%0 Journal Article %1 wilhelm2003prc %A Wilhelm, J.A. %A Confrey, Jere %D 2003 %I Taylor & Francis %J International Journal of Mathematical Education in Science and Technology %K change learning mathematics modelling money motion mythesis rate rateofhcange %N 6 %P 887-904 %T Projecting rate of change in the context of motion onto the context of money %U http://www.informaworld.com/smpp/content~content=a713748494~db=all %V 34 %X This paper reports a study designed to probe the abstraction ability that US Algebra I students can achieve in moving the concepts rate of change and accumulation between motion and money contexts. The Algebra I students used the technologies motion detectors and Interactive Banking software during a replacement unit focused on slope, ratio, and rate of change. Clinical interviews were conducted with four students at the end of the replacement unit testing their abstraction ability across the two contexts. Results revealed that some students do not have to completely understand the relationship between rate of change and accumulation within a single context in order to be able to understand and project the concepts separately into multiple contexts. Using multiple rate of change contexts allowed the learners the opportunity to see the 'like' in the contextually unlike situation, enabling them to project these concepts into novel situations. Few research studies have examined students' understanding of rate of change outside of the motion context, and therefore no studies, to the authors' knowledge, have explored students' abstraction ability between two different rate of change contexts. This paper reports a study designed to probe the abstraction ability that students can achieve in moving between the motion and money contexts.

@article{wilhelm2003prc, abstract = {This paper reports a study designed to probe the abstraction ability that US Algebra I students can achieve in moving the concepts rate of change and accumulation between motion and money contexts. The Algebra I students used the technologies motion detectors and Interactive Banking software during a replacement unit focused on slope, ratio, and rate of change. Clinical interviews were conducted with four students at the end of the replacement unit testing their abstraction ability across the two contexts. Results revealed that some students do not have to completely understand the relationship between rate of change and accumulation within a single context in order to be able to understand and project the concepts separately into multiple contexts. Using multiple rate of change contexts allowed the learners the opportunity to see the 'like' in the contextually unlike situation, enabling them to project these concepts into novel situations. Few research studies have examined students' understanding of rate of change outside of the motion context, and therefore no studies, to the authors' knowledge, have explored students' abstraction ability between two different rate of change contexts. This paper reports a study designed to probe the abstraction ability that students can achieve in moving between the motion and money contexts.}, added-at = {2008-05-30T05:46:27.000+0200}, author = {Wilhelm, J.A. and Confrey, Jere}, biburl = {https://www.bibsonomy.org/bibtex/25eb37c8115002432d97da72b81dc80fd/yish}, interhash = {b29905c8e45d01439b2fc0f72ffc0a48}, intrahash = {5eb37c8115002432d97da72b81dc80fd}, journal = {International Journal of Mathematical Education in Science and Technology}, keywords = {change learning mathematics modelling money motion mythesis rate rateofhcange}, number = 6, pages = {887-904}, publisher = {Taylor & Francis}, timestamp = {2008-05-30T05:46:29.000+0200}, title = {Projecting rate of change in the context of motion onto the context of money}, url = {http://www.informaworld.com/smpp/content~content=a713748494~db=all}, volume = 34, year = 2003 }