Co-Principal Investigator: Nathan, Mitchell

Purpose: The purpose of this project is to explore how the interaction between collaboration and multisensory experiences, referred to here as collaborative embodiment, affects students' geometric reasoning through the use of augmented reality (AR) technology. This research is significant because theories of embodiment are needed that take into account the multi-learner nature of mathematics classrooms and how learners can jointly embody mathematical ideas using different modalities. In addition, recent advances in multi-user instructional technology (including shared holographic AR) allow for new and important hypotheses about collaborative embodiment to be tested. The research team hypothesizes that different modalities for math learning (like a hologram, a set of physical manipulatives, a dynamic geometry system (DGS) on a tablet, or a piece of paper) have different affordances, including the degree to which they can represent dynamic transformations, represent objects and operations in 3 dimensions, support joint attention, and provide situational feedback.

Project Activities: Researchers will develop an experimental platform modeled after the Flatland novella that will facilitate data collection from students, situate experimental tasks in an engaging narrative story, and allow for the researcher to control key experimental variables. The overarching research questions that will be explored via this platform are (1) How do different modalities for collaborative embodiment, particularly shared AR, impact student understanding of geometric principles? And (2) how are these effects mediated by gesture, language, and actions, and how are they moderated by student and task characteristics?

Products: The research team will generate information about the malleable factors, mediators, and moderators associated with collaborative embodiment in the domain of geometric reasoning. They will share their results via conference presentations and peer-reviewed publications.

Structured Abstract

Setting: This research will take place in high schools in Texas and Wisconsin and in a university in Wisconsin.

Sample: This research will sample urban high school students enrolled in a college access program in Texas where the majority of students are racial/ethnic minorities, high school students in an urban Title I Wisconsin school where the majority of students are economically disadvantaged and the plurality are racial/ethnic minorities, and college students in Wisconsin. Study 1 will involve 160 undergraduate students from Wisconsin, Studies 2 and 3 will involve 190 high school students from Texas, and Study 4 will involve 9 intact high school geometry classes in Wisconsin and Texas.

Factors: In Studies 1, 2, and 4, researchers will examine how different modalities (e.g., AR, DGS,manipulatives) impact student outcomes, as mediated by students' use of action, language, and gesture, and moderated by student and, in Study 2, by task characteristics, too. In Study 3, the team will also look at how different collaborative configurations (e.g., individual work versus parallel collaboration versus joint collaboration) impact their mediators and student outcomes.

Research Design and Methods: Students will be assigned to different conditions individually or in pairs using a randomized block design. In Study 1, the research team will compare DGS use to no materials and working individually to. collaborative learning. In Study 2, researchers will compare shared AR to a DGS, for tasks involving both 2D and 3D shapes. In Study 3, they will compare three different configurations of collaboration in shared AR (parallel, observer, joint). In Study 4, the team will assign pairs of students to 4 conditions in a 2 by 2 design that contrasts dynamic (DGS, shared AR) with non-dynamic modalities (paper/pencil, manipulatives), and 3D (shared AR, manipulatives) with 2D modalities (DGS, paper/pencil).

Control Condition: In Study 1, the control will be a condition where students receive no materials. In Study 2, the control condition will be a DGS. In Study 3, the control is a parallel collaboration condition. In Study 4, the control is a pencil-and-paper condition.

Key Measures: The key outcome is whether students successfully formulate intuitions, insight, and proofs for geometric conjectures. Key mediators include whether students use different kinds of gestures, actions, and speech categories. Key moderators include geometry pretest score and spatial test score.

Data Analytic Strategy: Researchers will fit mixed effects logistic regression models predicting student outcomes (intuition, insight, proof), with conjecture and participant as random effects. Experimental condition will be a fixed effect, and the team will look at the interaction of condition with moderators. In addition, the project team will conduct causal mediation analyses using gesture, speech, and action variables.

Related Project: How Dynamic Gestures and Directed Actions Contribute to Mathematical Proof Practices (R305A160020)