Student Gestures and Penetrative Thinking

Overview of Penetrative Thinking in Geosciences

• Penetrative thinking is defined as the "ability to visualize the structure of an object from surface clues and project elements of that structure into the interior of a block or underground in order to make predictions about the location of individual elements at any arbitrary location or cross-section of that volume" (Alles and Riggs, 2011, p. 64).
• This skill is also known as visual penetrative ability (VPA: Kali and Orion, 1996).
• It is critical for success in many science disciplines, specifically the geosciences, where inferences about the Earth must be made from surface observations.
• Key geoscience concepts requiring penetrative thinking include:
  • Rock deformation.
  • Mineral structure.
  • Groundwater flow.
• Professional Application: Geologists use this skill in the field to predict how a structure visible at an outcrop (such as the strike and dip of tilted rock layers) extends into the subsurface to imagine their attitude at depth.
• Difficulty: Many students struggle with this because it requires making 3D inferences from 2D surface information and visualizing complex spatial relations.
• Malleability: Spatial skills, including penetrative thinking, are malleable (Uttal et al., 2013). Visualization training has been shown to facilitate the learning of geological content (Piburn et al., 2002).

The Theoretical Role of Gesture in Spatial Cognition

• Gestures are embodied representations of 3D spatial relationships and are more than just "hand-waving" (Goldin-Meadow, 2011).
• Research indicates that gesturing supports several aspects of spatial thinking:
  • Formation of Ideas: Gesturing helps speakers form and verbally articulate new ideas (Crowder, 1996; Roth, 2000). Crowder (1996) observed that 6th graders used gestures that foreshadowed ideas they would later articulate in speech when they were in the process of understanding new concepts.
  • Readiness to Learn: A student's gestures can reflect their readiness for new concepts. Ping et al. (2011) found that novice adults whose gestures added correct information to their speech (gestures-speech mismatch) showed improvement after instruction.
  • Attention Focus: Gesturing focuses attention on spatial information (Alibali, 2005; Alibali et al., 2011). Children (8-10 years old) produced more spatial information in speech when using gestures (Sauter et al., 2012).
• Representational Utility: Hand movements are 3D, allowing for the representation of 3D spatial properties of objects.
  • Geologists use 3D gestures to indicate the dip of a planar structure by tilting a flat hand (Atit et al., 2013).
  • Chemists use hands to represent molecules too small to see, using the whole hand for perspective visualization (Stieff and Raje, 2010) or fingers to represent protein loops (Becvar et al., 2005).

Study Methodology and Participants

• Participants: $92$ students from an introductory psychology class.
  • Demographics: $32$ men, $60$ women.
  • Mean Age: $M_{age} = 20.41\,\text{y}$.
  • Age Range: $18-36\,\text{y}$.
  • Major distribution: $36.9\%$ psychology majors, $21.7\%$ STEM majors.
• Justification for Subject Choice: Data suggested no overall difference in Geologic Block Cross-Sectioning Test (GBCT) performance between psychology students ($M = 4.15$, $SD = 2.35$) and undergraduate mineralogy students ($M = 3.60$, $SD = 1.9$).
• Group Assignments:
  • Gesture Group: $n = 33$ ($22$ women).
  • Gesture-Prohibited Group: $n = 25$ ($19$ women).
  • Test-Retest Group: $n = 32$ ($19$ women).

Materials and Measurement Tools

• Geologic Block Cross-Sectioning Test (GBCT): Measures the ability to visualize a cross-section produced by a specific cut through a 3D form (Ormand et al., 2013). Each version contains seven items matched for difficulty. Participants were given $4\,\text{min}$ per test.
• Vandenberg and Kuse Mental Rotation Test (1978): A redrawn version by Peters et al. (1995) containing $24$ items. Participants identify two identical but rotated 3D forms. Scoring requires both correct figures to be identified for credit (range $0-24$). Participants had $3\,\text{min}$ per part (two parts total).
• Intervention Diagrams: Seven cross-sectioning problems from the pretest, enlarged to $8.500 \times 11.00\,\text{inches}$ ($20 \times 28\,\text{cm}$).
• SET Card Game: A visual perception game used for the test-retest group to control for social engagement and attention without requiring penetrative thinking.

