Student roles in collaborative math groups
Creators: name: Brookes, Elijah A.
Publisher: name: No Publisher Supplied
Year: 2015

description: This study identifies student roles in collaborative mathematics groups and analyzes how these roles appear to impact learning. Perspectives on social and cognitive constructivism are presented as a lens for analysis. Descriptions of engagement behaviors are utilized to justify the grouping of student engagements into 8 categories of student roles. The longitudinal study student Jeff is followed through a problem task in each grade from 2 through 12: 2nd grade Counting Tasks, 3rd grade Mystery Box Task, 4th grade Towers Task, 5th grade Pizza Toppings Task, 6th grade Dice Games, 7th grade Inverse Function Activities, 8th grade Surface Area and Volume Activities, 9th grade Pirate's Treasure Exploration, 10th grade Ankur's Challenge, 11th grade Night Session Exploration of Pascal's Identity, and 12th grade Taxicab Geometry Activity. Session summary and analysis describes the actions of Jeff and his group members; descriptions of these actions form a grounded theory of mathematical engagement behaviors. Student engagement behaviors are qualitatively assessed for cognitive, social, and affectual elements. Longitudinal study data are triangulated using video data, transcripts, and student work. Critical learning events are identified and coded according to student roles. The utilization of student roles to code critical learning events in a learning series is verified through comparison with an external researcher’s coding. The questions that guided the study are: (1) what roles, if any, do individuals in mathematical groups exhibit?; what combination of roles, if any, can be characterized in mathematical problem solving? (2) How, if at all, might the presence and quality of each role have an effect on learning outcomes; how, if at all, are roles linked to the social negotiation of a valid justification in a group? (3) How, if at all, might the setting, defined here as the group size, task, and researcher interaction style, of a group be linked to specific roles? (4) How do group roles change, or remain consistent, over time?  STUDENT ROLES IN MATH 3  Twenty-five categories of student engagement behaviors that comprise student interactions and roles while collaborating on mathematics are identified. Jeff’s groups are successful because they produce mathematically valid solutions and justifications. Engagement behaviors linked to mathematical development are identified through descriptions of critical learning events. Fourteen engagement behaviors are reported during critical learning events; an additional 5 engagement behaviors are reported in high frequency within critical learning events. Specific examples are presented that describe the impact of each engagement behavior on the student’s learning outcomes. Selected examples also illustrate how administrative discussion, communication improvement, leadership, answer checking, and external interactions impact the student justification process. Examples are presented that demonstrate that group size, problem selection, student experiences, and researcher interaction style can each impact group structure, which impacts student interactions. Some engagement behaviors are identified as changing over time, but many remain consistent in purpose and implementation across the grades studied. While successfully investigating mathematical problems, Jeff’s groups demonstrate 8 naturally occurring roles: administrative discussion, answer checking, external interaction, indicating motivation, leadership, presentation, mathematical strategizing, and individual development. Data from this study are limited to the longitudinal students in Jeff’s group for a problem solving activity once per year. Future research with other groups is recommended to explore how similarities or differences impact the roles exhibited by students.