Abstract
We introduce two kinds of approaches, a normative approach and a constructive approach, into design activities, and we characterize these two approaches in our mathematical formulation of design or education. And then, we show that there are significant relations between constructive approaches and emergent phenomena. Through analysis of constructive approaches and emergent phenomena, we give a way to represent results of emergent phenomena in our mathematical formulation of design or education. Moreover we analyze General Design Theory in our mathematical formulation of design, and we find a way to extend General Design Theory in order to deal with emergent phenomena in its extended frame.