Asee peer logo

Scaffolding Student’s Conceptions Of Proportional Size And Scale Cognition With Analogies And Metaphors

Download Paper |

Conference

2008 Annual Conference & Exposition

Location

Pittsburgh, Pennsylvania

Publication Date

June 22, 2008

Start Date

June 22, 2008

End Date

June 25, 2008

ISSN

2153-5965

Conference Session

Innovative Instructional Strategies

Tagged Division

Mathematics

Page Count

13

Page Numbers

13.1063.1 - 13.1063.13

Permanent URL

https://peer.asee.org/4189

Download Count

34

Request a correction

Paper Authors

biography

Alejandra J. Magana

visit author page

Alejandra Magana is a Ph.D. student in Engineering Education at Purdue University. She holds a M.S. Ed. in Educational Technology from Purdue University and a M.S. in E-commerce from ITESM in Mexico City. She is currently working for the Network for Computational Nanotechnology at Purdue University as a Research Assistant and as an Instructional Designer.

visit author page

biography

Sean Brophy Purdue University

visit author page

Sean Brophy is an Assistant Professor in Engineering Education at Purdue University. He holds a Ph.D. in Education and Human Development (Technology in Education) from Vanderbilt University and a M.S. in Computer Science (Artificial Intelligence) from DePaul University.

visit author page

biography

Timothy Newby Purdue University

visit author page

Timothy J. Newby is a Professor in Curriculum and Instruction at Purdue University. He holds a Ph.D. in Instructional Psychology form the Brigham Young University.

visit author page

Download Paper |

Abstract
NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

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.

Introduction

Notions of scale have been identified as one of the four powerful common themes that transcend disciplinary boundaries and levels helping learners structuring knowledge (American Association for the Advancement of Science [AAAS] 2006) 1 . Scaling related concepts are directly applied to the study of phenomena in the micro, nano, and atomic level. As new tools, techniques, and instrumentations that allow study of phenomena in the micro and nano world are developed, new and complex technologies rise resulting in new fields of science and technology. As a consequence, new global markets emerge as well as the need of a workforce to meet them. 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.

Therefore, it has increased the importance for young learners to become scale-literate in order to

Magana, A. J., & Brophy, S., & Newby, T. (2008, June), Scaffolding Student’s Conceptions Of Proportional Size And Scale Cognition With Analogies And Metaphors Paper presented at 2008 Annual Conference & Exposition, Pittsburgh, Pennsylvania. https://peer.asee.org/4189

ASEE holds the copyright on this document. It may be read by the public free of charge. Authors may archive their work on personal websites or in institutional repositories with the following citation: © 2008 American Society for Engineering Education. Other scholars may excerpt or quote from these materials with the same citation. When excerpting or quoting from Conference Proceedings, authors should, in addition to noting the ASEE copyright, list all the original authors and their institutions and name the host city of the conference. - Last updated April 1, 2015