TY - JOUR
TI - Tracing beliefs and behaviors of a participant in a longitudinal study for the development of mathematical ideas and reasoning
DO - https://doi.org/doi:10.7282/T3C829D4
PY - 2010
AB - This research provides an analysis of the relationship between a student‘s beliefs and mathematical behaviors over a seventeen-year period. Romina, the student of focus in this case study, was among the original participants in a longitudinal study which explored how students build mathematical ideas when working collaboratively on problem-solving tasks with as little outside intervention as possible (Maher, 2005). A qualitative, phenomenological approach was taken in analyzing videotape recordings from the Rutgers-Kenilworth longitudinal study between February 6, 1992 and July 15, 2009 in the Robert B. Davis Institute of Learning archive, along with student work, questionnaires, and researcher field notes. To better understand the development of math ideas by tracing her knowing and sense-making, the research examined four sessions of Romina‘s problem-solving behavior in terms of justification, representation, and collaboration from fourth through twelfth grades. In addition, this study explored her mathematical beliefs based upon five interviews from high school, college, and her post-graduate career concerning her views about the knowledge, conditions, and processes of mathematical learning. Addressing a documented need in the literature for investigation of the interplay between personal epistemology and mathematical reasoning over time, this study contributes to a larger body of work considering how social interaction, teacher questioning, and task design affect a student‘s cognitive growth. The research suggests that Romina constructed mathematical ideas by building relationships among concepts and produced justifications through continuously evolving personal representations that promoted mathematical understanding. Further, the findings provide evidence that Romina engaged in a range of collaborative behaviors in which she questioned others‘ ideas, found teacher-researcher interaction a catalyst to her thinking, worked through frustration, and moved fluidly among many roles within the group – facilitator, manager, communicator, and secretary. Simultaneously, the data suggest she developed three very healthy mathematical beliefs involving the active construction of conceptual knowledge, learning environments that built ―comfortable‖ collaborative relationships while engaging in complex tasks over long periods of time, and, finally, a learning process of ―group thinking where personally relevant problems were shared, questioned, and argued. Through systematic examination of the relationship between Romina‘s beliefs and problem-solving behaviors, the results of this study imply specific instructional interventions that support the development of mathematical ideas and reasoning from elementary grades through college and into the workplace.
KW - Mathematics Education
KW - Mathematics--Study and teaching
KW - Mathematics--Study and teaching--Longitudinal studies
KW - Knowledge, Theory of
KW - Mathematics--Research
KW - Mathematics--Decision making
LA - English
ER -