573-1820 (Online)
DOI    10.1007/s10857-009-9132-1
Subject Collection    Humanities, Social Sciences and Law
SpringerLink Date    Tuesday, November 17, 2009

By Jinfa Cai and Tao Wang

Abstract  This study investigates Chinese and U.S. teachers’ cultural beliefs concerning effective mathematics teaching from the teachers’ perspectives. 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. These differences of teachers’ beliefs are discussed in a cultural context.

The last couple of days, two articles with a focus on using video as a tool for teacher learning and development have been published in Journal of Mathematics Teaching Education. The first articleinvestigates how prospective primary mathematics teachers might learn from on-line discussions.

Prospective primary mathematics teachers’ learning from on-line discussions in a virtual video-based environment

Journal    Journal of Mathematics Teacher Education
Publisher    Springer Netherlands
ISSN    1386-4416 (Print) 1573-1820 (Online)
DOI    10.1007/s10857-009-9133-0
SpringerLink Date    Wednesday, November 18, 2009

By Salvador Llinares and Julia Valls

Abstract The aim of this study was to investigate how participation and reification of ideas about mathematics teaching are constituted in on-line discussions when prospective primary mathematics teachers analysed video-cases about mathematics teaching. Prospective teachers enrolled in a mathematics methodology course participated for 4 weeks in two virtual learning environments that integrated the analysis of video-clips, on-line discussions and writing essays about key aspects of mathematics teaching. Three aspects were considered relevant to explain the prospective teachers’ learning: the way in which the theoretical information was used to frame and to interpret the events from mathematics teaching; the characteristics of engagement with others participating in the on-line discussions and the role played by prospective teachers’ beliefs. Possible reasons for the importance of these features include the specific questions posed in on-line discussions and the use of video-clips of mathematics teaching. These findings are considered useful in designing virtual learning environments and the kinds of tasks through which the understanding of mathematics teaching and learning-to-notice skills can be developed.

The other article also has a focus on using videos, by the use of so called “video clubs”.

The influence of video clubs on teachers’ thinking and practice

Journal    Journal of Mathematics Teacher Education
Publisher    Springer Netherlands
ISSN    1386-4416 (Print) 1573-1820 (Online)
DOI    10.1007/s10857-009-9130-3
SpringerLink Date    Saturday, November 14, 2009

By Elizabeth A. van Es and Miriam Gamoran Sherin

Abstract This article examines a model of professional development called “video clubs” in which teachers watch and discuss excerpts of videos from their classrooms. We investigate how participation in a video club influences teachers’ thinking and practice by exploring three related contexts: (a) teachers’ comments during video-club meetings, (b) teachers’ self-reports of the effects of the video club, and (c) teachers’ instruction across the year. Data analysis revealed changes in all three contexts. In the video-club meetings, teachers paid increased attention to student mathematical thinking over the course of the year. In interviews, teachers reported having learned about students’ mathematical thinking, about the importance of attending to student ideas during instruction, and about their school’s mathematics curriculum. Finally, shifts were also uncovered in the teachers’ instruction. By the end of the year, teachers increasingly made space for student thinking to emerge in the classroom, probed students’ underlying understandings, and learned from their students while teaching.