Lehrer, Konold & Kim (2006)

We describe the design and iterative implementation of a learning progression for supporting statistical reasoning as students construct data and model chance. From a disciplinary perspective, the learning trajectory is informed by the history of statistics, in which concepts of distribution and variation first arose as accounts of the structure inherent in the variability of measurements. Hence, students were introduced to variability as they repeatedly measured an attribute (most often, length), and then developed statistics as ways of describing "true" measure and precision. Both of these developments have historic parallels, and the intricate relation of measure and data are also key components of ongoing professional practice (see Hall et al., this symposium). From a learning perspective, the learning trajectory reflects a commitment to several related principles: (a) constituting a learning progression as encounters with a series of problematics; (b) representational fluency and meta-representational competence as constituents of conceptual development in a discipline; (c) invented measures as grounding students' understanding of statistics and (d) an agentive perspective for orienting student activity, according to which distribution of measures emerges as a result of the collective activity of measurer-agents. Instructional design and assessment design (see Wilson et al., this symposium) were developed in tandem, so that what we took as evidence for the instructional design was subjected to test as a model of assessment, resulting in revision to each.