I3T: Using Interactive Computer Graphics to Teach Geometric Transformations

Abstract

Geometric transformations play an important role in a vast variety of disciplines. Although they belong to the fundamental concepts, they are also difficult to comprehend. Thousands of students take courses of algebra every year and although they may conceptually understand the transformations and mechanically solve the presented problems, they often struggle in visualizing the effect of the transformation on 3D objects represented as matrices. We explored the hypothesis that using interactive 3D computer graphics to visualize the transformations has its learning benefit.We have developed a novel framework for interactive 3D transformations called Interactive 3D Transformations (I3T) that allows for exploring and visualizing immediate effect of 3D transformations on rigid objects. We tested nine graduate students with I3T and compared them with the control group of another nine participants that used traditional passive methods. Moreover, we have tested the students spatial abilities by using a standardized test and we have evaluated how this affects their ability to comprehend the 3D transformations. Overall results showed that students increased their understanding of transformations between the pretest and posttest in both groups. When comparing the two groups, although the mean score in the posttest was two times higher for the I3T group, it did not show that this was statistically significantly higher than for the Traditional Group. The written responses showed higher enthusiasm of the students who used the interactive tool as opposed to using the passive learning method.