ABSTRACT
Imagine that a bottle is being filled with water that is being dispensed at a constant rate 1 . How might one measure the amount of water in the bottle at any given time? How might the amount of water in the bottle relate to the height of the water in the bottle for differently shaped bottles? How might one relate the changing amount of water to the changing height of water? To respond to these questions, an individual would need to make sense of both the height of the water and the amount of the water as attributes that could be measured. Importantly, an individual would not necessarily need to measure (or know) particular numerical amounts to make sense of the situation. For example, dispensing water into a very wide bottle or a very narrow bottle would result in different relationships between the height and amount of water in the bottle. An individual’s responses to the questions would depend on how that individual interprets the context of the problem situation (Johnson, 2014). For example, the sound of the water filling into the bottle, bottles with which an individual might be familiar, or dispensers an individual has used might play a role. These introductory questions are intended to provide examples of prompts that could foster individuals’ quantitative reasoning.
