This project will research the relationship of proportional reasoning abilities to the development of scale concepts and will develop an instructional framework for learning about scale and scaling effects that builds on students' prior knowledge. How students and professionals in a variety of fields develop understandings of scale and scaling effects in science will be investigated. The first year will utilize written assessments and interviews to investigate students' existing conceptual ecologies with respect to scale conceptualizations and will involve students from elementary, middle, and high school as well as graduate students. The goal of this aspect of the research is to document the trajectory of scaling ideas that students hold as they mature. The second year will elaborate on this knowledge by researching conceptualizations of novice and experienced teachers as well as other adults in a variety of professions. Written assessments and interviews with adults will document concepts and experiences with scale and scaling effects and these results will allow the identification of applications of scaling, explore how different people develop scaling concepts, and identify sub-constructs inherent to scaling applications. The third will focus on applying knowledge gained from the first two years of research in regular science classes. Through pre- and post-instruction assessments the various webs of constructs students hold with respect to the unifying theme of scale and the relationship of mathematics to understandings of scale will be investigated and the influences guided educational practices in a natural setting have on these constructs will be identified. This research also seeks to identify how learning about scale concepts can be generalized and will research the transfer of such learning across domains. A strong foundation in understandings of scale as a scientific theme has the potential anchor science concepts and help students make cross-curricular connections. In addition, understanding how minorities and women learn scale and scaling concepts can potentially broaden the involvement of these underserved populations in science.
