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Have you ever seen a car that has been in an accident and tried to imagine what happened? Often it is possible to work backwards from the current shape of an object to deduce what happened to it, e.g., a head on collision with a tree. This reasoning requires a spatial cognitive skill - a mental transformation of an object. Mental transformation refers to the ability to alter an internal representation of an object in order to imagine what that object used to look like before some event or what it might look like in the future.

We are studying how people develop this skill. One avenue of our research has been to study mental transformation in experts. Strong mental transformation skills are essential in the field of geology. Geology is a historical science that takes what is observable and tries to deduce what has happened over time to result in the current state of affairs. In particular, geologists use the present spatial relations to figure out what transformations have occurred. This mental reasoning may take place at many scales, from tectonic to microscopic. For example, field geologists study the deformational history of rocks and regions by studying the spatial configuration of geological features in an outcrop and how they fit with other observations in a surrounding area. Just as the bent and rent metal of a car tells a story, so too the geological history is revealed by the bends and breaks, folds and faults, in rocks. (see fig. 1).

The current line of research aims to understand how expert geologists reason about mental transformations. Geologists self-report that they look at an outcrop and play back in their mind the sequence of transformations, mentally animating the transformations from the present spatial configurations back to horizontal sedimentary layers. An initial study examined if geologists are objectively able to make such mental transformations, and, if they are, is the skill domain specific or domain general. Previous studies of chess expertise (Chase & Simon, 1973) suggest that expert reasoning is domain specific, in which case geologists should only be able to perform mental transformations on objects that have been altered in geologically relevant ways. In contrast, if geologists are able to perform mental transformations on any object independent of the type of alteration it suggests they have a domain general skill.

Geologists (n=16) were compared to two control groups from other academic fields. All groups had the same level of education (Ph.D.). One control group came from another science that requires spatial reasoning (Chemists, n=14) and one that requires verbal reasoning (English Professors, n=10). The participants were presented with words that were transformed in one of three ways, and asked to identify the word. To make the task more demanding additional characters were added in between each letter of the word (see fig. 2). Words were broken up into pieces along diagonal lines. These pieces were translated as if faulted (see fig. 3) or were randomly displaced (see fig. 4).

Geologists were significantly better than both control groups suggesting the geologists have a domain general ability to make mental transformations that is superior to novices (Shipley et al, 2009). One explanation for this skill is that geologists are particularly good at disembedding - finding and attending to specific structures within a complex array. We tested this with another set of words where the transformation separated all of the pieces making it easier to see which pieces belonged together and thus mentally undo the transformation (see fig. 5).

All three groups performed better on these words, however Geologists still outperformed both control groups. This finding suggests that while disembedding is helpful for this task, it is not the sole explanation for the Geologist’s skill.

Geologists report that students often have trouble mentally transforming spatial structures. By characterizing this skill, we should be able to help educators provide students with strategies for visualizing such transformations. However, it is not yet clear what about geoscience education produces this skill. Future studies will examine how mental transformation skills develop, and study its importance for student retention and achievement.

References

• ♦Chase and Simon. (1973). Perception in Chess. Cognitive Psychology, 4.
• ♦Shipley, T., Manduca, C., Resnick, I. & Schilling, C. (2009, November). Expertise in Spatial Visualization: Can Geologists Reverse Time? Psychonomic Society, Boston.

LINK TO PRESENTATION:
Breaking the Mold: Altering Preschoolers’ Concepts of Geometric Shapes

Children’s early shape concepts represent the building blocks for later mathematical knowledge (Clements & Sarama, 2007). As preschoolers begin labeling shapes in their environment, they must distinguish features and patterns and create abstract categories of each shape. Yet young children find this very difficult! Preschool children start out categorizing shapes by visual similarity and orientation irrespective of geometric properties (Burger & Shaughnessy, 1986). These concepts are global and holistic in nature, in which the most salient shape properties bind together to form an overall feature or a ‘gestalt view’ of each shape (Ganel & Goodale, 2003; Keil, 1989; Smith, 1989; Tada & Stiles, 1996). For instance, the angle on top of a typical triangle is the most distinguishing feature and thus defines the overall concept for the child (e.g., triangles have a point on top and wide horizontal ‘bottoms’). If children see a triangle that is turned on its side or has irregular angles (e.g., obtuse, scalene triangles), they will say it is not a true triangle. Only later do they shift to rule-based classification systems that rely on the number of sides or angles for shape identification (Clements, Swaminathan, Hannibal, & Sarama, 1999; Keil, 1989).

In a series of studies we explore how different learning experiences influence children’s developing shape concepts. In one such study, we examine how dialogic inquiry (i.e., questions that pose a dilemma/prompt curiosity) and physical exploration influence preschool children’s shape learning.

Preschool children were randomly assigned to one of three groups. In guided play, the experimenter helped children ‘discover’ each shape’s features by asking questions and prompting physical exploration of circles, triangles, rectangles, and pentagons (+dialogic inquiry, + physical exploration). In direct instruction, children were taught rule-based classifications for shapes in a passive learning style (- dialogic inquiry, -physical exploration). In the control condition, children participated in a dialogic reading activity for approximately the same amount of time as the shape lessons. To assess shape knowledge, groups were asked to complete a shape sorting task (Satlow & Newcombe, 1998). Children were shown 10 novel instances of typical, atypical, and nonvalid forms of each shape (40 total) and asked to place ‘real’ instances of each shape in a special box and the ‘fake’ shapes in a trashcan.

To determine the extent children’s category decisions were guided by rule-based classification systems versus visual similarities, rates of rejection were calculated across typical, atypical, and nonvalid shapes. As hypothesized, children in the control condition appeared to rely on visual similarity when sorting shapes, signified by small rejection rates of typical shapes and larger rejection rates for atypical and nonvalid shapes (see Figure 1). Conversely, children in both experimental conditions used rule-based classification systems to sort shapes, indicated by small rejection rates for typical and atypical shapes. Also, guided play showed a slight advantage over direct instruction. In Figure 2, guided play and direct instruction appear equal in learning outcomes for simple, familiar shapes (e.g., circles), yet children in the guided play condition showed significantly superior geometric knowledge for a novel, highly complex shape (pentagon).

These results suggest both direct instruction and playful learning approaches promote rule-based shape concepts; however, guided play may be more advantageous for complex concepts. Future research should explore how guided play may facilitate knowledge acquisition and concept formation for complex concepts in other domains. Additional research should explore the differential impact of dialogic inquiry and active exploration on the learning process.