Do realistic contexts and graphical representations always have a beneficial impact on students’ performance? Negative evidence from a study on modelling non-linear geometry problems

The aim of the present study was to investigate the influence of authentic contexts and of self-made graphical representations on students’ well-documented tendency to improperly apply the linear model to represent and solve non-proportional word problems about area and volume. A paper-and-pencil test on this kind of geometrical problems was collectively administered in different experimental groups of 13–14- and 15–16-year old students. Problem authenticity was experimentally enhanced for half of the students by prefacing the test by an assembly of well-chosen video fragments telling the story of Gulliver’s visit to the world of the Lilliputians and by linking all test items directly to these video fragments. The impact of self-made graphical representations was examined by asking half of the students to draw a reduced copy of the geometrical figure described in the problem before actually solving it. None of the experimental manipulations yielded the expected results. To the contrary, both factors even yielded a negative effect on students’ performance. Several explanations for these unexpected results are discussed.