The following HTML text is provided to enhance online
readability. Many aspects of typography translate only awkwardly to HTML.
Please use the page image
as the authoritative form to ensure accuracy.
Learning To Think Spatially
Experts in one application of spatial thinking, such as architecture, may not find those skills useful in another application of spatial thinking, such as interpreting weather maps, because the representations and their underlying scientific principles are different. Clement (1998), for example, asked expert mathematicians to interpret visual displays of the behavior of springs varying in diameter and flexibility. The mathematicians behaved similarly to students encountering the material about springs for the first time (Clement, 1998). Lewis and Linn (1994) reported similar results when they asked expert chemists and physicists to explain everyday phenomena that exemplify principles that they understand well. One expert, for example, preferred aluminum foil over wool as an insulator because it is a common practice to wrap cold drinks in aluminum. Expertise is, therefore, domain specific. Expertise takes significant time to develop in depth.
4.3.2Developing Expertise Through the Understanding of Representations
Educators often devise new representations to help novices. Tests of these representations in contexts as diverse as weather maps (Edelson et al., 1999), molecular models (Linn and Hsi, 2000; Wiser and Carey, 1983), and the rock cycle (Kali et al., 2003) have proven humbling. Students cannot readily interpret diagrams and representations (Hegarty et al., 1999), and when they attempt to use them, they often become more, rather than less confused. Students have interpreted representations of heat that use color intensity as implying that heat has mass, for example. Most commonly colored weather maps show only the predicted weather on land rather than showing the weather patterns as extending over the oceans. The maps also show weather only over the United States rather than extending into both Canada and Mexico. Such representations can deter students from thinking about the weather as large-scale, complex systems influenced by differential surface temperatures over land and water (Edelson et al., 1999).
4.3.3Developing Expertise Through Challenging Projects
Interpretations of the superficial features of spatial information can persuade students that scientific phenomena follow different principles from those endorsed by experts. For example, novice observers of geological features such as rock outcrops, streams, or basins may impute formation processes that consider only surface features (Liben et al., 2002). Novice observers of patterns—the flight of flocks of birds or the flow of traffic—impute more causality to individuals and their actions than is justified (Resnick, 1994). Observers typically believe, for example, that a lead bird has special status, or that all traffic jams are caused by accidents, rather than recognizing the systemic nature of emergent phenomena (Resnick, 1994). Understanding can be improved by instructional programs that enable students to build models of these phenomena by embedding “instructions” in individual birds or cars and then observing the emergence of patterns.
Students pay attention to perceptual information that is salient but not necessarily relevant (Hegarty, 1992; Lowe, 2003; Morrison et al., 2002). To overcome distracting perceptual cues—when they are inevitable—students need supports including ways to structure information and opportunities to reflect in order to make connections among ideas (Reiser et al., 2001; Davis, 2003a,b; Linn and Hsi, 2000). Curriculum designers have identified ways to direct attention to important information using everything from overlays to simplified versions of the materials to translating the information into less complex representations.
To enable students to develop expertise in spatial thinking, it makes sense to engage them in extended projects that are challenging. In science, however, most students flounder when asked to undertake complex, multistage projects where they must manage and sequence multiple tasks: design methods for collecting data; devise representations for information; and combine principles, experimental results, and representations of results (Edelson, 1999; Feldman et al., 2000; Reiser et