Teaching proportion based on the stimulus equivalence paradigm

Abstract

Fifth grade Brazilian students frequently fail to solve problems which the concept of proportion with relative quantity is required. The present study verified whether teaching conditional relations between multiple exemplars of pictorial and numerical fraction stimuli could establish the concept of proportion. Ten fifth grade students with insufficient performance to solve problems of fraction learned to choose numeric fractions conditionally to a pictorial sample or other equivalent numerical fraction in a desktop computer. The numerators of all comparison stimuli were the same for five participants (E1) and varied for other five subjects (E2). All subjects learned relations between fractions directly trained and showed emergence of symmetric and transitive/equivalence relations: three classes of fraction (1/3, 1/4 and 1/5) with three members each (two numeric and one pictorial fractions) were formed. However, the expansion of the formed classes did not occur for the majority of the subjects after additional training of relations between new numeric fractions and the original pictorial fractions 1/3, 1/4 and 1/5. Assessments of generalized operant with new proportions repeated throughout the study showed scores over 50% correct. Global evaluations conducted as multiple choice exams and applied in classroom setting showed significant gains for experimental subjects but not for the control group (GC). Scores of training and test conditions for E1 were, in general, higher than for E2. The facilitative effect of the procedure and constant numerator on developing three-member equivalence classes of fractions, but not on the expansion of classes requires further investigation. The present study showed the utility of a methodology based on the stimulus equivalence paradigm to teach one of the math concepts which children often failure to learn with traditional methods.Keywords: stimulus control, equivalence stimulus, learning fractions, conditional control, concept of proportion.