How Dynamic Gestures and Directed Actions Contribute to Mathematical Proof Practices

High school students need to know how to produce geometric proofs, a skill essential for advanced mathematical reasoning and future studies and work in STEM fields.

This project explores how teacher-directed body movements and speech shape high-school students' geometric proof production.

Researchers will determine:
how simulated action (i.e., students' speech and gesture production) informs students' understandings of the proof process;
whether and how students’ task-relevant actions lead to improved mathematical insights and proof practices;
how teachers’ prompts to connect actions to mathematics 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.

This research takes place in high schools and colleges in urban and suburban areas of Texas and Wisconsin.

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 student population is racially and ethnically diverse and includes a large proportion of students who qualify for free/reduced-priced lunch.

For each study, the primary outcome measure is whether students formulate accurate proofs or recognize key mathematical insights to geometric conjectures.