ABSTRACT
Three studies investigated the role of perceptual and quantitative situational factors on the structure of 5th- and 6th-graders’ mental models. A task involved a carton of orange juice made from concentrate and water, and two glasses of different sizes filled from the carton. The children had to predict whether the two glasses would taste the same. We manipulated whether students were presented with physical, diagrammatic, photographic, or textual information. We also manipulated the type of relationship specified between quantities: qualitative, easy numerical, or difficult numerical. We found that for the diagram condition, difficult numerical relationships yielded poor performance, whereas the easy numerical and qualitative relationships yielded excellent performance. In contrast, in the physical condition, the easy numerical relationships yielded poor performance, whereas the difficult numerical and qualitative relationships yielded excellent performance. These and other results are interpreted by developing a sketch of the mental models pre-proportional children construct to reason about this quantitative situation, and describing how situational factors influence the construction of the models. For example, physical features led to models that captured the identity relationship between the juice in the glasses (e.g., the juice came from the same carton) whereas numerical features led to models that captured the relationship between the constituents of concentrate and water in each glass (e.g., within a glass there is more water than concentrate).
