Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
360829 | The Journal of Mathematical Behavior | 2011 | 20 Pages |
This study addresses the measures chosen by students when selecting or constructing indices to properties of distributions of data. A series of individual teaching experiments were conducted to provide insight into the development of five 4th to 8th grade students’ conceptualizations of distribution over the course of 8 weeks of instruction. During the course of the teaching experiment (emergent) statistical tasks and analogous teacher activities were created and refined in an effort to support the development of understanding. In the process of development, attempts were made by students to coordinate center and variability when constructing measures to index properties of distributions. The results indicate that consideration of representativeness was a major factor that motivated modification of approaches to constructing indices of distributions, and subsequent coordination of indices of variation and center. In particular, the defining features of student's self-constructed “typical” values and notions of spread were examined, resulting in a model of development constituting eight “categories” ranging from the construction of values that did not reflect properties of the data (Category 1) to measures employing conceptual use of the mean in combination with other indices of center and spread (Category 8).
► For children, the term “typicality” does not embody the notion of “representativeness.” ► Older children do not necessarily demonstrate more sophisticated approaches to identifying typical values implying that notions of representativeness may not develop unless specifically addressed in instruction. ► Children generally seemed satisfied with the notion of the mode as representing a typical value even when distributions are ambiguous and the mode is not located in the main body of data. ► Eight categories of approaches were used to embody typicality: exclusive use of the mode, specifying a range within which a typical value occurs, identifying a typical value located within a suitable range or interval of data values, adjustment from the mode, the median, the mean, the mean in combination with other strategies.