This article is devoted to the re-examination of extended surface heat transfer basic treatment that appears in heat transfer textbooks. It demonstrates that--unlike what is suggested in textbooks--the emphasis on efficiency should be shifted to effectiveness instead. Graphs display how the heat dissipation of a given fin is directly obtained without any reference to the efficiency, which is now the standard approach, and total effectiveness is proposed to replace the total efficiency. It is further shown that the effectiveness approach aids in verifying some of the simplifying assumptions and shows that extended surfaces must be thermally and geometrically thin in order to fulfill their function. The results of a brief excursion to the optimum fin problem will help students become involved in a preliminary fin design, a topic conspicuously absent from many textbooks. Three postulates extend certain results of the unidirectional analysis of the constant thickness fins to other shapes and two-dimensional problems.