Teaching Creativity in a Technological Design Context* KEES VAN OVERVELD, RENEÂ AHN, ISABELLE REYMEN and MAXIM IVASHKOV

ion in upward direction in the subsequent rows of Table 1. This table shows some aspects of using dialectics in design practice: . Notice that in this table, at every subsequent row the new thesis equals the previous synthesis. This is conforming Hegel's formulation of dialectics. In every new row, one new (thus far `hidden') attribute is introduced, and one previous attribute looses its distinguishing value. . It is very tempting to wander off into abstraction. Soon, however, one arrives at a concept labelled `everything', i.e., no attribute has a distinct value anymore. The lower most few rows of the table, however, won't be relevant in any practical context. The art (and the challenge!) of using dialectics is to use small steps of abstraction, and to keep a constant eye on the purpose. In the current case we didn't mention this purpose before hand; a possible purpose could be the extension of a product portfolio of a pencil manufacturer. Obviously, it then depends on the existing expertise, the production facilities, the market situation, etc., which abstractions are meaningful and which are not. At any time, we have the choice to proceed in three directions: . into increasing abstraction (as with the subsequent rows in the above table; in the diagram below, these are the upwards arrows in Fig. 4); . explore at the same level of abstraction (i.e., consider as much as possible hidden attributes of the current formulation of the concept, as we did in the bullet list above the table. In Fig. 4, these are the sideways arrows); or . to decrease the abstraction by considering the current concept as the root node of a hierarchy (in Fig. 4, they would correspond to recursive hierarchical partitioning according to the method under Hierarchy). . We observe that a hierarchic structure is a special case of a dialectic structure. (Indeed, a hierarchical partitioning is strictly top-down, whereas a dialectic structure allows expansion in all directions. Further, notice that a hierarchical structure doesn't necessarily requires a brainstorm as bootstrapping device. After some experience has been gained by hierarchically ordering the results from a brainstorm, one can start to suggest hierarchically ordered attributes, instead of proposing concepts in a brainstorm session, right away). We schematically depict part of the result of a dialectic session in Fig. 4. Compare this with the hierarchical partitions as discussed above. Notice that here nodes in the network refer to individual concepts, similar to the abstract concepts that were associated to the partitions under Hierarchy. Again we have a hierarchical (abstraction) relation between `synthesis'-nodes and the underlying `thesis'and `anti-thesis nodes'. Summary of the structured creativity methods The method of dimension lifting is mainly a didactic introduction to the usage of productive Fig. 4. schematic view of dialectics as a means to (partially) cover the option domain with a network of attributes and concepts. Concepts on one layer (say, levelˆ n) are at the same abstraction level. One layer higher, say n‡ 1, means one abstraction level higher (ˆone more degree of freedom). Attributes that are introduced in layer n have an underdetermined value in that layer; they have unique values in all layers hn, and they do not apply in layers in. For simplicity, we only give one anti-thesis per thesis; in general, however, there will be multiple attributes, and for any attribute, multiple values that all generate anti-theses. Also, expansion can occur in top-down direction. K. van Overveld et al. 268