Scaffolding student's conceptions of proportional size and scale cognition with analogies and metaphors

Abstract

The American Association for the Advancement of Science identifies scale as one of the four powerful common themes that transcend disciplinary boundaries and levels. Engineering is one of these disciplines that requires a strong spatial ability involving scale, as well as the ability to reason proportionally when using scale models. In addition, advancing nanosciences is opening new opportunities for engineers to pursue opportunities for designing nanotechnologies. However, today's middle school students do not demonstrate an adequate understanding of concepts of scale and size on the micro and the nano level. Students are unable to identify the relative sizes between micrometer-sized and nanometer-sized objects. The focus of this study is the role of proportional reasoning as one of the cognitive processes behind qualitative and quantitative proportional scale cognition. Proportional reasoning is the cognitive process that supports our ability to compare two rational expressions; it has also been recognized that proportional reasoning deals with one of the most common forms of structural similarity. Analogical reasoning involves a process of structural alignment and mapping between mental representations. Therefore, this study seeks to answer the following research question: Will analogies and metaphors scaffold proportional conceptions of size and scale? Participants for the initial study included 150 seventh graders from a science class of a Midwestern middle school. For identifying student's conceptions of the logical and numerical proportional scale cognition a mixed method procedure was designed. Data was analyzed by comparing among student's logical and mathematical proportional scale cognition as well as contrasted with similar results from the literature. This research was conducted to better understand the cognition associated with these skills and to design instructional methods to effectively develop these abilities in learners. We believe that the results of this study will inform the design of curricula that effectively convey scaling related concepts. Future work related to this area will also be discussed. © American Society for Engineering Education, 2008.