Linear and Planar Features
At the end of this exercise, students will:
- Understand how the linear trace of a planar feature is related to the plane.
- Understand that they need information from at least two surfaces to accurately predict the orientation of planar features. That is, they will know that features do not necessarily go straight into a volume, and that there are an infinite number of possible orientations of planes with the same linear trace.
- Use different gestures to convey linear and planar information.
Context for Use
We use this exercise to accompany a lecture on fractures in an undergraduate Structural Geology course. However, it could be used in any situation where you want to emphasize to students that what they see on the surface (of a hand sample, an outcrop, a map, ....) does not necessarily go straight into the object.
Because it is the first gesture exercise in the course, we begin with a brief description of what we know from research about gesture as a communication and learning tool (Goldin-Meadow, 2011; in short, gesture supports communicating and learning about spatial concepts). We also have students spend a couple of minutes explaining to their partner how to navigate (on foot or by car) from their house to the high school they attended. We ask for a volunteer to sit on their hands and tell us how to tie a bow with a piece of ribbon. These two brief warm-ups highlight the value of gesture in communicating spatial information.
After students have completed the exercise, we remind them that research shows that gesturing will help them to learn spatial concepts, and explain that the mechanism for this is that gesture allows for cognitive offloading (Goldin-Meadow et al., 2001).
Description and Teaching Materials
In this exercise, students use a pointer finger to gesture the orientations of linear features and use their hands (open and flat) to gesture the orientations of planar features. In the first part of the exercise, students can only see one surface of a wooden block, and are asked to speculate about how planar features penetrate through the interior. Later, they uncover the other faces of the block and gesture the actual orientations. This uses embodied learning to help students relate surficial (2D) observations to 3D interpretations. A key goal of the exercise is to help students see that surficial features often do not go "straight in."
We made the wooden blocks for this exercise by cutting scrap 2x4s into cubes, roughly 1.5" per side. Then we drew two different "planes" on each block (in different colors). Each plane was oblique to the faces of the cube to emphasize that features often don't go "straight in." We covered all but one face of each block with two layers of blue painters' tape (because it is opaque and easy to remove). We made enough blocks for each pair of students to have one.
Gesturing Linear and Planar Features (Microsoft Word 2007 (.docx) 2MB May19 15)
We walk around the room, watching and talking with the students as they work through the exercise, to watch student gestures and to listen to their discussions.
References and Resources
Goldin-Meadow, Susan (2011). Learning Through Gesture. Wiley Interdisciplinary Reviews: Cognitive Science, v. 2, n. 6, pp. 595–607.
Goldin-Meadow, Susan, Howard Nusbaum, Spencer D. Kelly, and Susan Wagner (2001). Explaining Math: Gesturing Lightens the Load. Psychological Science, v. 12, n. 6, pp. 516-522.