A didactical situation for the enhancement of meta-analogical awareness

The aim of this study was to propose a didactical situation for the confrontation of the epistemological obstacle of linearity (routine proportionality) and consequently for the enhancement of meta-analogical awareness. Errors caused by students’ spontaneous tendency to apply linear functions in various situations are strong, persistent and do not disappear with traditional instruction. The effects of a didactical situation on the way students perceive and handle proportional and non-proportional relations were examined. The situation consisted of four parts which referred to the situations of action, formulation, validation and institutionalisation and was presented as a game to four twelve-year students of different abilities. The results showed the potential of the application of a didactical situation towards enhancing students’ meta-analogical awareness and therefore their ability to discern and handle linear and non-proportional relations.

► The epistemological nature of errors related to the linear illusion is examined.
► A didactical situation for overcoming these errors is proposed and applied.
► The results support the confrontation of the epistemological obstacle of linearity.
► The didactical situation enhances students’ meta-analogical awareness.