Cognitive and Metacognitive Aspects of Proportional Reasoning

Abstract

In this study we attempt to propose a new model of proportional reasoning based both on bibliographical and research data. This is impelled with the help of three written tests involving analogical, proportional, and non-proportional situations that were administered to pupils from grade 7 to 9. The results suggest the existence of a multi-component model of proportional reasoning, contributing in this way to the reformulation of the concept. In this model, the components of analogical reasoning, routine proportionality, and meta-analogical awareness take a constitutive part. Thus, proportional reasoning does not coincide exclusively with success in solving a certain restricted range of proportional problems, as routine missing-value and comparison problems (routine proportionality), but it also involves handling verbal and arithmetical analogies (analogical reasoning) as well as the awareness of discerning non-proportional situations (meta-analogical awareness), which is metacognitive in nature.