Conceptions of Scale and Scaling: The Expert-Novice Continuum
Science education reform recommendations include incorporation o f big, overarching themes in K-12 science to reduce curricular fragmentation. One recommended unifying theme is scaling, but there appears to be a gap in the research literature on educators’ knowledge o f how students think about size and scale. This research investigated students’ conceptions of size and scale across a continuum from grade («=37), 7*’ grade («=71), 9*'’ grade («=59), 12*^ grade academically gifted («=38), to experts («=10).
Results showed that relative sizes of objects were more accurately conceptualized than absolute sizes for all groups. Objects that serve as size reference points were identified along with experiences that impact conceptions of scale. The size of a person was a major reference point for all groups. There were varying numbers of conceptually distinctsize categories for each group, with the expert group possessing more distinct as well as more clearly defined categories, particularly at scales smaller than a person. Objects larger than a person were categorized into size groupings based on the nature of experiences with those sizes - visual or kinesthetic, wholistic or sequential.
An asymmetry between conceptualizations of large and small scale was identified.
At scales larger than a person, conceptualizations degraded uniformly as the size increased, but at small scale this degradation occurred in a discontinuous manner at the boundary where objects become invisible to the unaided eye. Experts mentally manoeuvred across this discontinuity by conceptually jumping to a new scale world, using mathematics and various units o f measurement to provide resilient links between microscopic and macroscopic worlds. This research concludes with implications for teachers, parents, and curriculum developers to help students make better use of scaling concepts as a broad, unifying theme to create coherence in the science curriculum.