(Page 2 of 5) - Opportunities for linking in diverse mathematics classrooms authored by Hand, Victoria.

There is a common misperception that the domain of mathematics is too rigid or abstract

to lend itself to linking. Students do find mathematical achievement to be meaningful to them,
but often in the sense that it shapes their future success in higher education and professional
activities (D’Amato, 1996; Nasir & Hand, 2003). Attempts have been made to infuse relevancy
into mathematical activities, for example, by linking mathematical contexts to everyday contexts
with word problems, or more recently with problem-based learning. Yet all too often, students
find these contexts artificial, lacking true relevance to the things that they do in their everyday
lives (Boaler, 1997). In other words, to package mathematics in the trappings of the ‘real world’
does not guarantee increased meaningfulness.

Another way that the issue of relevancy has been addressed in mathematics education has

been through a reconsideration of what it means to learn mathematics. Greeno (1997) and other
researchers from situative and/or sociocultural perspectives have argued for mathematical
activity to be representative of the ways that people solve problems together in the world (Lave,
1988). Thus, the development of mathematical practices, or the ways in which students and
teachers engage in mathematical activity within and beyond the classroom, has become a core
concern of the mathematics reform movement. One way to conceptualize the work that has been
done in this area is along two broad lines of research: one line of research attempts to model
classroom mathematical practices on the practices of mathematicians and other individuals who
engage in real world mathematical activity, while another line of research attempts to model
classroom practices on the cultural practices students engage in as members of their local and
broader communities. (This is an admittedly cursory treatment of an extensive and diverse body
of research in mathematics education, learning, and culture.) Taken together, what these two
lines of work suggest is that it is important to consider both how the norms and practices guiding
classroom mathematical activity are meaningful to real world activity, and how alignment can be
promoted between the expectations held for students in their classroom participation, and the
expectations students hold for themselves and others in joint social activity.

This study examined the ways that teachers and students organized their activities within

mathematics classrooms towards the construction of mathematical activity that was meaningful
to both parties. Mathematical activity was examined in three reform-based mathematics
classrooms in a highly-diverse urban public high school that was notably successful at producing
strong mathematics learners (Boaler, 2003). As an instance of meaningful mathematical activity,
linking was operationalized at multiple levels—task, discourse practices, and participation
structures. Multi-level interaction analyses of videotape documentation and observation
transcripts collected over the course of a school year were triangulated with interviews, surveys,
and student shadowing transcripts to capture the nature of linking as it emerged in moment-to-
moment classroom interaction. At the first level of analysis, the moves that students and
teachers made to position themselves and each other in and around mathematical activity were
considered. At the second level, task affordances and constraints were considered. At the third
level, the analysis concentrated longitudinally on the features of the classroom activity system:
the development of classroom norms and practices, the trajectory of mathematical activity, and
opportunities for links to students’ social and cultural practices.

Analysis of classroom tasks that were designed to promote links to contexts familiar to

students from diverse social and cultural backgrounds (e.g., “youth culture”) revealed that the
discursive practices that emerged around these tasks were not necessarily engaging to students
(and sometimes supported the development of oppositional stances). This finding supports
Greeno and Hull’s (2002) contention that the contexts of information, or settings of mathematical