An Integrated Knowledge Framework to Characterize and Scaffold Size and Scale Cognition (FS2C)

Abstract

Size and scale cognition is a critical ability associated with reasoning with concepts in different disciplines of science, technology, engineering, and mathematics. As such, researchers and educators have identified the need for young learners and their educators to become scale-literate. Informed by developmental psychology literature and recent findings in nanoscale science and engineering education, we propose an integrated knowledge framework for characterizing and scaffolding size and scale cognition called the FS2C framework. Five ad hoc assessment tasks were designed informed by the FS2C framework with the goal of identifying participants' understandings of size and scale. Findings identified participants' difficulties to discern different sizes of microscale and nanoscale objects and a low level of sophistication on identifying scale worlds among participants. Results also identified that as bigger the difference between the sizes of the objects is, the more difficult was for participants to identify how many times an object is bigger or smaller than another one. Similarly, participants showed difficulties to estimate approximate sizes of sub-macroscopic objects as well as a difficulty for participants to estimate the size of very large objects. Participants' accurate location of objects on a logarithmic scale was also challenging.

Keywords:

• Size and scale
• Nanoscience
• Nanotechnology
• Assessment

Acknowledgements

This work was supported in part by the US National Science Foundation via National Science Foundation Grant # 0817486 and EEC-0634750. Support from the School of Engineering Education, College of Technology, and the Network for Computational Nanotechnology at Purdue is also gratefully acknowledged. Similarly, we would like to thank Bedrich Benes for his help in developing the scoring scheme and the computer program to code participants' responses, Scott Schaffer for his comments on the initial version of this study, and Timothy Newby for facilitating the access to the participants of the study.