Emergent Activity Frames in Facilitated Family Interactions at Math Exhibits

The purpose of this study was to explore whether the notion of activity frames might be a useful alternative to sociomathematical norms to help describe the behaviors of family members at interactive math exhibits. In this study, activity frames are defined as contextspecific, emergent understandings or expectations, either implicit or explicit, about the nature and goals of family and staff interactions at math exhibits (Pattison et al., in review; Pattison, Gontan, & Ramos-Montañez, in review). Researchers questioned not only whether activity frames could describe family behaviors, but also if they might influence the mathematical reasoning with which families engage at the exhibits. The motivation for studying activity frames stemmed from researchers’ objective to help exhibit facilitators adopt strategies for fostering deeper and more extended family interactions at math exhibits (Pattison et al., in review; Pattison et al., 2017). Earlier attempts by the team to use the construct of sociomathematical norms to describe family behaviors at math exhibits were not successful and activity frames emerged as an alternative.

This research was founded in a qualitative, inductive, culturally-responsive approach to identify possible activity frames that might influence math reasoning behaviors at two math exhibits and inform future research in service of practice. This research was guided by two questions related to visitors’ approaches to the mathematical challenge(s) posed by an exhibit or staff facilitator:

1. What activity frames are at play during families’ interactions with the math exhibits?
2. How might different activity frames influence the nature and outcomes of families’
experiences at the math exhibits?

These questions were addressed by REVEAL partners, researchers and educators working in collaboration to review a sample of video data collected during a prior REVEAL study. For each of 20 videos, researchers produced high-level summaries of visitors’ mathematical approaches to the exhibit challenges, including shifts in approaches, as the basis for identifying emergent and relevant group behaviors among family members. Research team members followed a series of steps to describe specific behaviors in family members’ approaches to the completion of the mathematical challenge, and developed video summaries that included mathematical reasoning behaviors relevant to each exhibit as outlined in a rubric created in the prior REVEAL quasi-experimental study (Pattison et al., 2017; Pattison et al., in review). The rubrics capture 2 the essence and intentions of the unique challenges posed by the two exhibits used in this study, “Balancing Art” and “Drawing in Motion.” The first priority of this study was to identify and describe emergent and prevalent activity frames at play during families’ interactions at math exhibits. This report presents and illustrates six activity frames presented as contrasting pairs (a) Completing and Refining, regarding how families perceive the completion of a challenge; (b) Teaching and Exploring, related to the families’ perception of the activity as a didactic activity and/or as exploration; and (c) Competing and Collaborating, involving how a family perceives they have to work together at the exhibit. In most of the 20 videos, more than one of these activity frames was apparent at any given time.

As a second priority, the REVEAL team speculated on these frames’ influence on the intended nature and outcomes of the math challenges posed by the exhibits. This study was not designed to capture correlation or causation between activity frames and mathematical outcomes, but utilizing the mathematical rubrics to view the activity frames begins to suggest relationships among activity frames and how exhibit designers and educators might intend for visitors to approach the exhibit. For instance, the mathematical reasoning rubrics for the two exhibits studied here prioritize iteration, accuracy (balance or intended line slope), exploration (multiple strategies) and collaboration (the family is the unit of analysis), among others. Identification of possible relationships between activity frames and mathematical reasoning behaviors could provide a basis for additional research to further understand this connection. As a service to practice for exhibit facilitators, these research findings are presented in a REVEAL professional development module https://reveal.terc.edu/Educator+Resources; Andanen et al., 2017) that encourages awareness of activity frames and how they might impact families’ experiences at museums.