The Development and Assessment of Cross-Sectioning Ability in Young Children

The Development and Assessment of Cross-Sectioning Ability in Young Children Kristin R. Ratliff (krratliff@uchicago.edu) Charlotte R. McGinnis (cmcginnis@uchicago.edu) Department of Psychology, 5848 S. University Ave. Chicago, IL 60637 USA Department of Psychology, 5848 S. University Ave. Chicago, IL 60637 USA Susan C. Levine (s-levine@uchicago.edu) Department of Psychology, 5848 S. University Ave. Chicago, IL 60637 USA Abstract In two experiments, we investigated the development of cross-sectioning ability using either three-dimensional (3D) or two-dimensional (2D) stimuli. Three to 9 year old children visualized cross-sections of either real 3D geometric shapes (Experiment 1) or 2D photographs of the shapes (Experiment 2). Performance on the 3D task was also analyzed to determine to what extent cross-sectioning ability is related to performance on more widely used spatial tasks including mental rotation and the water-level task. We found that performance on the cross-sectioning and mental rotation tasks were significantly correlated, and the 2D and 3D tasks were both successful in assessing cross-sectioning ability in young children. As expected, we also found a significant increase in cross-sectioning performance across age groups. Key Words: spatial development; cross-section; education. Introduction Spatial ability is important for success across a variety of academic subjects, particularly in the science, technology, engineering, and mathematics (STEM) disciplines. Spatial ability is also related to choosing technological and science- related careers and predicts the choice of math and science as college majors (Shea, Lubinski, & Benbow, 2001), as suggested by the fact that individual differences across verbal, quantitative, and spatial abilities at age 13 were predictive of educational and vocational group membership 20 years later. However, despite the importance of spatial ability, spatial training is not a regular part of school curricula and there are no national or state standards for spatial intelligence. Consequently, many students have difficulty with spatial tasks and lack the opportunity to improve their spatial reasoning skills. Spatial ability can refer to a wide range of skills, some of which focus on how individuals perceive and act on objects in space while others focus on how individuals orient and navigate within space. One category of spatial ability of particular interest is spatial visualization, or the ability to understand, mentally encode, and manipulate 3D forms (Carroll, 1993; Hegarty & Waller, 2004). Cross-sectioning, also referred to as “penetrative” thinking (Kali & Orion, 1996) is a particular spatial visualization skill that involves inferring a 2D representation of a 3D structure, and vice versa (Cohen & Hegarty, 2007). This imaginary slicing of a 3D object to a 2D plane is an essential skill for many of the sciences, ranging from anatomical cross-sections in biology and neuroscience to cross-sections of landforms in geology (Cohen & Hegarty, 2008). Conversely, in order to understand what is under a microscope, students must also be able to mentally reconstruct a 3D object from a given 2D image. Spatial visualization requires performing multistep manipulations of spatial representations, such as a paper- folding task that requires the ability to work quickly, rotate figures, and keep track of multiple operations. This is thought to be distinct from other spatial tasks such as spatial perception and mental rotation (Linn & Petersen, 1985). For example, the water-level task, which requires subjects to draw a horizontal line in a tilted bottle where they believe the water level would be, is categorized as a spatial perception task because it requires determining spatial relationships with respect to a given frame of reference. Linn and Petersen define mental rotation as a Gestalt-like analogue process that involves accurately mentally rotating a 2D or 3D figure. However, the development of cross- sectioning ability has not been compared to these other measures of spatial ability, in part because of a lack of adequate measures and the unknown age at which this ability emerges. Thus, we do not know whether it is more related to spatial visualization, spatial perception, or mental rotation. Cross-Sectioning Ability of Young Children There is disagreement about the age at which children are able to reason about cross-sections of 3D objects. In contrast to Piaget and Inhelder’s (1956) view that children should have achieved mastery of geometric sectioning by 12 years old, many studies have found that spatial visualization involving cross-sections does not develop until the teenage years. For example, most students do not accurately predict the appearance of a geometric plane intersecting a simple cone or sphere until sometime between the ages of 11 and 15 (Russell-Gebbett 1984, 1985), while even students in grades 8, 10, and 12 have difficulty accurately choosing a cross-section of simple geometric line drawings (Boe, 1968; Davis, 1973). The difficulty older children and adolescents have with these assessments may be in the presentation of the test