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Learning to Think Spatially: GIS as a Support System in the K-12 Curriculum http://www.nap.edu/catalog/11019.html SPATIAL THINKING IN EVERYDAY LIFE, AT WORK, AND IN SCIENCE 51 Preliminary Assembly continued from page 2. Pin Set E. 1. Take the ball & downrod and loosen the set screw in the ball. Remove the pin and the ball from the downrod. (If you have a longer downrod, use it now.) See Fig. 3 Fig. 3 F. 2. Feed the three wires from the top of the fan through the downrod and thread the downrod into the coupler. Align the holes in the downrod with the holes in the coupler. See Fig. 4 3. Insert the threaded pin and tighten it and the set screw. 4. Place the canopy around the downrod. Slide the ball onto the downrod and replace pin. See Fig. 5 5. Raise the ball so that the pin is in the slot and tighten the set screw. See Fig. 6 6. Make sure all of the screws are tight. At this time you may want to shorten the wires from the fan to 6" from the ball. This helps when you tuck the wires into outlet box. 1. Insert the two (2) Canopy Screws into Hanging Bracket loosely. Fig. 7 WARNING – To Reduce The Risk Of Fire, Electric Shock, Or Personal Injury Mount Fan To AN Outlet Box Marked “Acceptable For Fan Support” And Use The Mounting Screws Provided With The Outlet Box. 2. Take the hanging bracket and secure it to the outlet box (marked Acceptable for Fan Support) using the mounting screws provided with the outlet box. Tighten them evenly. If you are mounting the fan directly to the building structure, use the wood screws provided, and secure to a joist. 3. Make sure all of the wires are accessible and are not being pinched. Also, make sure the bracket doesn’t wobble. To begin with, the site of installation must be clear of any obstructions. Walls, cabinet or cupboard doors, and AC/heating vents (strong air currents will cause fan to wobble) are common obstructions. Also, you will need a securely mounted outlet box that is listed for fan support. Fig. 6 Fig. 4 The only tools you will need are: A medium Phillips screwdriver, common sense, and a little caution. FIGURE 3.1 A set of instructions for installing a ceiling fan. Note the appeal to common sense and caution. apartment. A trip to a supermarket to stock up on food for the refrigerator requires getting verbal driving directions from a neighbor, remembering and following them, and finding where things are located in a store that is organized in ways subtly different from the one that the family is used to. A written grocery list has to be mapped onto the floor plan of the supermarket in an efficient way. To amuse a younger child on the journey home, someone has to help her to put together pieces of a complex jigsaw puzzle. The journey home is complicated by the need to make a detour around construction that was not marked on the downloaded route map. It is also complicated by a flat tire: replacing it with the spare requires understanding the instructions on the side of the jack, removing the bolts and the wheel, and then tightening the bolts in the correct direction and sequence. Returning home, another son is asked to take over lawn mowing duties and has to find an efficient way to maneuver around flower beds and trees in the garden. The youngest child’s shoelace has come undone and there is yet another lesson in how to tie a shoelace properly, a double knot this time. The costume for the middle daughter’s school play has to be cut from fabric, fitted, and sewn by tomorrow’s dress rehearsal. Everyday life is impregnated with tasks that, on the surface, are routine and trivial. Viewed as problems requiring solutions, these tasks are far from trivial in nature. All of the tasks involve the Copyright © National Academy of Sciences. All rights reserved. Fig. 5 Fig. 7
Learning to Think Spatially: GIS as a Support System in the K-12 Curriculum http://www.nap.edu/catalog/11019.html 52 LEARNING TO THINK SPATIALLY concept of space in general and various spaces in particular: global time-space, car trunk space, neighborhood space, supermarket space, room space, machine space, puzzle space, garden space, the space of shoelaces, and the space of dress patterns. Many of the tasks involve graphic representations: the time zone diagram in the telephone directory, the web search engine map, the floor plan of the supermarket, the grocery list, the picture of the completed jigsaw puzzle, and the dress pattern. All tasks involve complex sequences of operations: finding the clock times of the two places and subtracting the right one to work out the time difference; choosing boxes of the right size for the space available, orienting and rotating them, and stacking them; rotating parts, twisting parts, and tightening fastenings; breaking an operation into discrete parts and demonstrating and explaining the operations; making a loop with one lace, putting the other part of the shoe lace over the top of the loop, and so forth. Some of the tasks can be taught formally, such as map reading, whereas others, such as dress making, are no longer taught formally in schools, and still others, such as tying shoelaces, are learned informally as part of everyday life. There is transfer of learning from one task to another; jigsaw puzzles and exercise machine assembly have things in common. Tasks can be performed in different ways. The web search engine offers three different representations: lists of text instructions, maps with straight-line segments, and conventional road maps. Strategies for solving jigsaw puzzles differ: some people sort straight edge pieces first, then match by shape. Others use color and patterns to make decisions. Some performance differences are significant and lead to faster and more efficient solutions: others, especially shoelace tying styles, are matters of preference (single versus double knots). There are differences based on age and sex in solving problems. Some people approach the trunk-packing task analytically, gauging the dimensions of boxes and thinking about alternative arrangements; others plunge ahead, using trial and error. For many activities, we are not consciously aware of spatial thinking; in other instances, the challenge is explicit and we monitor our own process. 3.3 SPATIAL THINKING AT WORK Spatial thinking at work begins before work, during the daily challenge of commuting. Many drivers simplify the complex two-dimensional plane between home and work to a line that contains a sequence of turns at landmarks. The rest of the environmental context is not relevant to the task of commuting and therefore is largely ignored during the commute. The path, specifying where to turn and which direction to take, is crucial. As a consequence, people pay more attention to landmarks that mark changes in direction, and they remember those landmarks better than other places along the route (Tom and Denis, 2004). The cognitive importance of landmarks and turns is reflected in neurophysiology. Using brain imaging technology, researchers have shown connections between cognitive processes and brain functioning (Aguirre et al., 1998; Maguire et al., 1997). There is a greater neurophysiological response to landmarks signaling turns than to landmarks that are simply en route in those areas of the brain underpinning the construction of mental maps (Janzen and van Turennout, 2003). These areas of the brain are larger in people who are expert at navigation, such as London taxi drivers who undergo considerable training before they are allowed to pursue their profession. Neurophysiological findings suggest that extensive spatial experience may lead to physical changes in the brain that may, in turn, further enhance spatial thinking. Experienced taxi drivers have more extensive and detailed mental maps of the areas they service than do ordinary residents. Nevertheless, taxi drivers’ mental maps are simplified in the same ways as those of regular commuters. For example, taxi drivers think about the main arteries of a city as being straighter and more aligned with cardinal directions than they actually are. This illustrates an important characteristic of expertise. Expertise draws on the same mechanisms as Copyright © National Academy of Sciences. All rights reserved.
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