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Diagrams (a) and (b) below show two possible diagrams representing layering of mental spaces (represented by individual triangles). Sign, referent, and schema are denoted S, R, and C respectively. Dashed arrows represent projections (or mappings) of elements in mental spaces. In diagram (a), the same sign (S1) cues an associated schema (C1) in each layer, associated with three different referents (R1-3). In diagram (b), several signs associate with several schemata and referents. Here, schemata are compiled into increasingly complex schemata by way of blending. These schemata come to associate with new referents, followed by further blending. The different blends are connected via a sign that remains constant throughout each blend (in this case, S1). For example, consider case (a) with S1 a sine wave, associated with the same schema (C1) for each referent. This would be initially productive if R1 were a wave on a string, but could lead to inappropriate mappings if R2 were a sound wave (e.g., mapping transverse wave). The EM wave example described by Podolefsky and Finkelstein* is based on diagram (b).
© PER@C Group, University of Colorado, 2007
*N. S. Podolefsky & N. D. Finkelstein, Analogical Scaffolding and the Learning of Abstract Ideas in Physics: An example from electromagnetic waves.