School Seminars and Colloquia

Confronting Our Assumptions: Lessons from Well-Taught Mathematics Classrooms Around the World


by Professor David Clarke

Institution: University of Melbourne, Department of Science and Mathematics Education
Date: Wed 19th October 2005
Time: 11:00 AM
Location: Russell Love Theatre, Richard Berry Building, University of Melbourne

Abstract: The research reported in this colloquium draws on analyses of
data from the 14-country "Learner's Perspective Study" (LPS). The LPS
project uses three video cameras supplemented by post-lesson interviews
with teachers and students to document the practices and learning outcomes
of well-taught mathematics classrooms around the world. In particular, the
inclusion of China, Japan, Korea and Singapore in the study provides an
opportunity to examine similarities and differences between classrooms
that might otherwise be simplistically characterised as "Asian". The
practices of such classrooms can then be compared with well-taught
mathematics classrooms in Australia, Germany, Sweden, the USA and other
"Western" school systems. This colloquium reports some of the key findings
of this international comparative project.

Oppositional dichotomies such as teacher-centred versus student-centred
classrooms, real-world versus abstract tasks, and telling versus
not-telling offer mathematics educators false choices, sanctifying one
alternative while demonising the other. International research offers
insight into possible explanatory frameworks within which such choices are
no longer oppositional or even dichotomous, but rather can be seen as
reflecting strategic and interrelated pedagogical decisions, dependent on
purpose and context. The careful analysis of classroom practice in
non-Western classrooms offers particularly useful insights, by
problematising many of our most fundamental assumptions.

Some of our most precious assumptions regarding effective practice may
only reflect our inability to see the alternatives. The alternative that
is being offered to the prevalent oppositional dichotomies is an
integrative perspective in which such alternatives are seen as
complementary and interrelated aspects of a broader conception. Such
broader, more inclusive, conceptions include:

* Reconceiving teaching/learning as a single collaborative practice,
within which teacher and students are co-participants, but differently

* Reconstructing the division between abstract mathematics and

"real-world mathematics" in favour of a conception that accords classroom
mathematical activity the same legitimacy as any other form of
mathematical activity;

* Discarding the misleading divisive dichotomy of teacher-centred
versus student-centred classrooms in favour of analyses based on the
distribution of responsibility for knowledge generation in the classroom;

* Acknowledging the legitimacy of teacher initiation of new
mathematics into classroom discussion (whether by "telling" or by any
other means) provided this is interwoven with the careful elicitation of
the students' mathematics both before and after such acts of teacher

International comparative research is our insurance against the inevitable
insularity of our attempts to document, theorise and consequently improve
the practices of our classrooms.

For More Information: Paul Norbury tel: 8344 5534, email:

Colloquium Website