Experimental Procedure

• Pretest: All participants completed one version of the seven-item GBCT.
• Intervention (Gesture and Gesture-Prohibited Groups):
  • Students were shown three example block diagrams (fault, fold, tilted S-shaped fold).
  • Gesture Group: Asked "using your hands, can you show me how you would build this structure from flat layers of Play-Doh."
  • Gesture-Prohibited Group: Asked to sit on their hands and provide verbal explanations.
  • Experimenter Control: The experimenter provided one explanation using iconic gestures for both groups after their explanation (e.g., cutting layers diagonally and shifting one half for a fault).
  • Students then imagined slicing the block at a indicated line and had to show (gesture) or explain (prohibited) the angle and viewing direction.
  • Students predicted the order of layers from top to bottom.
• Intervention (Test-Retest Group): Played the SET game for a duration matched to the average time taken by the gesture group to complete the intervention.
• Post-test: All participants completed a second version of the GBCT with seven new multiple-choice problems. No restrictions were placed on gesturing during the pre- or post-tests for any group.

Statistical Results

• Mental Rotation Baseline: No significant difference among groups ($M_{gesture} = 8.09$, $M_{gesture-prohibited} = 8.44$, $M_{test-retest} = 8.84$). One-way ANOVA: $F(2,87) = 0.79$, Not Significant (n.s.).
• GBCT Improvement (Average Question Score Increase):
  • Gesture Group: Improved by $1.33$ questions.
  • Gesture-Prohibited Group: Improved by $0.76$ questions.
  • Test-Retest Group: Improved by $0.41$ questions.
• ANOVA Performance Analysis:
  • Significant pre-to-post-intervention improvement: $F(1,56) = 16.47$, $p < 0.01$, partial $\eta^2 = 0.23$.
  • Effect of group: $F(1,56) = 5.54$, $p = 0.02$, partial $\eta^2 = 0.09$.
  • Bonferroni-corrected post-hoc comparisons revealed significant improvement only for the gesture group ($p < 0.05$).
• The test-retest group did not significantly improve: $t(31) = -1.12$, n.s.
• STEM versus non-STEM in gesture group: No significant difference in improvement: $t(31) = -1.52$, n.s.

Discussion and Theoretical Implications

• Conclusion: Using gestures when thinking about 3D block diagram structures facilitates penetrative thinking, whereas verbal explanation or simple test repetition does not.
• Mechanism 1: Body-Based Representation. Embodying spatial relations through hands supports children (Ehrlich et al., 2006) and adults in mental rotation and translation tasks.
• Mechanism 2: Analogical Learning. Gestures may support analogical mapping between base objects (the hand/gesture) and target objects (geologic diagrams) because gestures contain the common spatial structure (Atit et al., in press).
• Mechanism 3: Cognitive Off-loading. Gestures may off-load the cognitive demand of 3D spatial reasoning by externally representing complex transformations (Goldin-Meadow et al., 2001; Wagner et al., 2004).

Educational Implications for Geoscience Instructors

• Textbook Survey: Analysis of four major introductory geology textbooks (Marshak, 2012; Smith and Pun, 2009; Reynolds et al., 2012; Tarbuck et al., 2011) showed that approximately $18\%$ of all diagrams are "volumetric block diagrams" (conveying information on two or three sides).
• Instructional Recommendations:
  • Instructors should develop an awareness of their own hand gestures while teaching.
  • Students should be explicitly encouraged to use their hands to think through 3D spatial relationships.
  • Gestures can be used to interpret topographic maps (e.g., shaping the hand over the map to convey land surfaces from elevation contours).
  • Gesturing provides a tool to build 3D representations slowly by aligning the hand with 2D diagrams.
  • Feedback is essential; as with sketching (Gagnier et al., 2013), feedback on gestures ensures students retain accurate conceptual models.