Task 4: Different Simplified Ratios
More than 60% of the children in both groups gave a correct answer to this task (Figure 17), with the fifth graders in the Control group showing the best performance.
Justifications to correct answers to this task, however, were rarely based on proportionality. Instead, about one third of the answers in all groups and grades mentioned only either the difference in amounts of sugar or the difference in the amounts of water.
Our results indicate that children’s early difficulties may rest on conceptions about how sugar and water contribute to sweetness. For most children only the amount of sugar matters; for a few, more water makes the mixture sweeter. It also shows no evidence of influence of an intervention curriculum that did not directly focus on sugar and water mixtures or proportionality. They also suggest that, to help students develop an understanding of proportionality as it relates to mixtures, explicit and systematic experiences with the resulting mixtures, together with a stronger focus on quantification are needed.
