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

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.

[1]  Bruce K. Britton,et al.  The Psychology of Learning Science , 2012 .

[2]  C. W. Anderson,et al.  FOCUS ARTICLE: Implications of Research on Children's Learning for Standards and Assessment: A Proposed Learning Progression for Matter and the Atomic-Molecular Theory , 2006 .

[3]  Ravit Golan Duncan,et al.  A Learning Progression for Deepening Students' Understandings of Modern Genetics across the 5th-10th Grades. , 2009 .

[4]  Carolyn J. Boulter,et al.  Children's understanding of scale - the use of microscopes , 2001 .

[5]  Mihail C. Roco,et al.  Nanotechnology—A Frontier for Engineering Education* , 2002 .

[6]  Cindy E. Hmelo-Silver,et al.  Learning progressions: Aligning curriculum, instruction, and assessment , 2009 .

[7]  Ruth M. Beard,et al.  The Growth of Logical Thinking , 1972 .

[8]  E Weinan,et al.  Multi-scale Modeling and Computation , 2003 .

[9]  Robert M. Gagné,et al.  Instructional Technology: Foundations , 1988 .

[10]  Merlyn J. Behr,et al.  Number concepts and operations in the middle grades , 1988 .

[11]  M. G. Jones,et al.  Conceptual Boundaries and Distances: Students' and Experts' Concepts of the Scale of Scientific Phenomena , 2006 .

[12]  Sean Brophy,et al.  Scaffolding Student’s Conceptions Of Proportional Size And Scale Cognition With Analogies And Metaphors , 2008 .

[13]  Aaron Rogat,et al.  Learning Progressions in Science: An Evidence-Based Approach to Reform. CPRE Research Report # RR-63. , 2009 .

[14]  Shawn Y. Stevens,et al.  Developing a Hypothetical Multi-Dimensional Learning Progression for the Nature of Matter. , 2009 .

[15]  Mark F. Horstemeyer,et al.  Multiscale Modeling: A Review , 2009 .

[16]  Eric N. Wiebe,et al.  Understanding Scale: Powers of Ten , 2007 .

[17]  William W. Rozeboom,et al.  Scaling theory and the nature of measurement , 1966, Synthese.

[18]  G. Jones,et al.  Proportional Reasoning Ability and Concepts of Scale: Surface area to volume relationships in science , 2009 .

[19]  Anna M. Waldron,et al.  The current state of public understanding of nanotechnology , 2006 .

[20]  Yilmaz Saglam,et al.  Middle school students' beliefs about matter , 2005 .

[21]  H. Schweingruber,et al.  TAKING SCIENCE TO SCHOOL: LEARNING AND TEACHING SCIENCE IN GRADES K-8 , 2007 .

[22]  Bat-Sheva Eylon,et al.  Revision of Course Materials on the Basis of Research on Conceptual Difficulties. , 1986 .

[23]  Jamie I. D. Campbell.  Handbook of mathematical cognition , 2004 .

[24]  Scott Smidt.  Review of The Big Ideas of Nanoscale Science and Engineering: A Guidebook for Secondary Teachers , 2012 .

[25]  Russell M. Taylor,et al.  Remote atomic force microscopy of microscopic organisms: Technological innovations for hands-on science with middle and high school students , 2004 .