Modeling of Variability
Modeling Variability refers to the progression of reasoning about employing chance to model variable phenomena. MoV1 begins with attribution of variability to particular sources. This is an initial step in modeling. For example, students might attribute variability in the heights of a population of plants to differences in availability of resources.
Many students assume that variability arises from deterministic sources only, such as "mistakes" in measurement or predetermined "natural" variability, such as that found in any sample of people. However, at this initial level, students only need demonstrate some attribution about the source of variability, whether it be chance or completely determined. At MoV2, students informally order the contributions of different sources to variability, using language such as "a lot" or "a little." Students also describe mechanisms and/or processes that account for these distinctions, and they predict or account for the effects on variability of changes in these mechanisms or processes.
Levels
1 Identify sources of variability.
2 Informally describe the contribution of one or more sources of variability to variability observed in the system.
3 Use a chance device to represent a source of variability or the total variability of the system.
4 Develop emergent models of variability.
5 Judge model fit in light of variability across repeated simulation with the same model.