This paper articulates theoretical and practical considerations for designing a sequence of covariation tasks to support students’ reasoning about quantities involved in rate of change. Adapting the well-known bottle problem during two iterations of implementation and analysis, this researcher-developed task sequence incorporates dynamically linked geometric and graphical representations of covarying quantities and prompts fostering students’ coordination of quantities that are changing together. Taking into account students’ perspective of quantities involved, this task sequence is designed to support students’ progression in using nonnumerical quantitative reasoning to make predictions and create representations indicating how one quantity might change in relationship to another changing quantity.
Johnson, Heather L., "Designing Covariation Tasks to Support Students’ Reasoning about Quantities involved in Rate of Change" (2013). STEM Faculty Presentations. 45.