James Stigler and James Hiebert published in 1999 a book entitled The Teaching Gap. They report on, in a compelling and readable way, the results of their study of mathematics teaching in the USA, Germany and Japan. Primarily they highlight the differences in practice between the three jurisdictions.
This is not the only or, arguably, even the main contribution. A central theme is the idea of the cultural script, and how it influences classroom practice. It is not a new idea, but Stigler and Hiebert bring it to wider attention. This is because the comparison between practice and pedagogy, in different countries, reveals cultural practices; more so than through investigating practice in a single country.
They explain a cultural script as follows:
Family dinner is a cultural activity. Cultural activities are represented in cultural scripts, generalized knowledge about an event that resides in the heads of participants. These scripts guide behavior and also tell participants what to expect. Within a culture, these scripts are widely shared, and therefore they are hard to see. Family dinner is such a familiar activity that it sounds strange to point out all its customary features. We rarely think about how it might be different from what it is. On the other hand, we certainly would notice if a feature were violated; we’d be surprised, for example, to be offered a menu at a family dinner, or to be presented with a check at the end of the meal .
If you are a teacher or, indeed, any other kind of practitioner, think about how cultural scripts guide what you do in your professional and personal lives. Think of examples of cultural scripts that pervade your teaching.
Stigler and Hiebert argue that the reason cultural scripts are similar within a culture is because scripts are passed on between generations of teachers.
Cultural scripts are learned implicitly, through observation and participation, and not by deliberate study  … Teaching, like other cultural activities, is learned through informal participation over long periods of time. It is something one learns to do more by growing up in a culture than by studying it formally. Although most people have not studied to be teachers, most people have been students. People within a culture share a mental picture of what teaching is like. We call this mental picture a script … The difference is that the patterns were observable in the videotapes; scripts are mental models of these patterns. We believe that the scripts provide an explanation for why the lessons within a country followed distinctive patterns: the lessons were designed and taught by teachers who share the same scripts .
I discuss this from the perspective of social cognitive theory and observational learning in a previous post.
It makes me wonder how old some cultural scripts are in teaching? Decades? Centuries?
Stigler and Hiebert argue that cultural practices are underpinned by beliefs about teaching and learning.
The scripts for teaching in each country appear to rest on a relatively small and tacit set of core beliefs about the nature of the subject, about how students learn, and about the role that a teacher should play in the classroom. These beliefs, often implicit, serve to maintain the stability of cultural systems over time. Just as we have pointed out that features of teaching need to be understood in terms of the underlying systems in which they are embedded, so, too, these systems of teaching, because they are cultural, must be understood in relation to the cultural beliefs and assumptions that surround them .
This is where I disagree. But not with the idea of a cultural script. I argue in my previous post that the relationship between beliefs and practices is more complex. Teachers’ beliefs, about their subject, and how students learn, have a complex relationship with practices. It is the cultural script itself that has influence on thinking and practice. Beliefs are almost independent of practices.
 Stigler, James W.; Hiebert, James (2007-11-01). The Teaching Gap (Kindle Locations 1098-1103). Simon & Schuster UK. Kindle Edition.
 Kindle Locations1113-1118