The focus of this paper is the activity of comparison as this is undertaken in international cross-cultural comparative research. The dual demands of validity and comparability that constrain such acts of comparison lead to seven specific dilemmas confronting researchers who aspire to make international comparisons of either curricula or classroom practice. Existing research (Clarke, 2001, 2003, 2006, 2010) is used to illustrate these seven dilemmas. Dilemma 1: Cultural-specificity of Codes Use of culturally-specific categories for cross-cultural coding (eg participation, mathematics). Dilemma 2: Inclusive vs Distinctive Categories Use of inclusive categories to maximize applicability across cultures, thereby sacrificing distinctive and potentially explanatory detail (eg lesson structure). Dilemma 3: Evaluative Criteria Use of culturally-specific criteria for cross-cultural evaluation (eg student-student interaction). Dilemma 4: Form vs Function Confusion between form and function, where an activity coded on the basis of common form is employed in differently situated classrooms to serve quite different functions (eg. between desks instruction (kikan-shido)). Dilemma 5: Linguistic Preclusion Misrepresentation resulting from cultural or linguistic preclusion encrypted in discourse conventions (eg Japanese classrooms underplaying intellectual ownership). Dilemma 6: Omission Misrepresentation by omission, where the authoring culture of the researcher lacks an appropriate term or construct for the activity being observed (eg pudian (Chinese) has no English equivalent). Dilemma 7: Disconnection Misrepresentation by disconnection, where activities that derive their meaning from their interconnectedness in the context being studied are separated for independent analysis (eg obuchenie (teaching/learning)). Cross-cultural comparison must accommodate the limits to precision in the application of any construct beyond its authoring culture (implications of the universal use of English are profound). Cross-cultural comparative classroom research requires new forms of research partnership and communication in which local conventions, priorities, aspirations, and discourse form the basis for the negotiation of both the unit/s of analysis and the analytical frame/s applied.

Clarke, D.J. (2001). Teaching/Learning. Chapter 12 in D. J. Clarke (Ed.). Perspectives on practice and meaning in mathematics and science classrooms. Kluwer Academic Press: Dordrecht, Netherlands, 291-320. Clarke, D.J. (2003). International Comparative Studies in Mathematics Education. Chapter 5 in A.J. Bishop, M.A. Clements, C. Keitel, J. Kilpatrick, and F.K.S. Leung (eds.) Second International Handbook of Mathematics Education, Dordrecht: Kluwer Academic Publishers, 145-186. Clarke, D.J. (2006). Using International Comparative Research to Contest Prevalent Oppositional Dichotomies. Zentralblatt für Didaktik der Mathematik, 38(5), 376-387. Clarke, D.J. (2010). The Cultural Specificity of Accomplished Practice: Contingent Conceptions of Excellence. In Y. Shimizu, Y. Sekiguchi, & K. Hino (Eds.). In Search of Excellence in Mathematics Education. Proceedings of the 5th East Asia Regional Conference on Mathematics Education (EARCOME5), Tokyo: Japan Society of Mathematical Education, pp. 14-38.