The effect of tools of a computer microworld on students' strategies regarding the concept of conservation of area

This study focuses on the role oftools, provided by a computer microworld,(C.AR.ME) on the strategies developed by14-year-old students regarding the conceptof conservation of area of a non-convexpolygon. Students' strategies on atransformation and a comparison task wereinterpreted and classified into categoriesin terms of the tools used for thedevelopment of these tasks. The analysis ofthe data shows that the nature of the toolsused affected the nature of solutionstrategies that the students constructed.Three different approaches to the conceptof conservation of area emerged from thestrategies which were constructed by thestudents in this microworld: the intuitiveapproach involving the splitting of areasinto parts and recomposing them to produceequivalent areas, the enclosing of thenon-convex polygon in a minimum convexsuperset and the dynamic transformationapproach. Most students managed to use theabove approaches in combination therebyviewing the concept of conservation of areaas interrelated with the concept of areameasurement using spatial units and areaformulae. Almost all students experiencedqualitative aspects of the conservation ofarea through being involved in the processof splitting areas into parts andrecomposing them to produce equivalentareas. Most students experienced dynamicrepresentations of this concept throughexploring it in a variety of equivalentareas. Moreover, most students explored theconservation of area in classes ofequivalent parallelograms and triangles andthis illuminated serious difficulties, mostof which were overcome in this computerenvironment. Finally, the analysis of thedata shows that all students were involvedin the tasks and succeeded in completingthem with more than one correct solutionstrategy thereby developing a broader viewof the concept, although not all of themused the same strategies. This revised version was published online in August 2006 with corrections to the Cover Date.