Iconic mapping

Spencer, C., Harrison, N., and Darvizeh, Z. (1980). The development of iconic mapping ability in young children. International Journal of Early Childhood, 12, 57-64. 

View the contour map m several planes to see the general Torm of the distiibiiiioii. As long as you don t alter the molecular coordinates, you don t need to repeat th e wave function calculation. Use the left mouse button and the IlyperChem Rotation or Translation tools (or Tool icons ) to change the view of amolecnle without changing its atomic coordinates. 

Because the images in this chapter are reproduced in black and white, some of the information they are intended to portray has been lost. This is especially true for property maps, where a spectrum of colors is used to convey the value of a particular property. All images in this chapter have been provided as Spartan files on an accompanying CD-ROM. These are marked by an icon where 4 is the chapter number and y is the number of the Spartan file. 

These borders were all artificial in their origins, slicing various emergent ethnie in half and turning crucial crossroads and meeting places into remote peripheries of the new states. But in the twentieth century the boundaries impressed themselves on a new school-educated generation as fixed realities featured on the classroom maps. They became icons of the new nationalisms. 

Finally, the type of mapping described above is consistent with the constraints laid out in Gattis (this volume) for mapping between conceptual and spatial schemas. For example, the principle of iconicity constrains the mapping from the location and movement of the hands to the location and movement of objects described (whether abstract or concrete). Structural similarities constrain the mapping of relational structures, e.g., elements are mapped to elements (the hands to concepts) and relations are mapped to relations (the spatial relation of the hands is mapped to the relation of concepts, as in the poetry example). 

Unlike iconicity and associations, mappings of conceptual and spatial schemas based on polarity do not rely on perceptual resemblance, nor on previously experienced pairings between attributes and objects. Instead, polarity is based on the organizational structure underlying many perceptual and conceptual dimensions. Polarity constrains mappings of spatial and conceptual schemas when a spatial representation shares oppositional structure or directionality of dimension with the concept being represented. A simple way to envision this oppositional structure is as a continuum with asymmetrically weighted ends. 

While powerful, these three constraints—iconicity, associations, and polarity—do not fully account for the diverse mappings of conceptual and spatial schemas reported in studies of reasoning and interpretation of... 

Certainly it is the case that many representations are influenced by more than one form of similarity between concepts and spatial representations. Isotypes, for instance, are a form of bar graphs in which the bars are made of multiple icons of a commodity, such as barrels of oil (see Neurath, 1936, and Tversky, this volume). Within an isotype, the icons are a uniform size, and represent a uniform quantity. A bar composed of a large number of icons (relative to another bar) conveys more redundantly via at least two constraints. More oil barrows, for instance, communicate more oil via iconicity, and the greater vertical extent of the bar communicates more via the association between quantity and area. The interpretation of such a graphic could also be constrained by polarity, with the weighted continuum of big and small mapped to the continuum of more and less. 

A third plausible relation between the four constraints, which is also consistent with the results of Gattis and Holyoak is a hierarchical relation, perhaps with iconicity at the bottom and structural similarity at the top. A hierarchical view would predict that iconicity exerts an influence on mapping if it is the only similarity present, or if it is consistent with the higher-order constraints. In this view, structural similarity would be able to override any conflicting mappings created by iconicity, associations, or polarity. 

Iconicity constrains mapping when the spatial representation maintains some perceptual characteristics of the object or set of objects it represents. Associations constrain mapping when the spatial representation shares some properties with the object or concept being represented. 

ShowMe displays a correct plan of the solution.7 It first presents all the needed icons and all links that connect them. It subsequently focuses on each icon, one at a time, displaying its diagram in the Mapping Area Window with the correct elements already mapped. The student controls the speed with which the plan is shown by pressing the mouse button. 

The two windows on the right half of the screen contain visual displays solely upon student request. The top one is the Mapping Area Window. It can be entered by the student only when he or she has already placed at least one icon in the Student Work Area and has requested the Map option. Immediately below the Map-... 

One of its unique features is that PSE allows the student to make a visual model of the problem using the icons. It is a nondirective system, and it provides no feedback (except to check for the correctness of the final solution when the student desires). The student is free to explore the domain in any way that he or she chooses. While solving a problem, the student makes several decisions, such as opting to select other icons, to examine an already-selected icon more closely, or to ask for help. The student works at his or her own pace, moving back and forth between the Student Work Area and the Mapping Area to modify and confirm the situational elements found in the problem. 

Map. Whenever the student requests that an icon be displayed in the Mapping Area, this event is recorded, together with the name of the icon and its original ranking. The ranking is an important piece of data because it is possible for a problem to have two instances of the same situation (e.g., two Vary situations such as 2 pounds of cheese for 3.50 per pound and 3 quarts of milk for 99 cents each). PSE must keep track of which of these is mapped, modified, and/or linked to other situations. 

If successful in the initial (or revised) mapping, the student returned to the icon menu and selected another icon with which to work. At this point, two different strategies appeared. Some students immediately linked the two icons. Others performed a second mapping before attempting the linkage. 

More often, students displayed some uncertainty. In a few cases, this showed up in the PSE record as an aborted call to Link, with the student making the menu selection but failing to specify how to connect the two icons. Instead of trying anew to make the connection, the student opted to map the second icon, returning to link the icons after the mapping was completed. 

The majority of students made no attempt at linkages until problem elements had been mapped into both diagrams. Occasionally, a student went so far as to place the correct answer in the Final Answer Window. However, the student did not selea Done, the signal for PSE to check the correaness of the answer, until he or she had made the explicit link between icons. 

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