Understanding Sugar and Water Mixtures

We analyzed students’ understanding of proportionality as they compared mixtures of water and sugar in four tasks. Although some quantitative activities were included in the curriculum, such as seriating objects of different weights, there were no attempts to focus on proportional reasoning during the intervention. Also, even though students in the Intervention group did discuss conservation of amounts of dissolved sugar, they never discussed the idea of sweetness as a relation of sugar to water. Therefore the evaluation of their understanding of proportionality in sugar and water mixtures was only an attempt to determine the extent of their experiences’ influence on more complex understandings.

Each student was asked to make predictions about the relative sweetness of four pairs of mixtures and to explain their answers (Figure 13).