(Page 1 of 8) - Patterns of Secondary Mathematics Students' Representational Acts and Task Engagement in a Small-Group Technology-Intensive Context authored by Hollebrands, Karen. and Heid, M. Kathleen.

Lloyd, G. M., Wilson, M., Wilkins, J. L. M., & Behm, S. L. (Eds.). (2005).
Proceedings of the 27

annual meeting of the North American Chapter of

the International Group for the Psychology of Mathematics Education.

PATTERNS OF SECONDARY MATHEMATICS STUDENTS'

REPRESENTATIONAL ACTS AND TASK ENGAGEMENT IN A

SMALL-GROUP TECHNOLOGY INTENSIVE CONTEXT

Karen F. Hollebrands

M. Kathleen Heid

North Carolina State University

The Pennsylvania State University

## email not listed ##

This study investigates high school students' mathematical thinking in a technological context by
focusing on representational actions and engagement in mathematical tasks when students have
access to powerful technology tools. Two frameworks were employed in the analysis to
illuminate the interplay between representational acts, types of tasks, and technology use in
small-group and whole-class settings.

Purposes and Perspectives

When mathematics teaching and learning occurs in technology-intensive environments,

students often engage with tasks and use resources that differ markedly from what might be
available in non-technological contexts. Exploration, generalization, reasoning, and justification
tasks are but a few of the processes that technology can facilitate. Because students' performance
on various tasks may be influenced by the resources available to them in a technology-intensive
environment, one step in understanding the potential influence can be to determine the nature of
or patterns in students' use of resources, such as mathematical representations, as they engage in
tasks when they have access to technology.

This study addressed the research question: What are patterns of students' engagement in

representational acts and mathematics tasks in the context of a technology-intensive curriculum?
The way in which the notion of "task" was defined in this study differed somewhat from the way
"task" has been defined in other research literature (e.g., Friedman, 1976; Stein, Smith,
Henningsen, & Silver, 2000). Our definition of task assumes that tasks are goal-driven, may be
implicit or explicit, can be posed by the curriculum, teacher, researcher, or student, and as
students are working on a large task, subtasks may be introduced. Categories of tasks were
developed through a cyclical process involving coding and refinement.

As students engaged in different mathematical tasks while they had access to technology,

they made use of mathematical representations. In addition to coding the task on which students
were working, the research team also coded students' representational acts using the MAGICAL
framework (Zbiek, 2002). Coding of representational acts involved the identification of the
mathematical object represented (e.g., geometrical point, function, polygon), the type of
representation (e.g., graph, table, symbolic rule), and action performed by students. The two-
tiered coding process enabled the researchers to identify patterns of representational acts and task
engagement as students solved mathematics problems using technology.

Methods and Data Sources

The study took place in a heterogeneously grouped class focused on intermediate algebra.

The course was offered in block-scheduled format classes that were 85 minutes in length and met
five days per week for one semester. The course used three modules from the Technology-
Intensive Secondary School Mathematics Curriculum (TISSMC, Heid, Zbiek, Blume, Choate, &