            Problemsolving activity ancillary to the concept of area JOAA MAMOADOWS: University of Patras, Greece IOAIS PAPADOPOULOS: University of Patras, Greece ABSTRACT: This paper concerns the results of the second stage of a two tier program designed to enhance students' technique usage in area measurement. The first stage involves 11 year old students; certain techniques were didactically introduced with the dual purpose of cementing the concept of area and area preservation, and of giving the students tools for explicit area measurement (either exact or estimates). The second stage deals with the development of the same techniques, but the focus is not now primarily on the direct enhancement of the central concept (area) but on the re! assessing, re!examining and adapting of the techniques themselves. The paper reports on a case study concerning two 13!year old students' output analyzed from this latter context. Their work in particular shows several ways that they could refine the 'technique' of decomposition of plane figures. Key words: PROLOGUE Consider the following task: Given a triangle T with base a and height h, divide the triangle into three sub!regions such that the sub!regions can be re!positioned to form a rectangle, one side of which is a. Deduce the area of T in terms of a and h. The result is well known, but the method to obtain it might seem unorthodox. Lying this apart, simply suppose that you are asked about what domain is the task situated. From the perspective of the result, one might say area determination. From the perspective of the method, perhaps the re!arrangement of sub!regions forms the best candidate; in practical terms the concept of area takes a nominal role as long as some basic principles of area preservation are well understood. From the perspective of motivation, we come back to area determination; why should we be interested in the manipulation of the sub!regions unless it yields what we want? This example illustrates problem!solving activity that does not contribute to the enhancement of a concept that sponsors it, but at the same time it retains ties to that concept. This kind of situation we shall call ‘problem!solving activity ancillary to the concept’; we will expand on this idea, with its educational significance, in the next section.