Behind the scenes of pseudo-proportionality

Abstract

†Part of the paper was presented at the 30th Conference of the International Group for the Psychology of Mathematics Education (Prague, Czech Republic, July 16–21, 2006).

In this study, we attempt to put in question students’ spontaneous and uncritical application of the simple and neat mathematical formula of linearity. This is impelled with the help of a written test involving geometrical problems, which is based on an original experimental setting. In this setting, grade 9 and 10 students were instructed first to solve all the geometrical problems and then to select only one problem as the appropriate for a given numerical answer. The difficulty of this choice lied in fact that a superficial handling of each problem would resolve to the same numerical answer as the one given. The results show that students’ choices are systematic and based on the solutions given to the tasks. However, the experimental setting has managed to help students question in some degree the applicability of the linear model in situations that appear to be linear but are not.

Keywords:

• pseudo-proportionality
• linear model
• area
• volume
• geometrical problem solving

Notes

†Part of the paper was presented at the 30th Conference of the International Group for the Psychology of Mathematics Education (Prague, Czech Republic, July 16–21, 2006).

†The terms ‘linear’ and ‘proportional’ are used as synonyms referring to linear relations in a strict sense, i.e. relations of the form f(x) = ax (with a ≠ 0).