The Development of Proportional Scaling: Is 1/3 = 2/6 = 3/9 = 4/12?

The current experiments examined the role of scale factor in children’s proportional reasoning. Experiment 1 used a choice task and Experiment 2 used a production task to examine the abilities of kindergartners through fourth-graders to match equivalent, visually depicted proportional relations. The findings of both experiments show that accuracy decreased as the scaling magnitude between the equivalent proportions increased. In addition, children’s errors showed that the cost of scaling proportional relations is symmetrical for problems that involve scaling up and scaling down. These findings indicate that scaling has a cognitive cost that results in decreasing performance with increasing scaling magnitude. These scale factor effects are consistent with children’s use of intuitive strategies to solve proportional reasoning problems that may be important in scaffolding more formal mathematical understanding of proportional relations.