## Abstract

Much research over the last twenty years has documented the difficulties that students encounter when reasoning about and interpreting rates of change^{1, 2, 3}. The complexity of such reasoning has proven difficult for high achieving undergraduate mathematics students4 and students studying physics^{5, 6}. To reason about rates of change, students must be able to simultaneously attend to both the changing values of the outputs of a function and changing values of the inputs to the function^{7, 8}. In addition, students must be able to distinguish between the values of the outputs of a function and the values of the function's average rate of change over subintervals of the domain. When reasoning about changing phenomena, students often confuse these two quantities^{1, 2, 9} . Furthermore, students have difficulty in distinguishing between the amount of change in a function's output value over a subinterval and the average rate of change of the function over that subinterval. To meaningfully interpret the graph of a function that represents two quantities that co-vary, students need to be able to simultaneously attend to and distinguish among three quantities: the value of the output of a function, the change in the values of the function's output over a subinterval, and the change in values of the input to the function. Reasoning about the latter two quantities is a foundational understanding for average rates of change in pre-calculus and instantaneous rates of change in calculus.

Original language | English (US) |
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State | Published - 2013 |

Event | 120th ASEE Annual Conference and Exposition - Atlanta, GA, United States Duration: Jun 23 2013 → Jun 26 2013 |

### Other

Other | 120th ASEE Annual Conference and Exposition |
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Country/Territory | United States |

City | Atlanta, GA |

Period | 6/23/13 → 6/26/13 |

## ASJC Scopus subject areas

- Engineering(all)