Abstract
This article investigates the effect of instruction on junior college students' assessments of the area of enlarged / reduced geometrical figures. The area of a figure enlarges by a k' factor when the original figure is enlarged k times. This "k-squared rule" follows from the formula (height × width = area), yet many students fail to estimate the area of an enlarged figure correctly. In this experiment, such operation was transformed into manipulation of material objects. The transformation is referred to as "materialization". In practice, students covered both original and enlarged figures with small round seals and counted up the seals on each figure. As a result, many students were able to estimate the areas of enlarged figures correctly, but they were not equally successful in the case of reduced figures and/or of enlarged figures where the length was given. These results suggest that the students still need to integrate their understanding based on material objects into the multiplicative rule.
