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IES Grant

Title: How Dynamic Gestures and Directed Actions Contribute to Mathematical Proof Practices
Center: NCER Year: 2016
Principal Investigator: Nathan, Mitchell Awardee: University of Wisconsin, Madison
Program: Cognition and Student Learning      [Program Details]
Award Period: 4 years (7/1/20166/30/2020) Award Amount: $1,389,562
Type: Exploration Award Number: R305A160020

Co-Principal Investigators: Steiner, Peter M.; Walkington, Candace

Purpose: The research team will explore how directed actions—body movements that learners are instructed to formulate—and pedagogical language relate to high-school students' geometric proof production, a pre-college education topic essential for promoting advanced mathematical reasoning and future studies and work in STEM fields. The specific research aims include exploring how simulated action (i.e., students' speech and gesture production) informs students' understandings of the proof process; whether and how task-relevant actions students perform lead to improved mathematical insights and proof practices; how prompts to connect actions to mathematics further influence the quality of students' proof practices; and how observing, enacting, and creating arm motions for geometry learning impacts the speech, gesture, and proof practices of high-school students.

Project Activities: In Years 1 and 2, the research team will conduct two studies in each year to investigate the relationship between simulated action and proof performance. In Years 3 and 4, the research team will conduct one experiment each year to explore productive ways of supporting simulated action to support geometric proof production within high school classrooms.

Products: Researchers will provide preliminary evidence of potentially promising practices for improving students' geometric proof production and peer-reviewed publications.

Structured Abstract

Setting: This project will take place in high schools and colleges located in urban and suburban areas of Texas and Wisconsin.

Sample: Participants include approximately 168 college students (half math majors and half non-STEM majors) in Year 1, 152 high school students currently enrolled in geometry in Year 2, 76 high school students currently enrolled in geometry in Year 3, and 96 high school students currently enrolled in geometry in Year 4. The high school population from which the high school student sample will be drawn is racially and ethnically diverse and includes a large proportion of students who qualify for free/reduced-priced lunch.

Intervention: Due to the exploratory nature of this project, there is no intervention. The malleable factors studied here are directed actions and pedagogical language.

Research Design and Methods: The research team will conduct six studies over the course of the project. The research design for each study varies. The first two studies use a quasi-experimental design to identify differences between experts (college math majors) and novices (college non-STEM majors) in how simulated action supports proof performance. In these studies, college math majors and non-STEM majors will provide justifications for geometric conjectures (statements) while being observed to see how experts and novices differ in their use of simulated action. In addition, in the second study, participants' gestures will be inhibited for half of the conjectures to see how manipulating gesture production affects proof performance. In the remaining four studies, high school students will be presented with geometric conjectures within a motion capture video game that directs them to perform arm motions and detects their movements in real time. The first of these studies uses a between-subjects design, with students being randomly assigned to one of two conditions, to explore how pedagogical language affects proof performance. The remaining three studies use a within-subjects design to test (1) how the relevance of directed actions affects geometric proof performance; (2) whether students need to produce simulated actions themselves or if they can observe others producing them in order to benefit from simulated action; and (3) the potential for students to create tasks within the video game environment and whether this experience improves their understanding.

Control Condition: In the first two studies, novices (defined as college students who are non-STEM majors) will act as the comparison condition. In addition, in the second study, for all participants, gestures are inhibited for half of the geometric conjectures, which acts as a comparison to the remaining half of the conjectures where gesturing is allowable. In the remaining studies, the comparison condition varies as a function of the research question.

Key Measures: For each study, the primary outcome measure is whether students formulate accurate proofs or recognize key mathematical insights to geometric conjectures. Participants' prior knowledge will be measured through a researcher-developed test of geometry domain knowledge. Other measures include a researcher-developed measure of phonemic fluency and the Paper Folding Test from the Kit of Factor-Referenced Cognitive Tests. Using video recordings, the research team will also measure incidence of dynamic gestures and transformational speech.

Data Analytic Strategy: Researchers will fit logistic regression models using proof/insight performance (coded as 0/1) as the outcome, and condition as the predictor. The research team will also examine mediators such as incidence of dynamic gestures and transformational speech and moderators such as student demographics, phonemic fluency, and spatial visualization.


Journal article, monograph, or newsletter

Nathan, M.J. and Walkington, C. (2017). Grounded and Embodied Mathematical Cognition: Promoting Mathematical Insight and Proof Using Action and Language. Cognitive Research: Principles and Implications, 2(1).