Culture and mathematics teaching

Teachers are proxies for an educational system’s values and there is growing evidence that mathematics teachers in one country behave in ways that identify them more closely with teachers in their own country than teachers elsewhere. Much of this research draws on the perception that "teaching and learning are cultural activities (which)... often have a routine about them that ensures a degree of consistency and predictability. Lessons are the daily routine of teaching and learning and are often organised in a certain way that is commonly accepted in each culture" (Kawanaka, 1999: 91). This sense of routine predictability has been variously described as the traditions of classroom mathematics (Cobb et al, 1992), the cultural script (Stigler and Hiebert, 1999), lesson signatures (Hiebert et al, 2003) or the characteristic pedagogical flow of a lesson (Schmidt et al, 1996). The latter embodies the pedagogical strategies which, through repeated enactment, are typical of a country’s lessons, routine, and beneath the consciousness of most teachers (Cogan and Schmidt 1999). Explanations for such patterns draw on beliefs that cultures "shape the classroom processes and teaching practices within countries, as well as how students, parents and teachers perceive them" (Knipping 2003: 282), to the extent that many of the processes of teaching are so "deep in the background of the schooling process ... so taken-for-granted… as to be beneath mention” (Hufton and

Elliott, 2000: 117).

In this regard, there is a growing body of research highlighting substantial national variation not only in the ways in which teachers act out their roles but also in the resources available to them. For example Kaiser et al. (2006) have offered persuasive summaries of the distinguishing characteristics of English, French, German and Japanese mathematics teaching, particularly in respect of proof and the structural properties of mathematics. The two TIMSS video studies have examined a range of teacher practices in Australia, the Czech Republic, Hong Kong SAR, the Netherlands, Switzerland, the United States and Japan. Huegener et al (2009) have focused on differences in the ways teachers present the theorem of Pythagoras in Germany and Switzerland, while Santagata (2005) has highlighted substantial differences in the ways in teachers handle students’ mathematical errors in Italy and the US. Campbell and Kyriakides (2000) and Haggarty and Pepin (2002) have shown how school texts reflect differences in systemic expectations and traditions. An et al. 2004) have identified culturally located differences in teachers’ mathematical content knowledge, while Correa et al. (2008) have done the same for teachers’ mathematics related beliefs. Finally, although it is acknowledged that the scope of this paper presents an extensive review, it is important to acknowledge the Learner’s Perspective Study. In this respect, Clarke and his many colleagues have contributed much to our collective understanding of differences in the ways in which mathematics teachers around the world construe their roles (Clarke et al 2006a, 2006b).

With regard to my own and my colleagues' work, we have examined the ways in which teachers present mathematics to students in the age range 10-14 . The episodes of videotaped lessons were coded against a framework developed iteratively and collaboratively over the course of a year (Andrews 2007a), where an episode was that part of a lesson in which the teacher's observable didactic intention remained constant. In terms of teachers’ observable learning objectives, the project found (Andrews 2009a) that teachers in all four countries privileged the development of both conceptual procedural knowledge in high and comparable proportions. The major variation lay in the other outcomes. For example, Some teachers placed a higher emphasis on the structural properties (links within and between topics), mathematical efficiency (comparing solutions strategies for elegance and efficiency), problem solving and reasoning than elsewhere. In similar vein, some teachers were rarely seen to encourage structural links or efficiency. Such differences reflect not only differing curricular expectations but long standing mathematics teaching norms. The same study (Andrews 2009b) found, in relation to the observable didactic strategies employed by teachers, that teachers

explain regularly and in comparable proportions irrespective of country. However, all other strategies distinguished between the didactical practices of project teachers. For example, some teachers were exploited explicit motivational strategies in smaller proportions than elsewhere, while some teachers employed them in over half of all observed episodes. Many teachers very rarely questioned (used higher order questions) while some teachers did so constantly. Other teacher coached  offered hints and suggestions to facilitate their students’ successful completion of given tasks - in more than three quarters of observed episodes, while teachers elsewhere did so in equal and significantly smaller proportions. Some teachers invited students to share publicly their solution strategies in almost every episode while teachers elsewhere did so consistently at around the 60 per cent level.

Of course, cultural emphases do not end with learning outcomes and didactic strategies. In a comparison of Hungarian and English mathematics teachers’ beliefs Andrews and Hatch (2000) found that while English teachers valued the systematic decorating of their classrooms with examples of students’ work or mathematical posters, such practices were alien to Hungarian teachers who tended to work within classrooms with, essentially, bare walls. In a second study Andrews (2007b) found English teachers espousing collective beliefs about the value of school mathematics lying in its applicability to a world beyond school, while Hungarian teachers articulated a collective belief whereby the value of mathematics lay within mathematics itself. In short, the ways in which teachers conceptualize and present mathematics to their learners, the environments they create and their beliefs as to the nature and importance of the subject highlight well that mathematics teaching, in all aspects, is a cultural activity that differs significantly from one country to another.

In conclusion, my appeal to colleagues researching any aspect of mathematics teaching and learning is that they make explicit in the reporting of their work the cultural context in which it was undertaken. Too frequently research is reported with no indication, other than the authors’ designation, of a study’s location. Moreover, and I know I am equally to blame in this regard, writers assume when synthesizing the literature, that generalities derived from a study undertaken in one cultural context are generalizable to another. That is, when constructing the theoretical frames within which we conduct our research, too frequently we ignore the cultural implications embedded in the studies we analyse. Such assumptions, that literature can be synthesized independently of context, may lead to poorly designed and reported studies.